Modelling and simulation methodology for unidirectional composite laminates in a Virtual Test Lab framework

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Composite Structures
journal homepage: www.elsevier.com/locate/compstruct
Modelling and simulation methodology for unidirectional composite
laminates in a Virtual Test Lab framework
O. Falcóa
, R.L. Ávilab
, B. Tijsc
, C.S. Lopesa,⁎
a
IMDEA Materials – Madrid Institute for Advanced Studies of Materials, c/Eric Kandel, 2, Parque Científico y Tecnológico—Tecnogetafe, 28906 Getafe, Madrid, Spain
b
Autonomous University of Coahuila, Saltillo, Mexico
c
GKN Aerospace: Fokker, Papendrecht, The Netherlands
A R T I C L E I N F O
Keywords:
Finite element analysis (FEA)
Composite laminates
Progressive failure analyses (PFA)
Computational modelling
Virtual testing
A B S T R A C T
A reliable virtual testing framework for unidirectionally laminated composites is presented that allows the
prediction of failure loads and modes of general in-plane coupons with great realism. This is a toolset based on
finite element analysis that relies on a cohesive-frictional constitutive formulation coupled with the kinematics
of penalty-based contact surfaces, on sophisticated three-dimensional continuum damage models, and overall on
a modelling approach based on mesh structuring and crack-band erosion to capture the appropriate crack paths
in unidirectional fibre reinforced plies. An extensive and rigorous validation of the overall approach is presented,
demonstrating that the virtual testing laboratory is robust and can be reliably used in for composite materials
screening, design and certification.
1. Introduction
Fibre Reinforced Polymers (FRP) have become widely used in
structural applications for the aerospace, automotive, energy and sports
sectors. Owing to their unique combination of specific mechanical
properties (high stiffness, strength, toughness and energy absorption
combined with low density), these materials are excellent candidates
for lightweight structures, in spite of their high cost. To improve the
economic case in favour of FRP, the reduction of costs related to their
manufacturing, design and certification is imperative and constitutes
one of the pressing engineering issues of today. Whilst efficiency gains
on the production side are being achieved with out-of-autoclave and
automated manufacturing technologies, design and certification re-
quirements still imply extensive and costly experimental test pro-
grammes which could turn out to be infeasible due to the large number
of design possibilities, large number of material properties and vari-
ables to study, combined with the absence of reliable design tools [1].
To face the challenge of cost reduction on this side, the development of
reliable computational tools able to accurately predict the full me-
chanical response of FRP from elastic behaviour to damage onset and
progressive structural collapse is inevitable. Reliable Virtual Testing
can accelerate materials screening and design processes, which are
specially complex in the aeronautical sector, and lead to an effective
simplification of certification procedures. Moreover, an accessible vir-
tual testing, screening and design approach is possibly the way to
expand the application of FRP to other sectors of economical activity.
Virtual testing of laminated composites involves the use of the
meso-scale, in this way accounting for the individual plies and ply in-
terfaces within a finite element (FE) analysis approach. At this scale, the
complex ply and interface damage and failure mechanisms, as well as
their interactions, can be simulated in order to predict the final failure
of FRP specimens. In this way, it is possible to establish laminate ma-
terial allowables that can be used for the purpose of laminate design.
However, due to the complex nature of the sub-critical damage modes
such as transverse matrix cracks, axial splits (fibre/matrix shearing) and
delamination, the prediction of ultimate strength is one of the major
challenges in virtual testing of composites [2,3]. In recent years, sig-
nificant progress has been made in meso-modelling of FRP laminates,
specially at material constitutive level, but several issues still remain a
challenge, such as the physically-sound simulation of the progression of
damage mechanisms that lead to the final failure of composite coupons.
Because the possible failure mode and loci are known in advance,
the usual approach to model delamination is the explicit introduction of
split planes at the ply interfaces whose traction-separation behaviour is
governed by cohesive laws. The appropriate kinematic description is
achieved by means of cohesive elements, which require through-
thickness conforming meshes, or by means cohesive contact surface
behaviour that allows the flexibility of distinct meshes on different
plies. On the other hand, the possible intralaminar failure modes and
location are not known a priori. Therefore, the most common
https://doi.org/10.1016/j.compstruct.2018.02.016
Received 13 September 2017; Received in revised form 31 December 2017; Accepted 8 February 2018
⁎
Corresponding author.
E-mail address: claudiosaul.lopes@imdea.org (C.S. Lopes).
Composite Structures 190 (2018) 137–159
Available online 10 February 2018
0263-8223/ © 2018 Elsevier Ltd. All rights reserved.
T

methodology to simulate the behaviour of the plies is Continuum
Damage Modelling (CDM). However, due to its dependency on mesh
size and orientation of mesh lines, by itself, the CDM approach cannot
ensure the correct kinematic representation of the laminate damage
modes, in this way compromising the accurate determination of failure
loads. In order to force damage localization along physically-sound
crack paths, several authors have proposed the introduction of artificial
split planes in the ply FE discretization whose traction-separation be-
haviour is determined by cohesive laws, e.g. [4–6]. A more general
solution is the extension of the traditional FE method to include extra
degrees of freedom and displacement functions, the so-called extended
FE methods (e.g. [7–9]). Owing to the use of these discrete crack
methods, the correct representation of failure modes in particular
composite coupons, e.g. open-hole tension, has been achieved [10,11].
Moreover, it has been shown that these techniques are well suited to
tackle competing laminate damage mechanisms such as delamination
and matrix cracking, allowing the correct representation of event such
as delamination migration [12,13]. However, these numerical strate-
gies are computationally expensive in comparison with CDM which
limits their potential use in larger structures.
Although accurate numerical approaches have been proposed for
particular configurations, to the knowledge of the authors there is no
efficient and reliable numerical framework for physically-based simu-
lation of general virtual testing of composites coupons including mul-
tiple test standard used for material certification such as in-plane un-
notched tension/compression (UNT/UNC), in-plane shear (IPS), open-
hole tension/compression (OHT/OHC), low velocity impact (LVI),
compression after impact (CAI), bolt bearing, etc. This paper presents
an efficient and robust virtual testing toolset to perform reliable si-
mulation of unidirectional composite laminated coupons that predicts
competing ply and interface damage mechanisms and, overall, laminate
failure modes with great realism. This virtual test framework consists of
several tools, namely: i a commercially-available explicit FE solver tool
(ABAQUS/Explicit [14]) to tackle the numerous sources of non-linear-
ities in the models in an efficient way; ii) a sophisticated three-di-
mensional CDM for unidirectional FRP plies, implemented by means of
a user subroutine in the FE solver, that enforces element erosion; iii) a
surface-based cohesive-frictional modelling algorithm (native of
ABAQUS/Explicit) to model ply interfaces; iv) a purpose-built auto-
mated ABAQUS plug-in, based on Python code, for the meso-modelling
of unidirectional laminated coupons that applies regularized meshes,
i.e. controlled mesh size, mesh-alignment and directional biasing, in
this way enforcing damage localization along physically-sound crack
paths. A similar strategy has been previously applied by the authors, in
a less systematic way, in the simulation of LVI [15] and in the nu-
merical analysis of effects of defects [16]. It will be demonstrated that
this numerical framework guarantees the appropriate constitutive and
kinematic simulation of the damage and failure of composite coupons.
Henceforth, the terms ‘laboratory’, ‘framework’ and ‘toolset’ will be
used interchangeably in the context of virtual testing.
This work demonstrates that the sound kinematic simulation of
composite damage modes and the accurate prediction of failure loads
can be achieved by combining conventional constitutive approaches
with appropriate discretization and meshing of ply and interfaces. For
the sake of contextualization, and to highlight key elements, the con-
stitutive models are briefly introduced, with emphasis given to the their
input properties. Then, the paper focuses on the details of the dis-
cretization and meshing procedures used in the virtual representation
of composite coupons. The modelling tool has been scripted in the
programming language Python which allows the direct interaction with
ABAQUS pre-processing, simulation and post-processing capabilities.
An extensive and rigorous validation of the virtual testing toolset is
presented, involving the correlation between experimental and simu-
lated failure modes and loads resulting of standard UNT, UNC, OHT and
OHC tests. These analyses were performed on different laminates
commonly used in design space of aeronautical structures, and on
configurations containing clusters of plies with the same fibre orienta-
tion, which are not commonly used in aeronautical design, i.e. off-de-
sign configurations.
2. Modelling the deformation behaviour of unidirectional FRP
The major part of past research efforts on the simulation of com-
posite materials has been directed at the constitutive modelling of the
deformation mechanisms. However, if the appropriate kinematic si-
mulation is not possible, the material is unable of deforming to re-
present those mechanisms. In general progressive failure of composite
laminates, there are several potential damage modes that interact with
each other, and their kinematic representation becomes a necessary
condition to accurately predict the final failure of the material. This
section starts by presenting the constitutive models adopted in the
virtual testing framework and then focuses on the key aspects that
allow the appropriate kinematic simulation of unidirectional composite
coupons.
2.1. Constitutive modelling
Two distinct numerical approaches are used to model all relevant
damage modes in unidirectional laminates. While interlaminar damage
is assumed to occur in the form of delaminations along predefined and
discrete crack planes, intralaminar damage might occur in the form of
fibre breakage, fibre pull-out, kink-banding and matrix cracking at any
location within the plies. While the first method is readily available in
ABAQUS/Explicit [14], the second has been implemented in Fortran-
coded ‘VUMAT’ subroutine to be used with a numerically explicit in-
tegration scheme (ABAQUS/Explicit [14]).
2.1.1. Interlaminar behaviour
The ply interface response is modelled by means of a general mixed-
mode cohesive zone method coupled with frictional behaviour. The
coupled cohesive-frictional approach is adopted to include the possible
effects of ply friction during and after delamination. In this way, the
shear stresses caused by friction at the interface are ramped progres-
sively and proportional to the degradation of the interface, thus once
the interface is fully delaminated, the surface interaction is uniquely
governed by a pure Coulomb model. For the pure cohesive response,
damage onset is identified by means of a quadratic interaction criterion
that is a function of the interlaminar strength values for each of the
damage modes. Once delamination is initiated, the cohesive tractions
transferred through the interface decrease linearly to zero dissipating
the fracture energy corresponding to the specific mixed-mode loading
mode, as given by the BK damage propagation criterion [17]. This
approach, previously used by the authors [15,16], is based on the
mixed-mode cohesive zone models proposed by Camanho et al. [18]
and Turon et al. [19] and is implemented in the kinematics of surface
contact interaction algorithms available in ABAQUS/Explicit [14].
The combined effects of friction and cohesive behaviour has been
addressed by other authors, e.g. [20], whose works eventually led to the
development of cohesive element formulations that take both me-
chanisms into account; a capability similar to the one used in this work
with cohesive-frictional surface interactions. The effect of friction on
the failure of the in-plane loaded specimens analysed in this work is
expected to be limited. However, the proposed methodology is meant to
be applied in the virtual testing of a wide range of composite coupons,
including the out-of-plane loaded drop-weight impact test, wherein
friction plays a more pronounce effect on ply interface behaviour [15].
2.1.2. Ply behaviour
The unidirectional FRP plies are modelled by means of a thermo-
dynamically-consistent CDM, based on the work of Maimí et al.
[21,22], that guarantees the appropriate energy dissipation for different
physically-observed fracture modes. Important modifications were
O. Falcó et al. Composite Structures 190 (2018) 137–159
138

