![Calculation of Force andCalculation of Force and
AccelerationAcceleration
[ ]fi
vvmKE 22
2
1
−=
U
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π
η
2
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maF =
0
0.5
1
1.5
2
2.5
3
0 1 2 3 4 5 6 7
EnergyReturn(ergs)EnergyReturn(ergs)
Time (ms)Time (ms)
Energy Return =Energy Return = ERER == CC11 xx FF22](https://image.slidesharecdn.com/phd-1226923424544043-9/85/PhD-Dissertation-Defense-8-320.jpg)
PhD Dissertation Defense
- 1. Modeling the PercussionModeling the Percussion Response of LaminatedResponse of Laminated Materials and Glass ColumnsMaterials and Glass Columns through the use ofthrough the use of Computational MethodsComputational Methods Ian NievesIan Nieves
- 2. ObjectivesObjectives • Damping and PercussionDamping and Percussion • PeriometerPeriometer • Modeling with Finite ElementModeling with Finite Element Analysis (FEA)Analysis (FEA) • Modeling Periometer TestingModeling Periometer Testing Laminated Materials - DampingLaminated Materials - Damping Glass Columns - DefectsGlass Columns - Defects
- 3. DampingDamping • Energy dissipation during mechanical actionEnergy dissipation during mechanical action • Intrinsic dampingIntrinsic damping: energy thermally: energy thermally dissipated through microstructural changesdissipated through microstructural changes • Damping a function of material structureDamping a function of material structure U D π η 2 = δη tan ' " == E E
- 4. Intrinsic Damping and TissueIntrinsic Damping and Tissue RegenerationRegeneration • Dominant paradigm of bone maintenance (Mechanostat) = skeletal remodeling and repair mediated by damping + dynamic stresses • Clinical studies implement damping in prosthetics integration2 22 James C. Earthman, Cherilyn Sheets, J. Paquete, et al, Tissue EngineeringJames C. Earthman, Cherilyn Sheets, J. Paquete, et al, Tissue Engineering in Dentistry,in Dentistry, Clin. Plastic Surg.Clin. Plastic Surg., Vol. 30, pp. 621 – 639, 2003, Vol. 30, pp. 621 – 639, 2003 22 James C. Earthman, Cherilyn Sheets, J. Paquete, et al, Tissue EngineeringJames C. Earthman, Cherilyn Sheets, J. Paquete, et al, Tissue Engineering in Dentistry,in Dentistry, Clin. Plastic Surg.Clin. Plastic Surg., Vol. 30, pp. 621 – 639, 2003, Vol. 30, pp. 621 – 639, 2003
- 5. PercussionPercussion • Generate mechanical pulses through impactGenerate mechanical pulses through impact • Pulse parameters (intensity, duration, etc.)Pulse parameters (intensity, duration, etc.) modified in situ through dampingmodified in situ through damping • Pulsate mechanics similar to biologicalPulsate mechanics similar to biological activities (Running, etc.)activities (Running, etc.) *Bakos et al., Acta Veterinaria Hungarica (2003).
- 6. PeriometerPeriometer Workstation withWorkstation with VirtualVirtual InstrumentationInstrumentation PercussionPercussion ProbeProbe ControlControl InstrumentInstrument ation andation and SensorsSensors
- 8. Calculation of Force andCalculation of Force and AccelerationAcceleration [ ]fi vvmKE 22 2 1 −= U CUER π η 2 2 −−= maF = 0 0.5 1 1.5 2 2.5 3 0 1 2 3 4 5 6 7 EnergyReturn(ergs)EnergyReturn(ergs) Time (ms)Time (ms) Energy Return =Energy Return = ERER == CC11 xx FF22
- 9. Periometer Wave DynamicsPeriometer Wave Dynamics
- 11. Modeling PercussionModeling Percussion • Validate percussion responseValidate percussion response • Elucidate mechanisms underlyingElucidate mechanisms underlying responseresponse • Predict facets of percussion profilePredict facets of percussion profile • Taylor and refine detection capabilitiesTaylor and refine detection capabilities • Facilitate construction of “PercussionFacilitate construction of “Percussion Spectrum”Spectrum”