introduced to improve the constitutive representation. The original
plane-stress formulation was extended to take into account three-di-
mensional stress states. Nonlinear elastic-plastic behaviours were
adopted for in-plane and out-of-plane shear responses based on Ram-
berg-Osgood laws [23], as in [24]. First-ply failure is detected by means
of physically-based three-dimensional failure criteria proposed by
Catalanotti et al. [25]. As proposed by Maimí et al. [21,22], the gradual
unloading of a ply after the onset of damage is simulated according to
different damage evolution laws in different orthotropic directions as-
sociated with damage variables dM ( = + − + −M 1 ,1 ,2 ,2 ,6), respec-
tively for damages in fibre/longitudinal ( = ±M 1 ), matrix/transverse
( = ±M 2 ), and matrix/shear ( =M 6) directions. Exponential damage
laws are used to model material softening corresponding to the damage
processes of fibre kinking and matrix cracking. To simulate ply failure
under longitudinal tensile loads, a coupled linear-exponential softening
law is used to model separately the mechanisms of fibre breakage and
fibre pull-out [21,22]. In this work, the parameters of this softening law
are derived from the analysis of the experimentally-obtained crack re-
sistance curve (R-curve) by applying the data reduction method pro-
posed by Dávila et al. [26]. Moreover, matrix cracking is assumed to
occur under general mixed-mode conditions, with onset load and
fracture angle predicted by the maximization of quadratic-interactive
three-dimensional failure criteria [25]. The propagation of matrix
cracking is determined by the energy-based Benzeggagh-Kenane (BK)
criterion [17] that accounts for the dependence of the fracture energy
dissipation on the mode mixity ratio, as in [27].
2.1.3. Material property inputs for the models
One of the key important factors in the predictive capability of
material models is a reliable set of material input properties. In the case
of unidirectional FRP, this implies a thorough characterization en-
deavour involving the use of standard and non-standard test methods to
measure ply elastic properties, thermal expansion coefficients, as well
as ply and interface strength values and critical energy release rates, in
three material directions (longitudinal, transverse and shear).
Moreover, the differentiation of load directionality is paramount as
different properties and failure modes are observed in these materials
depending on whether they are submitted to tension or compression.
The material properties, and respective characterization methods, re-
quired as inputs to the ply and ply-interface models are summarized in
Table 1 (specific values are presented for the case of AS4/8552 prepreg
material used for the validation of the methodology – see Section 4).
Six independent ply elastic parameters (E E E G ν, , , ,t c1 1 2 12 12 and ν23) are
required as inputs to the ply model, since the remaining three-dimen-
sional elastic parameters can be deduced from these ones. According to
previous works [28,29], the origin of the difference between E E,t c1 1 can
be attributed either to the initial fibre misalignment or to different fibre
behaviours in tension and compression. The micromechanical analysis
performed in [28] concludes that the later justification is more plau-
sible. In addition, the ply longitudinal and transverse thermal expan-
sion coefficients (α1 and α2, respectively) allow the computation of or-
thotropic thermal expansion and corresponding stresses such as the
ones resulting from material curing cool-down. Four independent ply
strength values need to be provided (X X Y, ,T C C and SL) corresponding to
the longitudinal tensile/compressive, transverse compressive and in-
plane shear loads. These properties can be measured using test stan-
dards defined by the American Society for test Standards (ASTMD3039,
ASTMD3410 and ASTMD3518 [30–32]).
The transverse tensile strength of a unidirectional ply, YT, is affected
by in situ ply-blocking and thickness effects. This property is calculated
as function of the transverse fracture toughness, G +2 , as proposed by
Camanho et al. [33]. The in-plane shear strength, SL, is considered to be
affected only by ply-blocking, and the authors propose the interlaminar
shear strength (ILSS) test ASTM D2344M [34] to estimate the in situ
value of this property.
An approach that is gradually becoming an alternative to
experimental testing for the determination of ply elastic and resistance
properties is computational micromechanics, based on the properties of
the constituent material phases (fibre, matrix and fibre/matrix inter-
faces) measured in situ. Recent advances in this field forecast a state of
sufficient reliability and robustness in the near future [1,35–38].
The ply constitutive model requires five independent fracture en-
ergy values corresponding to four main modes of ply damage and
failure: fibre kinking (G −1 ); mixed-mode transverse cracking (G +2 and
G6); fibre breakage (G b1 ) and fibre pull-out (G po1 ), corresponding to the
dissipated longitudinal tensile failure energy of the ply
(G G G= ++ b po1 1 1 ) [21,22]. The values of G b1 and G po1 are obtained by
applying the data reduction method proposed by Dávila et al. [26] to
the longitudinal tensile crack resistance curve (R-curve) obtained ex-
perimentally by means of Compact Tension (CT) tests [39]. The method
[26] makes use of the length of the fracture process zone, lFPZ, which
can also be determined from the R-curve. Considerable in situ effects on
G +1 were identified by Laffan et al. [40]. Regrettably, these are not
taken into account in the present work, and this is likely to affect the
virtual tests on coupons with clustered 0° plies.
The appropriate approach to characterize the longitudinal com-
pressive crack resistance curve of composites and corresponding critical
energy release rate (G −1 ) is the method developed by Catalanotti et al.
[41] that uses a size effect law. Transverse fracture under general
mixed-mode loading conditions can be considered to propagate under
similar conditions as interlaminar cracking along °0 ply interfaces.
Hence, the values of pure mode-I (G +2 ) and pure mode-II (G6) transverse
Table 1
Material properties used as inputs for the ply and interface model. Values are specific for
HexPly AS4/8552 unidirectional prepreg CFRP with nominal density ρ = 1.58⋅10−6
kg/
mm3
and nominal ply thickness tp = 0.184 mm. The ply elastic, resistance and thermal
expansion properties were measured by Fokker. The ply longitudinal tensile fracture
behaviour (R-curve) and interface fracture energies were characterized by IMDEA
Materials. The ply longitudinal compressive fracture energy was taken from [41].
Property Test Standard Specimen number: 6
Mean (CV %)
Ply elastic properties
E (GPa)t1 ASTM D3039M [30] 137.1 (1.4)
E (GPa)c1 ASTM D3410M [31] 114.3 (0.9)
E (GPa)t2 ASTM D3039M [30] 8.8 (0.3)
E (GPa)c2 ASTM D3410M [31] 10.1 (0.8)
=G G (GPa)12 13 ASTM D3518M [32] 4.9 (0.8)
=v v12 13 ASTM D3039M [30] 0.314
v23 0.487
Ply strengths properties
X (MPa)T ASTM D3039M [30] 2106.4 (8.2)
X (MPa)C ASTM D3410M [31] 1675.9 (5.2)
Y (MPa)T ASTM D3039M [30] 74.2 (6.3)
Y (MPa)C ASTM D3410M [31] 322.0 (1.7)
S (MPa)L ASTM D2344M [34] 110.4 (1.3)
Thermal expansion coefficient
° −α ( C 1)1 −e0.21 06
° −α ( C 1)2 −e3.30 05
Ply fracture energies
G +(kJ/m )1
2 Pinho et al. [39] 125.0
G −(kJ/m )1
2 Catalanotti et al. [41] 61.0
G +(kJ/m )2
2 ASTMD5528 [42] 0.30
G (kJ/m )6
2 ASTMD7905 [43] 0.87
Interface properties
τ (MPa)3
0 ASTM D3039M [30] 74.2
τ (MPa)sh ASTM D2344M [34] 110.4
= °G (kJ/m )θIc, 0
2 ASTMD5528 [42] 0.30 ± 0.01
= °G (kJ/m )θIIc, 0
2 ASTMD7905 [43] 0.87 ± 0.06
ηbk 1.45
139

cracking are considered equal to mode-I and mode-II interlaminar
fracture energies measured with the Double Cantilever Beam (DCB;
ASTMD5528 [42]) and End Notch Flexure (ENF; ASTMD7905 [43]),GIc
and GIIc, respectively. The values corresponding to general mixed-mode
conditions are interpolated from delamination tests, conducted at dif-
ferent mixed-mode ratios according to the test standard ASTMD6671
[44], with the BK damage propagation criterion [17] that requires the
mixed-mode interaction parameter ηbk as only input.
The standard DCB, ENF and mixed-mode methods [42,43] are set to
characterize the propagation of delamination in ° °0 /0 ply interfaces.
Nevertheless, delamination usually occurs at interfaces between plies at
different angles. In–house experiments corroborate the literature in that
GIc and GIIc increase with interface angle, θΔ in approximately linear
forms [45–47]. Based on DCB and ENF experiments on AS4/8552
coupons designed to develop delaminations at interfaces with different
mismatch angles, the interface critical energy release rate values for
each interface were set according to the following expressions:
G G= +=θ θ J m(Δ ) 1.7Δ [ / ]Ic Ic θ,Δ 0
2 and G G= +=θ θ J m(Δ ) 8.9Δ [ / ]IIc IIc θ,Δ 0
2
for ° ⩽ ⩽ °θ0 Δ 90 .
Regarding delamination initiation, the ply interface shear strength
is considered to be the same as the ply in-plane shear strength, and it is
determined by means of the ILSS test [34]. The interface normal
strength is considered equal to the value of the transverse tensile
strength for a thick embedded ply (calculated according to [33]).
In a similar way as to the critical energy release rate, the friction
between delaminated surfaces appears to be a function of the interface
angle, θ. For ° °0 /0 interfaces the friction coefficient, μ, can be as low as
0.2 whilst for ° °90 /90 interfaces it can be as high as 0.8, varying ap-
proximately in a linear way [48]. In this work, a linear fitting between
these values was used to determine μ for a given ply-interface angle.
2.2. Kinematic modelling
Besides appropriate meso-scale discretization in plies and ply-in-
terfaces, the proposed key modelling aspects to allow the appropriate
kinematic simulation of unidirectional composite laminates are mesh
size regularization, mesh-alignment with directional biasing and crack-
band erosion, as described below. The whole of these techniques are
herein refereed to as ‘kinematic modelling’.
2.2.1. Mesh size regularization
The continuum damage formulation used in this work models the
damage mechanisms occurring at spatially-discrete locations, as if they
are smeared over the finite size of the elements. In this way, a zero-
thickness mesocrack is simulated by the failure of a band of solid ele-
ments. With crack progression, the crack energy release rate (GM), for
each damage mode M ( = ± ±M 1 ,2 ,6), must be properly computed by
the numerical model. However, the standard implementation of strain-
softening constitutive models leads to mesh-dependent results, i.e. the
solution is non-objective with respect to the mesh refinement, and the
computed energy dissipated decreases with the reduction in the ele-
ment size. The mesh regularization scheme proposed by Bažant and Oh
[49] is employed to assure objective solutions, i.e. to guarantee that
G=∗l gM M, wherein gM is the energy release per unit volume and ∗l is
the element characteristic length and represents a typical cracking
distance across the surface of an element [50].
For squared elements with an aspect ratio approximately equal to
one, the characteristic element length can be approximated by [49]:
=∗l
A
cos γ( )
IP
(1)
wherein ⩽γ| | 45deg is the angle between the mesh lines and the
cracking direction, and AIP is the area associated with an integration
point projected in the plane of crack propagation. In this work, a single
layer of reduced-integration 3D elements (C3DR8 in ABAQUS [14];
single integration point) is used to model a composite ply, hence AIP
coincides with the element ply surface area [50].
By following Bažant’s crack band model [49], there is a maximum
element size that guarantees the correct representation of both material
strength and fracture energy dissipation simultaneously,
G
= = ± ±∗
l
E
X
M
2
, 1 ,2 ,6max
M M
M
2
(2)
wherein EM and XM are the Young modulus and ply strengths corre-
sponding to each failure mode [51]. If an element is so large such that
its potential for elastic energy accumulation (per unit surface area) is
higher than the material fracture energy, a local snap-back in the stress-
strain relation would be required which would be impossible to solve
with standard FE approaches based on the Newton-Raphson integration
method. In dynamic explicit integration procedures, such as the one
approach used in this work, the model would most likely over-predict
the energy dissipation by damping the nodal velocities. In the limit, the
use of ∗
lmax as defined above would still lead to a sudden drop in the
stress-strain relation introducing artificial local vibrations requiring
damping. To ensure a gradual material softening the maximum element
size was set to 0.85 ∗
l· max.
In addition, for the compressive damage modes, there is a minimum
element size that ensures a complete dissipation of fracture energy
before the element totally collapses, i.e.
G ∫= ∊ ∊ ∊ ⩽ = − −∗
−
l σ d M( ) , 0 and 1 ,2M min
1
0
(3)
The element erosion strategy used in this work (see Section 2.2.3)
avoids excessive element deformation which would introduce spurious
effects in the computation of stresses and reduce the efficiency of the
analyses.
2.2.2. Mesh-alignment and directional biasing
Another source of mesh-dependence in strain-localization models is
mesh-induced direction bias. The misalignment between crack band
direction and mesh lines induces stresses locking because of the con-
tinuity in displacement of the FE method [52]. Advanced numerical
techniques are available to mitigate this pathological behaviour for
general crack paths [53]. In unidirectional composites, microstructure
dictates that matrix cracks develop along the longitudinal direction
while fibre breakage and kinking tend to occur transverse to it.
Therefore, a practical solution to mitigate mesh-induced directional
bias in these materials consists in the alignment of mesh lines with
orthotropic material directions, as demonstrated in [15,16,54].
In arbitrarily-aligned meshes the effective thickness of the softening
band depends on the orientation of the crack with respect to the mesh
lines. For a squared-surface element mesh, the thickness of a zig-zag
band in the diagonal direction is 2 times larger than if the band
propagates parallel to the element sides [52]. For an arbitrary direction
of crack propagation, the average of ∗l defined in Eq. 1 can be used in
the mesh regularization scheme, =l A* 1. 12 IP . For material-aligned
meshes, ∗l tends to be equal to AIP ( =γ 0) [51]. However, for highly
orthotropic materials such as unidirectional composites, mesh-align-
ment is not entirely sufficient to avoid mesh-induced direction bias,
because without information of the microstructure at the mesoscale,
crack progression can still be controlled by principal meso-stresses ra-
ther than by representative deformation micromechanisms.
To demonstrate this, Fig. 1 shows four simulations of the 10° off-axis
tensile test using four distinct meshing approaches. This test was in-
itially proposed by Chamis and Sinclair [55] for the measurement of in-
plane shear strength of unidirectional fibre composites since theoretical
and experimental investigations led to the conclusion that when failure
occurs in off-axis coupons oriented at 10°, the in-plane shear stress is
near its critical value [56]. This means that for tensile specimens with
lower off-axis angles, the failure mode is likely to be fibre breakage.
Altogether, this virtual test constitutes a great challenge for FE
140

simulations with continuum damage models. The coupon simulation
using a regular mesh, i.e. not aligned with material directions, leads to a
wrong and non-physical prediction of failure mechanisms (Fig. 1(a)).
Coupon failure is predicted to start by diffuse transverse damage at
opposite specimen edges and opposite load-ends that eventually con-
nect by shear damage. This shear damage does not define a clear shear
crack oriented at 10°. Moreover, there is crack-band broadening and
branching at several locations in the virtual coupon. The three simu-
lations with material-aligned meshes correctly predict specimen failure
by two parallel shear cracks originating at opposite specimen edges and
load-ends, but with significant differences (Fig. 1(b)). A mesh ratio of
1.4–1 (longitudinal to transverse material directions) produces crack-
band broadening and limited crack-band branching. In a mesh ratio of
2.8–1, crack-band branching is not observed but still some crack-band
broadening and deviation from mesh lines occurs. A mesh relation of
5.6–1 produces two clean shear cracks advancing in single element
bands at 10°, therefore dissipating the correct amount of energy. The
stress-strain behaviour of these four coupons is slightly nonlinear, due
to the nonlinear response associated with the shear load component.
Their failure is essentially brittle because of the crack initiation at a
rather higher applied load and propagates rapidly due to the high
available energy in the coupons. The ultimate strength values predicted
by the four simulations are presented in Fig. 1. A higher load is pre-
dicted by the simulation with regular mesh. The failure load drops
about 7% with the change to material aligned mesh but then slightly
increases with the increase of aspect ratio. The load drop for material
aligned meshes is associated with the significantly better prediction of
the damage initiation mode and location. The load increase with ele-
ment aspect ratio is likely related to the discretization around that crack
initiation point. A negligible increase occurs between models with as-
pect ratios of 1.4 and 2.8, while the most significant is between aspect
ratios of 2.8 and 5.6, possibly indicating the detrimental effect of less
accurate resolution of the fracture process zone.
The previous results demonstrate that to simulate the correct phy-
sical propagation of transverse cracks in unidirectional FRP, mesh-
alignment is not sufficient. In addition, a large element aspect ratio (in
longitudinal to transverse material directions) is needed to prevent the
crack from deviating from its microstructure-allowed path. This in-
crease of the element aspect ratio represents a directional biasing of the
degrees of freedom (DOF) available in the model that prevents crack
deviation from their microstructure-constrained path. This strategy
constitutes an impoverishment of the deformation possibilities in the
model and can be regarded as a ‘double reverse’ approach with respect
to extended finite element techniques that apply enrichment of the
deformation functions in the model to increase crack path possibilities.
The remarkable advantage of the strategy proposed herein is the no-
torious decrease number of elements and DOF required to reliably si-
mulate the °10 off-axis test (Fig. 1).
It is fortunate that for material-aligned meshes in unidirectional
composites, two independent characteristic lengths, + −
∗
l1 ,1 and + −
∗
l2 ,2 ,6
can be devised, respectively for fibre and matrix crack banding, that
correspond exactly with element surface sides, hence allowing rectan-
gular elements and directional mesh biasing (see Fig. 2)). Furthermore,
Eqs. (2) and (3) dictate that the element dimensions in longitudinal
direction can typically be an order of magnitude larger than in trans-
verse direction. However, the are a number of other factors that need to
be considered when setting the element aspect ratio, such as crack di-
rectionality enforcement, stress accuracy, stress field resolution, re-
presentation of the fracture process zone (intra- and interlaminar),
crack constraining, avoidance of numerical difficulties and spurious
deformation modes, to name a few. A large number of parameters
might actually influence the ‘optimal’ element aspect ratio which will
result of the trade-off between several opposing factors. This optimi-
zation is, however, out of the scope of this work wherein the target
element aspect ratio for further analyses was set to 3 (longitudinal di-
rection) to 1 (transverse direction).
Fig. 1. Prediction of transverse cracks in a virtual °10 off-axis tensile test using different meshing strategies: (a) regular mesh; (b) material-aligned meshes with different element aspect
ratios.
141