- 12. Finite Element Analysis (FEA)Finite Element Analysis (FEA) Creates representations of geometryCreates representations of geometry Uses geometry as template for networkUses geometry as template for network (mesh) of discrete lattice points (nodes)(mesh) of discrete lattice points (nodes) Nodes are vertices for line, planar orNodes are vertices for line, planar or polyhedral elementspolyhedral elements Uses Shape Functions to solve to produceUses Shape Functions to solve to produce predictions of nodal (acceleration,predictions of nodal (acceleration, displacement) and elemental (stress) resultsdisplacement) and elemental (stress) results in response to inputs (initial and boundaryin response to inputs (initial and boundary conditions)conditions)
- 13. ElementsElements Idealized Hexagonal element used forIdealized Hexagonal element used for virgin testing materials and full-scalevirgin testing materials and full-scale Hexagonal elements in cylindricalHexagonal elements in cylindrical probe with nodes adjacent toprobe with nodes adjacent to accelerometeraccelerometer
- 14. Dytran vs.Dytran vs. MARCMARC • Dytran specialized forDytran specialized for ballistic modelingballistic modeling –– moremore detailed resultsdetailed results • Explicit solver –Explicit solver – ∆t∆tCritCrit automatically calculatedautomatically calculated • DYMAT 24 PiecewiseDYMAT 24 Piecewise Linear PlasticityLinear Plasticity (elastoplastic) material(elastoplastic) material modelmodel • Matrig rigid materialMatrig rigid material model – only requiresmodel – only requires mass inputmass input • MARC capable of ballisticMARC capable of ballistic modeling, specialized formodeling, specialized for elastomeric analysiselastomeric analysis • Implicit Solver -Implicit Solver - ∆t∆tCritCrit calculated throughcalculated through inspectioninspection • Elastic Material modelElastic Material model • Rayleigh damping modelRayleigh damping model – intrinsic damping input– intrinsic damping input DytranDytran MARCMARC
- 16. Rigid Probe and Glass Column Construction
- 17. MeshesMeshes
- 18. Boundary Conditions forBoundary Conditions for Laminated MaterialsLaminated Materials
- 19. Initial and Boundary ConditionsInitial and Boundary Conditions for Rigid Probe and Glass Columnsfor Rigid Probe and Glass Columns
- 20. Material ParametersMaterial Parameters Material Model Material E (KPa) ρ (kg/mm3 ) ν σys (KPa) Code DYMAT 24 Steel 1.93108 8.00x10-6 0.30 4.40x104 Dytran Al 6061 7.00x107 2.70x10-6 0.35 3.95x105 PTFE 5.00x105 2.10x10-6 0.40 9.00x104 Glass 7.03x107 2.47x10-6 0.22 6.90x104 PMMA 3.30x106 1.19x10-6 0.37 1.07x105 PLGA 3.50x106 1.19x10-6 0.40 4.4x104 Elastic Steel 1.93108 8.00x10-6 0.30 MARC Al 6061 7.00x107 2.70x10-6 0.35 PTFE 5.00x105 2.10x10-6 0.40 Glass 7.03x107 2.47x10-6 0.22 PMMA 3.30x106 1.19x10-6 0.37 PLGA 3.50x106 1.19x10-6 0.40
- 21. Intrinsic Damping in MARCIntrinsic Damping in MARC Material Al PTFE PMMA η 0.0003 0.1038 0.0400 • Rayleigh Damping Function: C = αM + (β+gt)K, MRayleigh Damping Function: C = αM + (β+gt)K, M = Mass Matrix, K = Stiffness Matrix, C = Damping= Mass Matrix, K = Stiffness Matrix, C = Damping MatrixMatrix • Damping is proportional to stiffness and massDamping is proportional to stiffness and mass • Stiffness Matrix Factor(Stiffness Matrix Factor(β) = 2(η)/π(lowest modalβ) = 2(η)/π(lowest modal frequency(Hz))frequency(Hz)) • η = Loss Coefficientη = Loss Coefficient • Modal frequency material specific, derivedModal frequency material specific, derived through MARC modal analysisthrough MARC modal analysis
- 23. 3.175 mm thick Al Monolith: Results3.175 mm thick Al Monolith: Results Stepped ProbeStepped Probe Stepped Probe: MARCStepped Probe: MARC Cylindrical Probe: DytranCylindrical Probe: Dytran Cylindrical Probe:Cylindrical Probe: DytranDytran Cylindrical Probe: MARCCylindrical Probe: MARC
- 24. Size Effects: 500 x 500 x 3.175 mm Al MonolithSize Effects: 500 x 500 x 3.175 mm Al Monolith and 27 gram Probeand 27 gram Probe k m T = 27 gram Probe27 gram Probe 500 mm x 500 mm x 3.175 mm Monolith500 mm x 500 mm x 3.175 mm Monolith