2.2.3. Element erosion and crack representation
Another advantage of using material-aligned meshes is that it fa-
cilitates the use of element erosion to simulate material cracks in the
strong sense. i.e. with kinematic discontinuities between crack faces.
Once an element is removed from the mesh, penalty-based frictional
contact conditions are enforced at the free faces of the neighbouring
elements to model the crack faces, avoiding interpenetration and al-
lowing stress transfer in case of crack closure. A second motivation for
element erosion is the avoidance of excessive element distortions that
would condition the efficiency of the simulations and compromise the
accuracy of the solutions. The disadvantages of eroding the smeared-
damage crack band are the removal of potentially available energy from
the system and that crack faces are generated at a relative distance
between each other, corresponding to the finite thickness of the crack-
band. The first effect is mitigated by the fact that stresses around a
crack need a finite distance to recover to nominal values, according to a
shear-lag assumption. The second consequence of crack-band erosion
would only have effect on compressive and shear dominated cracking.
To model opening cracks, element erosion is enforced when +d1 or
+d2 reach values close to unity. Under compressive loads, the crushing
damage is considered smeared over the element, ideally until its emi-
nent collapse, i.e. when the compressive strains are close to unit values.
In such case, a closed crack would be simulated by the neighbouring
element contact faces which, at this point, are at a short distance from
each other, hence avoiding large displacement discontinuities.
However, under a such limiting case, the element would be highly
distorted and would need to be removed from the analysis. Hence, these
strain levels are never achieved in practice.
In order to avoid highly distorted elements, the determinant of the
deformation gradient (det F), a variable passed directly from ABAQUS/
Explicit [14] to the ‘VUMAT’ subroutine, was used in the criteria of
element erosion, as proposed by Tan et al. [57]. This variable is defined
as the ratio between the deformed (V) and undeformed (V0) volumes of
an element:
=
V
V
Fdet
0 (4)
Wide limits on det F were established based on trials to achieve a
good compromise between crack representation, numerical efficiency
and solution accuracy. Another factor taken into account was the as-
surance of the correct dissipation of the mode-dependent fracture en-
ergy in general, i.e. that the limits on det F do not collide with max-
imum allowed values of dM. In summary, the following criteria were
applied to element erosion:
=
⎧
⎨
⎩
⩾
∊ ⩽ −
⩽ ⩾
⎫
⎬
⎭
+ +d
F F
Delete element if
0.999999
1.0
det 0.1 or det 5.0
1 ,2
1,2
(5)
3. Virtual testing laboratory
A dedicated ABAQUS plug-in was built on purpose for the meso-
modelling of unidirectional FRP coupons according to the presented
approach. The tool has been implemented by means of the program-
ming language Python using ABAQUS scripting commands [14] and
includes a Graphical User Interface (GUI), as shown in Fig. 3. This tool
is completely automated without the need for the use of any third-party
software or manual intervention, except for the introduction of model
inputs. Although only in-plane coupon testing was addressed in this
work, the plug-in can eventually be expanded to perform damage and
failure analyses of different configurations and loading cases such as
impact, compression-after-impact and crushing.
3.1. Coupon modelling approach
The main characteristics of the coupon modelling tool are schema-
tically illustrated in Fig. 4 and can be described in the following se-
quence of steps:
Step 1: Selection of virtual test and coupon geometry.
The modelling process starts with the selection of the required vir-
tual test from the list of currently available AITM and ASTM test-
standards for composites e.g. (AITM 1-0007 [58]; AITM 1-0008
[59]; ASTMD6484/D6484M-09 [60]; ASTMD5766/D5766M-07
[61]). In this step, the geometric specifications of the specimen e.g.
(coupon dimensions, ply-thickness and stacking sequence) are set
and the analysis procedure is defined.
Step 2: Coupon assembly and meshing.
The laminated FRP specimen with the desired stacking sequence is
assembled from several parts (see Fig. 5)). The coupons are divided
in three zones with two different levels of discretization in order to
minimize the necessary computational resources and ensure the
localization of failure mechanisms in the central sections of the
specimens (Fig. 5(a)). In these sections (see Fig. 5(a)) – Damage
zone) each ply is discretized by means of a structured aligned
meshing technique with a refined layer of reduced integration solid
elements (C3D8R in ABAQUS [14]). A mesh generator was devel-
oped for this specific purpose and has been implemented using an
external graphical library ‘pyGraph.lib’ following the methodology
explained in Section 3.2.
Zero-thickness ply interfaces are modelled by means of a surface-
base cohesive-frictional formulation coupled to a penalty contact
algorithm, as explained in Section 2.1.1 (see Fig. 5(c)). The local
characteristic lengths of elements (Fig. 5(d)) are calculated taking
into account the specification described in Section 2.2.2. Away from
the centre, around the load application edges, the orthotropic layers
are assumed to behave elastically and are modelled by coarse solid-
like continuum shell elements with one integration point per ply.
Fig. 2. Orthotropic mesh regularization strategy used in the composite ply damage model. Wherein ∗l is the element characteristic length, G E X, ,M M m and ′Xm are the fracture energy,
Young modulus, ply nominal strengths and reduced ply nominal strengths respectively, for each damage mode M ( = ± ±M 1 ,2 ,6).
142

The three regions with different discretizations are kinematically
constrained to enforce continuity of displacements and rotations
across their boundaries. Specially in the cases of un-notched cou-
pons, the damage zone is guaranteed to be long enough to represent
ply and interface damage accumulation before their final failure. In
order to avoid spurious damage due to unrealistic stress oscillations,
stress softening is prevented in plies and interfaces in smooth tran-
sition zones close to the regions of kinematic constraining. Although
this problem has been tackled by means of more sophisticated ap-
proaches [62], the proposed modelling technique is practical, robust
and leads to reliable results.
The parametric modelling capability allows the selection of
Fig. 3. Graphical User Interface (GUI) of the Virtual Test Lab plug-in in the Abaqus/CAE environment.
Fig. 4. Workflow of the ABAQUS-embedded Virtual Test Lab for the FE simulation of composites coupons.
143

conventional (0°, 90° and ± 45°) and non-conventional ply or-
ientation angles. This freedom is useful to the simulation of non-
conventional laminate with dispersed stacking sequences [63]. For
symmetric layups, symmetry boundary conditions are applied on the
mid-plane of the virtual specimen.
Step 3: Assignation of material behaviour and properties.
The plies in the central zone of the specimens are assigned the
constitutive model for unidirectional composite materials in-
troduced in Section 2.1.2 which has been coded in a double-preci-
sion Fortran-written user material subroutine ‘VUMAT’ for
ABAQUS/Explicit [14]. The ply interface behaviour is taken into
account by means of the ABAQUS-native surface-based cohesive-
frictional interactions that facilitate the use of non-conformal ply
meshes, hence allowing the use of mesh alignment, mesh directional
biasing and different element sizes in different plies, according to
the requirements imposed by their ‘in situ’ properties (see Fig. 7(b)).
Step 4: Definition of analysis steps, loading and boundary condi-
tions.
In order to conduct practical explicit dynamic simulations, me-
chanical loads are applied to the specimens by means of a velocity
amplitude profile imposed on one of its end-edge surfaces, starting
from rest and linearly increasing at 500 mm/s2
up to a maximum
velocity of 10 mm/s. The remaining fixed model boundaries, ac-
cording to the standard test selected, are enforced by means of
conditions of zero velocity. Moreover, mass scaling is used (1000×)
to increase the explicit analysis stable time increment to practical
levels, improving the computation time. These conditions ensure the
quasi-static nature of coupon deformation which is guaranteed by
keeping the specimen kinetic at a level two orders of magnitude
lower than its internal energy and by observing that there are no
dynamic oscillations in the load-displacement results.
A thermal analysis step is conducted prior to the application of
mechanical loading, in order to simulate the influence of thermal
residual stress resulting from curing cool-down. As discussed in
[64], the representation of the process by a simple cooling from
stress-free temperature to room temperature using constant thermal
expansion coefficients overestimates the resulting residual stresses
due to the attenuating influences of other parameters which are
difficult to predict, such as humidity and moisture ingression. Puck
and Shürmann [65] estimate that the true residual stresses reach
about half the values calculated from this approach [64]. Accord-
ingly, in this work, half the temperature drop from the stress-free
temperature (180 °C for the 8552 resin) to ambient temperature
(20 °C) is applied.
Step 5: Virtual analysis procedure.
The explicit FE method implemented in ABAQUS/Explicit [14] was
the approach selected to carry the coupon simulation in the Virtual
Test Lab. Numerical schemes based on explicit time integration are
the adequate choice for solving highly nonlinear dynamic problems.
In the current coupon simulations, sources of nonlinearity include
large displacements, non-linear material constitutive behaviour in-
cluding damage, complex contact interactions and frictional beha-
viour. Under these conditions, implicit integration procedures
would require a large number of iterations in order to achieve an
equilibrium solution, hence calling for large computational re-
sources and calculation times, if not impossible at all.
Explicit integration schemes do not require the solution of a global
set of equilibrium equations as the accelerations, velocities and
displacements are calculated explicitly at each node recurring to a
simple central differences rule applied over a time increment. The
computational cost is proportional to the number of elements and
inversely proportional to the smallest element dimension which
determines the stable time increment. The stable time increment is
defined in terms of the highest element frequency in the model,
associated with the dilatational mode of deformation. With the
element characteristic length, ∗l , and the dilatational wave speed in
the material, cd, the stable time increment is defined as [14]
= ∗t l cΔ /stable d. For a linear elastic material with a Poisson’s ratio of
Fig. 5. Coupon FE modelling showing structured aligned meshes in damageable zones with cohesive-frictional contact surfaces taking into account characteristic element length ∗
le (see
Section 2.2.2).
144

zero, =cd
E
ρ
, where E is the material Young’s modulus and ρ its
density. As previously mentioned, mass scaling (1000ρ) was used in
this work to increase the stable time increment and increase the
efficiency of the analyses without significantly altering the quasi-
static nature of the tests or compromising the accuracy of the results.
The virtual tests take in the order of the hour to carry using High
Performance Computing resources (2x Intel Xeon IvyBridge 20-core
computing node). A load/displacement analysis monitoring cap-
ability is implemented in the Virtual Test Lab to track the ultimate
failure of the specimen and stop the running analysis when a large
and sudden load drop is detected. At this point the virtual test re-
sults become ready to be analysed.
3.2. Generation of material-aligned meshes by means of a grid-based
method
To ensure mesh alignment with material directions at all locations
of the meso-modelled section of the virtual coupons, including free
edges, and since the automated meshing algorithms available in
ABAQUS [14] were found not to be able to accomplish this objective,
special meshing techniques were developed and implemented in the
python-based modelling plug-in.
The approach developed in this work relies on the creation of grids
of ply partitions aligned with the ply fibre orientation, as shown in
Fig. 6(a). Refined partitions, in the order of the element size are needed
Fig. 6. Illustration of the procedure to obtain structured aligned meshes in an automated way: (a) partition of faces by means of 2D sketches including hole cutting; (b) controlled mesh
seeding, mesh generation and section material definition.
145

close to the ply edges but an excessive number of partitions imposes a
high penalty in terms of modelling time. Therefore, the partition pro-
cess is performed in two steps, addressing central areas and areas close
to edges differently. In the first step, an optimal number of large par-
titions (tiles) is created, minimizing the areas close to the free edges, as
illustrated in face f1 in Fig. 6(a). The second step consists in refining the
partitioning around the edges using an structured sketch, as represented
in face f2 in Fig. 6(a). For the cases of open-holed specimens, partition
refinement is also needed around the holes (see face f4 of cell C1 in
Fig. 6(a)). This last operation uses a specific algorithm explained in
Section 3.3.
A more detailed representation of this partitioning and meshing
process is illustrated in Fig. 6(b). Both coarse and refined structured
(material-aligned) partitions are controlled by a normalized critical
element length ∗
len
. In the central area with large partitions the element
size is controlled by locals seeds with value ±
∗
le 1n
and ±
∗
le 2n
(see Fig. 6b).
The meshing in the central partitions is performed exclusively with
C3D8R brick elements, while in the edge partitions a combination of
C3D8R and C3D6 wedge elements is used [14] (see Fig. 6(b)). A free-
mesh technique is applied in the discretization of the zones of transition
to continuum-shell elements using a C3D8R dominated meshing, as in
Face f3 (see Fig. 6(b)).
3.3. Automated material-aligned structured mesh generation for open hole
laminates
To address the automated meshing of three-dimensional coupons
with holes, a hole cutting algorithm has been implemented as described
in Appendix A. This hole cutting procedure ensures material-aligned
biased meshes and allows different design possibilities and element
aspect ratios. In addition, the algorithm can be extended to general
boundary shapes although it was developed in this work for the specific
purpose of meshing open-hole coupons.
A comparison between different meshing strategies for open-hole
coupons is illustrated in Fig. 7(a). The ‘non-structured mesh’ corre-
sponds to a simple regular mesh around the hole, with mesh lines
generally parallel and perpendicular to specimen edges, whereas the
other cases apply some form of material-alignment meshing. In these
cases, the region around the hole has been isolated and different
techniques used for comparison purposes. The cases ‘free mesh’ and
‘semi-structured’ where obtained by using the ‘advancing front’ and
‘medial axis’ algorithms native of ABAQUS [14] which do neither en-
sure the best quality of the mesh nor the critical element length di-
mensions around the hole. The ‘structured aligned meshing’ strategy
corresponds to the material-aligned meshing technique developed in
this work. A comparison between non-structured and fully material-
aligned structured meshing in terms of the prediction of damage in the
multi-directional quasi-isotropic OHT coupon analysed in Section 4 is
Fig. 7. (a; b; c) Different strategies for meshing around a open hole in a laminate − −[45/0/ 45/90/( 45 /45 ) ]s2 2 2 . (d) Material-aligned structured meshing adopted in this work. (e; f)
comparison of longitudinal stress field in plies oriented at ± °45 and crack predictions for both non-structured and material-aligned structured mesh approach.
146

illustrated in Figs. 7(e) and (f). Mesh alignment and biasing allow the
correct capturing of matrix cracks tangent to the hole and parallel to
fibre directions. Since the cracks advance in different directions, ac-
cording to respective ply angles, delaminations appear to interconnect
those cracks and produce the final failure of the specimen, as observed
experimentally (e.g. [66]). Without mesh structuring, a brittle failure
mode is predicted with all ply failure mechanisms occurring in a single
through-thickness crack plane, typically aligned with the °90 or one of
the ± °45 directions.
4. Virtual Test Lab demonstration and validation
Experimental tests on Un-Notched (UN) and Open-Hole (OH) cou-
pons of different layup configurations were simulated by means of the
Fig. 8. Graphical correlation between experimental and virtual test results of un-notched tension/compression (UNT/UNC) and open-hole tension/compression (OHT/OHC) coupons of
aeronautical design-space configurations.
Table 2
Correlation of strength results between experimental and virtual tests of several configurations on laminates used in the aeronautical design space. Note: OHT/OHC coupons with hole
diameter =D 6.35 mm.
Design space laminates: Width FOKKER NCAMP Virtual test FOKKER NCAMP
(mm) MPa (CV %) MPa (CV %) [67] MPa Err (%) Err (%)
Un-notched Tension (UNT) ASTM D3039 [72] ASTM D3039 [72]
‘Hard’ (50/40/10) 25 1105.5 (3.4) 1072.8 (3.8) 1107.7 0.2 3.2
Quasi Isotropic (25/50/25) 25 651.1 (1.1) 624.1 (4.9) 708.5 8.8 13.5
‘Soft’ (10/80/10) 25 421.9 (2.0) 448.1 (2.0) 420.6 −0.3 −6.1
Un-notched Compression (UNC) ASTM D3410 [70] ASTMD6641 [69]
‘Hard’ (50/40/10) 25 787.2 (5.5) 923.0 (3.8) 907.7 15.3 −1.7
Quasi Isotropic (25/50/25) 25 554.5 (3.4) 572.7 (7.2) 591.1 6.6 3.2
‘Soft’ (10/80/10) 25 414.1 (4.5) 439.6 (4.2) 399.3 −3.6 −9.2
Open-hole Tension (OHT) ASTM 5766 [61] ASTM 5766 [61]
‘Hard’ (50/40/10) 38.1 526.7 (4.3) 482.8 (4.5) 538.7 2.3 11.6
Quasi Isotropic (25/50/25) 38.1 370.9 (3.4) 335.5 (2.8) 371.1 0.05 10.6
‘Soft’ (10/80/10) 38.1 289.3 (2.2) 275.9 (2.2) 300.7 3.9 9.0
Open-hole Compression (OHC) NASA Report [71] ASTMD6484 [60]
‘Hard’ (50/40/10) 38.1 425.7 (5.8) 442.2 (3.7) 452.1 6.2 2.2
Quasi Isotropic (25/50/25) 38.1 301.8 (2.9) 333.0 (1.7) 345.9 14.6 3.9
‘Soft’ (10/80/10) 38.1 269.8 (3.2) 286.2 (5.2) 299.8 11.0 4.8
147