- 25. Al – PTFE Scaffolds withAl – PTFE Scaffolds with Rigid ProbeRigid Probe
- 26. Al – PTFE Scaffolds withAl – PTFE Scaffolds with Stepped Probe and IntrinsicStepped Probe and Intrinsic DampingDamping
- 27. 3.175 PTFE: 3.175 Al3.175 PTFE: 3.175 Al 1.58 PTFE: 3.175 Al1.58 PTFE: 3.175 Al
- 28. PMMA Scaffold with IntrinsicPMMA Scaffold with Intrinsic DampingDamping Scaffold and ProbeScaffold and Probe Layer with DefectLayer with Defect
- 29. PMMA Scaffold with IntrinsicPMMA Scaffold with Intrinsic Damping: Origin of ShoulderDamping: Origin of Shoulder Intrinsic DampingIntrinsic Damping No Intrinsic DampingNo Intrinsic Damping
- 30. PLGA Scaffold: Mesh re-Enforcement andPLGA Scaffold: Mesh re-Enforcement and Stress AttenuationStress Attenuation 1 J. Calvert, L. Weiss, New Frontiers in Bone Tissue Engineering, Clin. Plast. Surg., Vol. 30, pp. 641 – 648, 2003 • PLGA demonstrated toPLGA demonstrated to stimulate bonestimulate bone and vascular regenerationand vascular regeneration11 Re-enforcedRe-enforced VirginVirgin
- 31. Glass DefectGlass Defect 0.2 mm0.2 mm Glass used to model rigid biological materials:Glass used to model rigid biological materials: bone, enamel, etc.bone, enamel, etc.
- 32. Cylindrical Probe and Glass ControlCylindrical Probe and Glass Control MARCMARC DytranDytran
- 33. Stepped Probe and Glass Control:Stepped Probe and Glass Control: Acceleration ResultsAcceleration Results T ≈ 0.18 msecT ≈ 0.18 msec T ≈ 0.25 msecT ≈ 0.25 msec T ≈ 0.25 msecT ≈ 0.25 msec MARCMARC DytranDytran
- 34. Rigid Probe and Glass ControlRigid Probe and Glass Control
- 35. Stepped Probe and Trench DefectStepped Probe and Trench Defect “T” ≈0.58 msec “T” ≈0.58 msec
- 36. Trench Crack: Averaged ProbeTrench Crack: Averaged Probe Acceleration (Dytran)Acceleration (Dytran) Averaged Probe nodalAveraged Probe nodal accelerationsaccelerations for indicated planesfor indicated planes
- 37. Wedge Crack GeometryWedge Crack Geometry Shoulder Peak
- 38. Shoulder Peak Semi-Circular Aligned Crack:Semi-Circular Aligned Crack: AccelerationAcceleration 1 mmCross SectionCross Section PerpendicularPerpendicular to Impactto Impact PlanePlane
- 39. Crack Boundary EffectsCrack Boundary Effects
- 40. Rigid Probe with 1 mm transverse Crack
- 41. Glass Controls: FEA vs. Percussion Y–AxisAcceleration(mm/secY–AxisAcceleration(mm/sec22 ) Time (sec)Time (sec) Glass control acceleration accurately modeled with stepped probe
- 42. Cracked Glass : FEA vs. Percussion Y–AxisAcceleration(mm/secY–AxisAcceleration(mm/sec22 ) Y–AxisAcceleration(mm/secY–AxisAcceleration(mm/sec22 ) Y–AxisAcceleration(mm/secY–AxisAcceleration(mm/sec22 ) Time (sec)Time (sec) Time (sec)Time (sec) Time (sec)Time (sec)
- 43. Crack Stresses (KPa) Semi-circular crack withSemi-circular crack with square edgesquare edge Semi- circular crack with round edge Wedge-formWedge-form crackcrack with roundwith round edgeedge
- 45. Summary • FEA can elucidate mechanical origin of probeFEA can elucidate mechanical origin of probe signalssignals • FEA – based modeling can accurately modelFEA – based modeling can accurately model defect detection in rigid materialsdefect detection in rigid materials • FEA can qualitatively evaluate energyFEA can qualitatively evaluate energy dissipation in biomedical scaffoldsdissipation in biomedical scaffolds • Modeling indicates dependence ofModeling indicates dependence of Periometer function on interference effectsPeriometer function on interference effects • Further modeling – experimental is requiredFurther modeling – experimental is required to refine intrinsic damping modelingto refine intrinsic damping modeling
- 46. AcknowledgementsAcknowledgements • Dr. James Earthman • MSC Software Corporation, Santa Ana, CA