described approach. The corresponding results are correlated in this
section. A first correlation campaign was conducted on configurations
commonly used in the design of aeronautical structures (design-space
laminates), including quasi-isotropic (QI) and non-QI laminates. A
second campaign was performed on configurations that are not com-
monly used in aeronautical structures (off-design laminates), essentially
to explore the capabilities of the approach when applied to laminates
with clustered plies wherein delamination is a more critical damage
mode and its interaction with ply cracking is a higher challenge for the
simulations.
4.1. Design-space laminates
Virtual tests were conducted on AS4/8552 laminate configurations
analysed by Fokker Aerostructures1
and the National Center for Ad-
vanced Materials Performance (NCAMP) [67] through independent
extensive experimental campaigns intended to provide material design
allowable values for laminate configurations commonly used to design
and certify aircraft structures, and to fulfil base material qualification
requirements [67,68]. The configurations constitute limits of the design
space in terms of stiffness properties. This is reflected in the following
percentage ratios of plies in the °0 , ± °45 , and °90 directions: 50/40/10
(fibre-dominated or ‘hard’); 25/50/25 (QI); and 10/80/10 (transversely
dominated or ‘soft’). The corresponding stacking sequences are, re-
spectively, − −[0/45/0/90/0/ 45/0/45/0/ 45]s, −[ 45/0/45/90] s2 and
− − − −[45/ 45/0/45/ 45/90/45/ 45/45/ 45]s. The constitutive AS4/8552 ply
properties are reported in Table 1, reflecting the elasticity and strength
characterization performed by Fokker on relevant material batches.
Slightly different values for these properties are reported by NCAMP
[67], but these were not used in the simulations. The average char-
acteristic element lengths were ≈+ −
∗
l 0.22 ,2 ,6 (calculated according to
Eq. 2) and ≈+ −
∗
l 0.61 ,1 , to maintain an approximate aspect ratio of 3
(longitudinal direction) to 1 (transverse direction).
Standard tension and compression tests were performed on Un-
Notched (UNT/UNC) and Open–Hole (OHT/OHC) coupons of the three
different laminates. However, whilst for the tensile cases, the same test
standard was followed by both institutions, for the compressive cases,
different test standards were used by Fokker and NCAMP. The simila-
rities and differences in material batches and applied test standards
affect the correlation between experimental results obtained on both
sides, and reported in Fig. 8 and Table 2 (the minimum and maximum
experimental values obtained for each test configuration are also in-
dicated in the figure). Fokker tensile test results are systematically
higher than NCAMP’s, reflecting the differences in material batch (and
processing conditions). On the other hand, for compression tests,
Fokker values are systematically lower than NCAMP’s, as result of dif-
ferent material batches and test conditions. This is because the ex-
perimental methods used by NCAMP are notably more effective in
preventing unwanted deformation modes before specimen failure such
as end-load crushing (Combined Loading Clamping (CLC) test fixture
for UNC test, ASTMD6641 [69]) and out-of-plane instabilities (side-
supported ASTMD6484 [60] for the OHC test) than the ones used by
Fokker (ASTMD3410 [70] and NASA Short Block [71], respectively). A
detailed discussion on these test methods is out of the scope of the
present work, but the implications are that the simulations of the tensile
tests are more comparable to Fokker experiments, due to more re-
presentative material properties, while NCAMP compression test results
can be considered to have a higher relevance due to the similarities
between experimental and virtual test conditions.
Correlations between predicted and experimentally-obtained
average strengths are also given in Table 2 and Fig. 8. In general lines,
the tensile virtual test results fall within the scatter of Fokker’s ex-
perimental results while compression test simulations correlate better
with NCAMP’s experimental scatter. The numerically-predicted curves
relating remotely applied stress with specimen strain are plotted in
Fig. 9. Unfortunately, the equivalent experimental results are not
available for correlation, either from Fokker or from NCAMP. The
curves evidence the difference in stiffness of the configurations as well
as in their and un-notched and open–hole strengths. As the result of
their higher content of °0 plies, the ‘hard’ configuration shows a highly
linear and brittle behaviour. The response becomes slightly less linear
and more ductile as the fraction of ± °45 plies increases. Nevertheless,
the dominating behaviour of the °0 plies is present in all configurations.
The controlling effect of the °0 plies also determines that the tensile/
compressive strain-to-failure of UNT/UNC specimens is similar. De-
tailed discussions on the simulations of these configurations are per-
formed in the next sections.
4.1.1. Un-notched tension/compression tests (UNT/UNC)
Three main different failure mechanisms were observed in failed
UNT specimens (25 mm in width), as shown in Fig. 10(a). For the hard
(50/40/10) configuration, the failure mode was mainly driven by fibre
breakage. The brittle failure response of these coupons, dominated by a
fracture plane transverse to the loading direction, was due to the high
percent of plies aligned with the loading direction. The failure of QI
configurations (25/50/25) combined both fibre breakage and matrix
cracking. Fig. 10(a) shows that, in general, °0 plies failed by fibre
breakage whilst ± °45 layers failed by matrix shear cracking. However,
some of the ± °45 plies are also visibly sheared transversely to fibre
direction. The failure of the soft (10/80/10) laminates, owing to the
large percentage of ± °45 plies, was driven by transverse cracking
Fig. 9. Predicted stress vs. strain responses of un-notched and open-hole coupons of ‘design-space’ configurations under (a) tension and (b) compression.
1
Not publicly available elsewhere
148

parallel to fibres and triangular-shaped delaminations interconnecting
those cracks.
The numerical simulations of these UNT configurations show good
agreement with the test results in both the sub-critical damage me-
chanisms and the prediction of ultimate stresses (see Fig. 8 and
Table 2). In general, the simulations over-predict the experimental
values within a 10% margin with respect to Fokker average experi-
mental results. The highest error (8.8%) corresponds to the QI config-
uration and might be related with the use of a simple non-interactive
ply longitudinal failure criterion, thus incapable of taking into account
the possible effect of shear stresses in this failure mode.
The simulations of intralaminar and interlaminar cracking for the
quasi-isotropic and soft laminates are shown in Fig. 10(b) and (c), re-
spectively. In both configurations, sub-critical delaminations near the
free-edge effect are predicted. These are accompanied by short ply
matrix cracks that grow parallel to fibre direction. At a certain critical
load and at some location in the specimen, these cracks grow further in
combination with large delamination extensions that eventually inter-
connect them. As in the experimental results (see Fig. 10(a)), ply cracks
generally follow the material orthotropic orientations but are also af-
fected by the damage of their neighbouring plies. The ultimate failure
of the specimens is triggered by fibre breakage in the load-aligned plies
but the simulations are also able to capture fibre breakage in the ± °45
layers.
The correlation between experimental results in Fig. 10(a) and si-
mulations shown in Fig. 10(c) puts in evidence that the experimentally-
obtained damage pattern appears more concentrated to a band. This is
because the simulated images are also showing secondary failure bands,
occurring after the moment of maximum load, that are due to travelling
stress waves. Experimentally failed coupons can also show this
Fig. 10. Experimentally-observed (a) and simulated (b; c) failure mechanisms resulting from UNT tests on different laminates (photos: Fokker). (b) Matrix cracking, fibre failure and
delamination damages in the four outer plies in the QI laminate ( − +45 0 45 90[ / / / ] s2 ). (c) Matrix cracking and delamination damages in the three plies (identified in bold) of the soft
laminate − − − −45 45 90[45/ /0/ / 45/ /45/ 45/45/ 45]s.
149

Fig. 11. Experimentally-observed (a) and simulated (b) failure mechanisms resulting from UNC tests on diﬀerent laminates (photos: Fokker). (b) Longitudinal stresses and damage in four
plies (identiﬁed in bold) of the soft laminate − − − −45 0 90 45[ / 45/ /45/ 45/ /45/ /45/ 45]s.
Fig. 12. Experimentally-observed (c) and simulated (a; b) progression of failure mechanisms in OHT specimens of soft laminates (10/80/10): (a) undeformed damage evolution of
delamination and matrix cracking. b) realistic transverse cracks simulated by means of crack-band erosion. c) experimentally-observed failure modes in failed specimens (photo: Fokker).
150

behaviour, specially ‘hard’ ones which free high amounts of energy. In
contrast, most virtual coupons show this post-collapse behaviour that
can be attributed to the artificial effects of mass scaling.
Independently of the layup, the failure of un-notched coupons under
compression is dominated by crushing of the plies (with entanglement
of fibre splits), extensive delaminations and out-of-plane deformation of
the outer delaminated plies or sublaminates, as captured by Fokker in
Fig. 11(a). These mechanisms are well predicted by the simulations, as
for example the one corresponding to the soft laminate shown in
Fig. 11(b). The virtual test also shows that the initial mechanism that
triggers the instability and collapse of this configuration is shear
cracking of the ± °45 which influences the subsequent damage me-
chanisms. It also gives indication that the experimental test method
adopted by Fokker might leave a too short free test area to fully capture
these affects.
Although all the virtual test results for UNC coupons are found in-
side the range of experimental scatter, considering both Fokker and
NCAMP results, the values predicted correlate better with the average
Fig. 13. Experimentally-observed (d) and simulated (a; b; c; e) failure mechanisms in OHT specimens of quasi-isotropic laminates (25/50/25): (a) Field of surface longitudinal stresses
before ultimate failure; (b) simulated delamination and matrix cracking before and after the ultimate failure; (c) predicted matrix cracks in different plies; (d) experimentally-observed
failure mode in several specimen replicates (photo: Fokker); (e) simulated failure mode.
Fig. 14. Experimentally-observed (c) and simulated (a; b) failure mechanisms in OHT specimens of hard laminates (50/40/10 – − −[0/45/0/90/0/ 45/0/45/0/ 45]s): (a) predicted matrix
damage at specimen failure load; (b) predicted delamination and damage in fibre direction ( +d1 ) at the point of ultimate failure; (c) experimentally-observed failure mode in failed
specimens (photo: Fokker).
151

NCAMP measurements. As mentioned above, it is likely that the mis-
match is due to the different test methods used at each institution.
While Fokker applied the ASTMD3410 [70], with a IITRI test fixture
that applies pure shear loading by means of wedges and a guidance
system to prevent lateral instability, NCAMP used the ASTMD6641 [69]
with a combined shear/end-loading (CLC) test fixture. Studies on the
CLC fixture demonstrated that a high ratio of end-loading, with just
enough shear loading to prevent end-load crushing, provides consistent
results [68]. High shear loading ratios resulted in a decrease of strength
on the CLC fixture. Hence, it is likely that Fokker results are affected by
the test method considering the lower strength and large variation
measured, especially in the case of the hard laminate which requires the
highest failure load, thus increasing the clamping pressure of the
wedges.
4.1.2. Open-hole tension/compression tests (OHT/OHC)
Virtual tests were performed on OHT and OHC specimens
(width = 38.1 mm; hole diameter = 6.35 mm) and the ultimate
strength results are correlated with the corresponding experimental
values in Fig. 8 and Table 2. As for the un-notched cases, and due to
similar reasons, the virtual OHT results compare better with Fokker
measurements while OHC predictions have higher correlation with
NCAMP values.
As expected, a progressive failure behaviour with interacting ply
failure modes was observed in the OHT specimens, with damage in-
itiating around the hole and propagating towards the free edges (see
Fig. 12). Distinct final failure mechanisms were observed for distinct
configurations, and these were remarkably captured by the simulations
in similar fashion to the phenomena reported for un-notched speci-
mens.
For soft laminates, Fig. 12(a) shows that sub-critical damage in-
itiates at low load levels by means of small matrix cracking and isolated
delamination regions around the hole edge and specimen borders. De-
laminations are triggered by the three-dimensional interlaminar stress
state along the free edges. Eventually, delaminations are affected by the
progression of matrix cracks. With increasing applied load, matrix
Fig. 15. Experimentally-observed (c) and simulated (a; b; d) failure mechanisms in OHC specimens of quasi-isotropic laminates (25/50/25 – −[ 45/0/45/90] s2 ): (a) fibre direction stress
field in the outer − °45 ply before and after ultimate failure; (b) simulation of specimen crushing; (c) Experimentally-observed failure mode in specimens of the same configuration (photo:
Fokker); (d) Simulated damage modes at specimen collapse.
152

cracks gradually grow from the hole, across the width of the specimen
towards the edges, following the directions of the fibres. These cracks
are followed by extensive triangular-shaped delaminations until the
eventual specimen collapse by the pull-out of cracked and delaminated
plies, as shown in Fig. 12(c). This behaviour is well simulated owing to
the crack-band erosion technique which creates internal free edges,
hence promoting the development of local three-dimensional stresses
that drive the delaminations that accompany matrix cracking
(Fig. 12(c)).
The failure initiation mechanisms in quasi-isotropic OHT config-
urations are similar to the ones described for the soft laminates, but the
final failure of the specimens is driven by the breakage of the °0 plies
transversely to the load direction. These phenomena are illustrated in
Fig. 13.
The hard laminate failed in a brittle way. This failure mode,
dominated by the sudden fibre breakage and high energy released by
the °0 plies, was well predicted by virtual testing, as shown in Fig. 14. In
essence, the damage and failure of all plies are concentrated around a
single fracture plane that crosses the hole and is perpendicular to the
applied load direction. Also, the delamination area is smaller in com-
parison with soft and QI laminates and concentrated around the frac-
ture plane.
It is worth remarking at this point that the prediction of these three
different OHT coupon failure modes is not achievable without a ply-by-
ply material-aligned and biased mesh. With a non-structured mesh
approach, with mesh lines parallel/perpendicular to coupon edges and
conforming through-the thickness, the simulated failure mode is brittle
for all laminate configurations (see Fig. 7). This entails effects on the
prediction of final failure loads as well, except for the hard laminate.
The accuracy of the predictions for the other laminates is worsened by
4% on average.
The phenomena associated with ultimate failure of OHC specimens
are similar to ones observed in UNC coupons (crushing of the plies with
entanglement of fibre splits, extensive delaminations and out-of-plane
deformation of the outer delaminated plies or sublaminates), however
they progress in a more gradual way, as illustrated by means of ex-
perimental and simulation results in Fig. 15 for a QI laminate. Inter-
laminar damage is promoted by three-dimensional stress states around
the specimen free edges (see Fig. 15(d) on the right). The increasing
load causes the instability and buckling of the delaminated outer plies
or sublaminates which promotes further propagation of delaminations.
These buckled plies finally fail by an interconnection of matrix cracks
and fibre breaks in a ‘zigzag’ pattern causing the collapse of the spe-
cimen.
4.2. Off-design, clustered-ply laminates
In order to fully test the robustness and reliability of the proposed
virtual testing strategy, laminates not commonly used in the design of
aerostructures were simulated. To a large extent, these configurations
contain plies clustered at the same ply angle, a feature known to pro-
mote matrix cracking, due to the reduction of in situ strengths [33], and
delamination, due to the enhancement of interlaminar stresses. Un-
notched and open–hole coupons with two different layups were simu-
lated under in-plane tension and compression loading conditions, and
the corresponding predictions compared with experimental results
available in the literature. One of the layups,
− −[45/0/ 45/90/( 45 /45 ) ]s2 2 2 was analysed by the present authors in
[16,73]. The corresponding coupons were produced with AS4/8552
prepreg material whose properties are given in Table 1. The other la-
minate configuration is −[45 /90 / 45 /0 ]s4 4 4 4 ; the corresponding coupons
were produced with IM7/8552 prepreg plies and were investigated in
experimental analyses reported in [66,74]. While in the latter config-
uration all plies have four times the nominal ply thickness (clusters of
four plies), the former presents a combination of thin (nominal) and
thick (clustered) plies.
The ultimate strength values obtained for these configurations by
means of experimental and virtual tests are correlated in Table 3. The
IM7/8552 material properties used in the simulations were taken from
[2,4]. The failure mechanisms obtained by both methods are analysed
in the following sections.
4.2.1. Un-notched and open-hole tension tests
The UNT and OHT experiments on the −[45 /90 / 45 /0 ]s4 4 4 4 laminate
showed extensive delamination and matrix cracking before the collapse
of the specimens which was caused by the fibre breakage of the °0
clustered plies (see Fig. 16). In the OHT coupons, the first sign of loss of
structural integrity was a major delamination at the −( 45/0) interfaces
[66,74]. These failure mechanisms were properly predicted by the si-
mulations. As illustrated in Fig. 16, the predicted delamination at the
−( 45/0) interface spreads over a wide extension of the laminate. Matrix
cracking was experimentally analysed by means of X-ray computed
tomography of a damage OHT specimen just before its ultimate failure,
as shown in Fig. 16(b) [66,74]. The correlation with simulations shows
that the present virtual testing approach predicts reasonably well the
evolution of matrix cracks along fibre directions until the final pull-out
of the broken plies. The major splitting cracks on the ± °45 plies are
correctly predicted to initiate tangentially to the hole. However, this is
not the case for the clustered °0 were the major splitting cracks tan-
gential to the hole are not well predicted. The reason behind this dif-
ficulty is not exactly clear but might be related with the crack-band
erosion strategy. The over-prediction of the ultimate strength by 13.3%
could be an associated effect. More representative simulations of these
mechanisms can be achieved with extended FE methods [10]. It is also
worth noting that the effect of ply thickness/clustering on G +1 [40] was
not taken into account in the simulations, and this is likely to affect the
results.
The UNT tests on laminate − −[45/0/ 45/90/( 45 /45 ) ]s2 2 2 followed the
standard procedure AITM 1–0007 [58]. The stress vs. strain response
was monitored experimentally by means of strain gauges as well as
Digital Image Correlation (DIC) [73]. Both measurements are correlated
with the corresponding simulated results in Fig. 17(a). The comparison
shows that although the final failure load was under-predicted by 8.8%
(see Table 3), the specimen nonlinear response (due to the significant
number of ± °45 plies in its layup) was well captured. The correlation
between experimentally-obtained and numerically-predicted failure
mechanisms on OHT specimens of this configuration are illustrated in
Fig. 17(c), as reported in [16]. In similar ways to the cases above,
Table 3
Strength results of experimental and virtual tests of several configurations on off-design
laminates. Note: OHT/OHC coupons with hole diameter =D 6.35 mm.
Off-design space clustered laminates: Width Virtual test Exp. Test Err
(mm) MPa MPa (CV
%)
(%)
Material: IM7/8552
Layup: + −[ 45 /90 / 45 /0 ]s4 4 4 4 [66,74,75]
UNT 32 453.7 458.0
(5.8)
−0.9
OHT 32 322.9 285.0
(5.17)
13.3
Material: AS4/8552
Layup: + − − +[ 45/0/ 45/90/( 45 / 45 ) ]s2 2 2
[16,73]
AITM
[58,59]
UNT 32 355.1 389.2
(0.2)
−8.8
OHT 32 235.3 225.6
(2.7)
4.3
UNC 32 360.4 336.9
(1.9)
7.0
OHC 32 271.1 238.5
(5.4)
13.6
153

matrix cracks in fibre directions, major fibre splits emanating tangen-
tially from the hole, triangular shaped delaminations, and specimen
collapse with pull-out of the broken plies are mechanisms properly
captured in the simulations.
4.2.2. Un-notched and open–hole compression tests
A comparison between simulated and experimentally-observed
failure mechanisms on UNC and OHC AS5/8552 coupons with
− −[45/0/ 45/90/( 45 /45 ) ]s2 2 2 layup is shown in Fig. 18. The experiments
followed the standard AITM 1–0008 [59] and the virtual tests were
performed accordingly. Photos were taken at the moments (applied
displacements) just before and after the collapse of the specimens to
validate the final failure mechanisms predicted with virtual testing. As
demonstrated by the simulations, extensive delaminations left the outer
plies/sublaminates prone to instability. When buckled, intraply
transverse (due to out-of-plane bending) and shear stresses (owing the
large number of ± °45 plies) developed on the delaminated plies that
triggered extensive matrix cracking. Without the support of the outer
plies, the inner plies could not bear the applied load and crushed. While
the sequence of events in UNC coupons occurs in a rapid way, the
failure of the OHC specimens is less brittle, with the progressive
growing of delaminations from the edges of the hole and specimen
borders until they eventually meet and trigger final collapse.
5. Conclusions
A novel computational framework, consisting of several numerical
tools, has been implemented to address the challenges of virtual testing
of unidirectional FRP at coupon level. By means of the combination of
physically-based constitutive damage models and modelling techniques
Fig. 16. Simulated failure mechanisms resulting from UNT (a) and OHT (b; c; d) tests of clustered laminate −[45 /90 / 45 /0 ]s4 4 4 4 : (a) matrix cracking and delamination in UNT coupon; (b)
correlation between simulated and X-ray tomography [66] of transverse cracking before final failure; (c) realistic simulation of failure mode; (d) predicted matrix cracking at each ply and
delamination at each ply-interface.
154

that guarantee the proper kinematic simulation of damage, the highly
nonlinear laminate response that entails the competition of different
failure mechanisms is realistically simulated. A three-dimensional
continuum damage methodology was used to account for the initiation
and propagation of the relevant ply failure modes whereas delamina-
tions were predicted by means of a cohesive-frictional constitutive
formulation coupled with the kinematics of penalty-based contact sur-
faces. The structuring of the mesh by aligning mesh lines with the or-
thotropic material orientations, the biasing of the available degrees of
freedom to prevent crack deviation from their expected path, and crack-
band erosion are techniques proposed to properly simulate matrix
cracking and its interaction with delaminations. A grid-based method
was developed as a practical solution for optimal control of the meshing
process. In addition, for notched laminates, a hole-cutting algorithm
was implemented to obtain aligned meshes around the holes in an
automated way.
In order to validate the reliability and robustness of the virtual test
laboratory, simulations of a wide range of different laminates (fibre-
dominated, quasi-isotropic and matrix-dominated) and test
configurations (un-notched tension/compression; open-hole tension/
compression) have been exhaustively compared with experimental re-
sults. It was demonstrated that the proposed combination of con-
stitutive modelling and kinematic strategy allows the realistic simula-
tion of the evolution and competition of damage mechanisms until
structural collapse. The prediction of failure mechanisms and ultimate
strengths was remarkably accurate considering the wide range of con-
figurations analysed.
Hence, the feasibility of a Virtual Test Lab solution for the screening
of materials and configurations has been demonstrated. The presented
framework constitutes a promising computational tool for virtual
testing of unidirectional composite laminates under general loading
conditions. In this way, standard experimental tests can be reliably si-
mulated in a computational environment allowing for an effective re-
duction of time-consuming and costly physical test campaigns. This
Virtual Test Lab constitutes a powerful tool for structural design and
certification of composite structures in the aeronautical sector and
others alike.
Fig. 17. Experimental observations and simulations of UNT (a; b) and OHT (c) tests of clustered laminate − −[45/0/ 45/90/( 45 /45 ) ]s2 2 2 : (a) stress-strain curves measured in UNT tests; (b)
Experimental observations of UNT specimen before and after failure; (c) Correlation between simulated (left) and experimentally-obtained (right) failure mode.
155

Acknowledgements
The research leading to the developments described was funded
within the framework of the project VIRTEST (Multiscale Virtual
Testing of CFRP Samples), a collaboration between IMDEA Materials
Institute and GKN Aerospace: Fokker. C.S. Lopes acknowledges the
support of the Spanish Ministry of Economy and Competitiveness
through the Ramón y Cajal fellowship (grant RYC-2013-14271). The
authors are grateful to Héctor Navarro for his valuable contribution in
the development of the Graphical User Interface of the ABAQUS plug-
in.
Fig. 18. Experimental observations and simulations of UNC (a; b) and OHC (c; d; e) tests of clustered laminate − −[45/0/ 45/90/( 45 /45 ) ]s2 2 2 : (a) experimentally-observed UNC specimen
deformation state before and after collapse at −47.3 kN (photo: O. Falcó); (b) virtual prediction of UNC specimen failure mode; (c) experimental evolution of damage in a OHC specimen
up to failure (photo: O. Falcó); (d) simulated evolution of damage accumulation in a OHC specimen; (e) virtually-predicted ﬁnal collapse the same OHC specimen (rotated view with
respect to (d)) at −17.5 kN applied load (transverse damage identiﬁed in red and cracks simulated by eroded elements).
156

Appendix A. Appendix A: Hole cutting algorithm and vertex adjustment.
The hole cutting algorithm follows the general steps used in the Cartesian grid methods found in [76,77] and can be described through different
steps, as represented in Fig. 19.
The method consists in the creation of an irregular (cut-out) cartesian grid, or mesh, resulting from the intersection between an initial two-
dimensional regular grid and geometrical boundaries, e.g holes. The characteristics of the final mesh are to be: i) a grid of rectangles with parametric
dimensions in both longitudinal and transverse direction and degenerate elements around the edge, and ii) alignment with the orthotropic material
orientations. Firstly, the inner (inside the hole), outer and edge-intercepted cells from the initial mesh (Fig. 19(a)) are determined and the first ones
are eliminated (Fig. 19(b)). Then, the algorithm addresses the intercepted cells by determining the relative position of each one with respect to the
edge. For this operation, a function ‘point_in_Polygon(P C,i )’ is used by the algorithm to determine wether a point Pi lies inside a polygon C [78].
In the present case the polygon is defined by the hole-edge circle, whereas points Pi define each Celli. Sixteen positioning options are taken into
account, as shown in Fig. 19(e). All interception points between the edge and each individual cell (Celli) are then identified. By connecting these with
the Celli points outside the circle, a new list of polygons with three, four and five vertexes (Fig. 19(c)) is created. The points inside the circle are
removed.
At this point, a vertex adjustment is performed in order to avoid cells with five vertexes or that do not satisfy the critical element length
conditions (see Section 2.2.1). These particular cases are illustrated in Fig. 19(f). Poor-quality cells, e.g. P P P[ , , ]A B K and ′[ ]P P P P, , ,A B K K (cellk highlighted
in yellow), are eliminated and an adjustment of closer vertexes (e.g. PK) belonging to adjacent cells is performed by means of a radial translation of to
a new location at the hole boundary (e.g. PN). This last operation ensures the quality of the mesh, as shown in Fig. 19(d), avoiding cells with more
than four vertexes which would have to be split in two or more element.
This procedure is given in the form of pseudo-code in Table 4.
Fig. 19. Hole cutting method: (a) structured grid; (b) entity interceptions; (c) segment cutting; (d) vertex adjustment; (e) interception cases; and (f) vertex adjustment cases.
157
PN
PC PN PN'
P2 P3
PN
P3
P1
P2
Pc
Inner cells
Overlay grid / circle
D
Vertex adjustment
remainder
vertex
(a) (b) (c) (d)
Intercept Cutting
Outer cells Intercepted cells
Interception cases
Pk'
P2 P3
Cell i
Pk
PA PB
< lcrit*
R
P1
P2 P3
Pk
PA
Cell i
R
P1
Pk
P2 P3
Cell i
Pk
PA
PB
Cell k
< lcrit*
R
Cell k
(e)
(f)
Vertex adjustment
cases
y
x

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Table 4
Pseudo-code for the automatic hole cutting algorithm to create material-aligned meshes in open-hole coupons.
rectanglePositionInMesh(INPUT parameters: the_mesh, the_polygon = ‘CIRCLE’)
{
foreach rectangle in mesh {
if rectangleInPolygon (rectangle, polygon) == TRUE
Append() to list of classified rectangle as ‘INSIDE’.
—These will NO be displayed
// Extract segments si from rectangle and verify interception respect to polygon
if circleSegmentIntercept (s1 or s2 or s3 or s4, polygon) == TRUE {
Append() to list of classified rectangle as ‘INTERCEPT’.
—These will be displayed just the part outside the polygon.
Here, the rectangle portion inside the polygon have to be removed.
—All interception points are determined by:
(solve the system equation between construction lines/circle).
// Quality validation of the intercepted rectangles cellsint
vertexAdjustment (cellsint, critical_length) }
else
Append() to list of classified rectangle as ‘OUTSIDE’.
—These will be displayed completely }
return OUTPUT: list of classified and adjusted cells
}// End of algorithm
158

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