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- 5. Nonlinear Elasticity Theory and Applications 1st Edition Y. B. Fu Digital Instant Download Author(s): Y. B. Fu, R. W. Ogden ISBN(s): 9780521796958, 0521796954 Edition: 1 File Details: PDF, 11.49 MB Year: 2009 Language: english
- 6. LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES Managing Editor: Professor N.J. Hitchin, Mathematical Institute, University of Oxford, 24-29 St Giles, Oxford 0X1 3LB, United Kingdom The titles below are available from booksellers, or, in case of difficulty, from Cambridge University Press. 46 /?-adic Analysis: a short course on recent work, N. KOBLITZ 59 Applicable differential geometry, M. CRAMPIN & F.A.E. PIRANI 66 Several complex variables and complex manifolds II, MJ. FIELD 86 Topological topics, I.M. JAMES (ed) 88 FPF ring theory, C. FAITH & S. PAGE 90 Polytopes and symmetry, S.A. ROBERTSON 96 Diophantine equations over function fields, R.C. MASON 97 Varieties of constructive mathematics, D.S. BRIDGES & F. RICHMAN 99 Methods of differential geometry in algebraic topology, M. KAROUBI & C. LERUSTE 100 Stopping time techniques for analysts and probabilists, L. EGGHE 104 Elliptic structures on 3-manifolds, C.B. THOMAS 105 A local spectral theory for closed operators, I. ERDELYI & WANG SHENGWANG 107 Compactification of Siegel moduli schemes, C.-L. CHAI 109 Diophantine analysis, J. LOXTON & A. VAN DER POORTEN (eds) 113 Lectures on the asymptotic theory of ideals, D. REES 116 Representations of algebras, P.J. WEBB (ed) 119 Triangulated categories in the representation theory of finite-dimensional algebras, D. HAPPEL 121 Proceedings of Groups - St Andrews 1985, E. ROBERTSON & C. CAMPBELL (eds) 128 Descriptive set theory and the structure of sets of uniqueness, A.S. KECHRIS & A. LOUVEAU 130 Model theory and modules, M. PREST 131 Algebraic, extremal & metric combinatorics, M.-M. DEZA, P. FRANKL & I.G. ROSENBERG (eds) 138 Analysis at Urbana, II, E. BERKSON, T. PECK, & J. UHL (eds) 139 Advances in homotopy theory, S. SALAMON, B. STEER & W. SUTHERLAND (eds) 140 Geometric aspects of Banach spaces, E.M. PEINADOR & A. RODES (eds) 141 Surveys in combinatorics 1989, J. SIEMONS (ed) 144 Introduction to uniform spaces, I.M. JAMES 146 Cohen-Macaulay modules over Cohen-Macaulay rings, Y. YOSHINO 148 Helices and vector bundles, A.N. RUDAKOV et al 149 Solitons, nonlinear evolution equations and inverse scattering, M. ABLOWITZ & P. CLARKSON 150 Geometry of low-dimensional manifolds 1, S. DONALDSON & C.B. THOMAS (eds) 151 Geometry of low-dimensional manifolds 2, S. DONALDSON & C.B. THOMAS (eds) 152 Oligomorphic permutation groups, P. CAMERON 153 L-functions and arithmetic, J. COATES & M.J. TAYLOR (eds) 155 Classification theories of polarized varieties, TAKAO FUJITA 158 Geometry of Banach spaces, P.F.X. MULLER & W. SCHACHERMAYER (eds) 159 Groups St Andrews 1989 volume 1, CM. CAMPBELL & E.F. ROBERTSON (eds) 160 Groups St Andrews 1989 volume 2, CM. CAMPBELL & E.F. ROBERTSON (eds) 161 Lectures on block theory, BURKHARD KULSHAMMER 163 Topics in varieties of group representations, S.M. VOVSI 164 Quasi-symmetric designs, M.S. SHRIKANDE & S.S. SANE 166 Surveys in combinatorics, 1991, A.D. KEEDWELL (ed) 168 Representations of algebras, H. TACHIKAWA & S. BRENNER (eds) 169 Boolean function complexity, M.S. PATERSON (ed) 170 Manifolds with singularities and the Adams-Novikov spectral sequence, B. BOTVINNIK 171 Squares, A.R. RAJWADE 172 Algebraic varieties, GEORGE R. KEMPF 173 Discrete groups and geometry, W.J. HARVEY & C. MACLACHLAN (eds) 174 Lectures on mechanics, J.E. MARSDEN 175 Adams memorial symposium on algebraic topology 1, N. RAY & G. WALKER (eds) 176 Adams memorial symposium on algebraic topology 2, N. RAY & G. WALKER (eds) 177 Applications of categories in computer science, M. FOURMAN, P. JOHNSTONE & A. PITTS (eds) 178 Lower K-and L-theory, A.RAN1CKI 179 Complex projective geometry, G. ELLINGSRUD et al 180 Lectures on ergodic theory and Pesin theory on compact manifolds, M. POLLICOTT 181 Geometric group theory I, G.A. NIBLO & M.A. ROLLER (eds) 182 Geometric group theory II, G.A. NIBLO & M.A. ROLLER (eds) 183 Shintani zeta functions, A. YUKIE 184 Arithmetical functions, W. SCHWARZ & J. SPILKER 185 Representations of solvable groups, O. MANZ & T.R. WOLF 186 Complexity: knots, colourings and counting, D.J.A. WELSH 187 Surveys in combinatorics, 1993, K. WALKER (ed) 188 Local analysis for the odd order theorem, H. BENDER & G. GLAUBERMAN 189 Locally presentable and accessible categories, J. ADAMEK & J. ROSICKY 190 Polynomial invariants of finite groups, D.J. BENSON 191 Finite geometry and combinatorics, F. DE CLERCK et al 192 Symplectic geometry, D. SALAMON (ed) 194 Independent random variables and rearrangement invariant spaces, M. BRAVERMAN 195 Arithmetic of blowup algebras, WOLMER VASCONCELOS 196 Microlocal analysis for differential operators, A. GRIGIS & J. SJOSTRAND 197 Two-dimensional homotopy and combinatorial group theory, C. HOG-ANGELONI et al 198 The algebraic characterization of geometric 4-manifolds, J.A. HILLMAN
- 7. 199 Invariant potential theory in the unit ball of C1 , MANFRED STOLL 200 The Grothendieck theory of dessins d'enfant, L. SCHNEPS (ed) 201 Singularities, JEAN-PAUL BRASSELET (ed) 202 The technique of pseudodifferential operators, H.O. CORDES 203 Hochschild cohomology of von Neumann algebras, A. SINCLAIR & R. SMITH 204 Combinatorial and geometric group theory, AJ. DUNCAN, N.D. GILBERT & J. HOWIE (eds) 205 Ergodic theory and its connections with harmonic analysis, K. PETERSEN & I. SALAMA (eds) 207 Groups of Lie type and their geometries, W.M. KANTOR & L. DIMARTINO (eds) 208 Vector bundles in algebraic geometry, N.J. HITCHIN, P. NEWSTEAD & W.M. OXBURY (eds) 209 Arithmetic of diagonal hypersurfaces over finite fields, F.Q. GOUVEA & N. YUI 210 HilbertC*-modules, EC.LANCE 211 Groups 93 Galway / St Andrews I, CM. CAMPBELL et al (eds) 212 Groups 93 Galway/St Andrews II, CM. CAMPBELL et al (eds) 214 Generalised Eulcr-Jacobi inversion formula and asymptotics beyond all orders, V. KOWALENKO et al 215 Number theory 1992-93, S. DAVID (ed) 216 Stochastic partial differential equations, A. ETHERIDGE (ed) 217 Quadratic forms with applications to algebraic geometry and topology, A. PFISTER 218 Surveys in combinatorics, 1995, PETER ROWLINSON (ed) 220 Algebraic set theory, A. JOYAL & I. MOERDIJK 221 Harmonic approximation, S.J.GARDINER 222 Advances in linear logic, J.-Y. GIRARD, Y. LAFONT & L. REGNIER (eds) 223 Analytic semigroups and semilinear initial boundary value problems, KAZUAK1TAIRA 224 Computability, enumerability, unsolvability, S.B. COOPER, T.A. SLAMAN & S.S. WAINER (eds) 225 A mathematical introduction to string theory, S. ALBEVERIO, J. JOST, S. PAYCHA, S. SCARLATTI 226 Novikov conjectures, index theorems and rigidity I, S. FERRY, A. RANICKI & J. ROSENBERG (eds) 227 Novikov conjectures, index theorems and rigidity II, S. FERRY, A. RANICKI & J. ROSENBERG (eds) 228 Ergodic theory of Zd actions, M. POLLICOTT & K. SCHMIDT (eds) 229 Ergodicity for infinite dimensional systems, G. DA PRATO & J. ZABCZYK 230 Prolegomena to a middlebrow arithmetic of curves of genus 2, J.W.S. CASSELS & E.V. FLYNN 231 Semigroup theory and its applications, K.H. HOFMANN & M.W. MISLOVE (eds) 232 The descriptive set theory of Polish group actions, H. BECKER & A.S. KECHRIS 233 Finite fields and applications, S. COHEN & H. NIEDERREITER (eds) 234 Introduction to subfactors, V. JONES & V.S. SUNDER 235 Number theory 1993-94, S. DAVID (ed) 236 The James forest, H. FETTER & B. GAMBOA DE BUEN 237 Sieve methods, exponential sums, and their applications in number theory, G.R.H. GREAVES et al 238 Representation theory and algebraic geometry, A. MARTSINKOVSKY & G. TODOROV (eds) 239 Clifford algebras and spinors, P. LOUNESTO 240 Stable groups, FRANK O. WAGNER 241 Surveys in combinatorics, 1997, R.A. BAILEY (ed) 242 Geometric Galois actions I, L. SCHNEPS & P. LOCHAK (eds) 243 Geometric Galois actions II, L. SCHNEPS & P. LOCHAK (eds) 244 Model theory of groups and automorphism groups, D. EVANS (ed) 245 Geometry, combinatorial designs and related structures, J.W.P. HIRSCHFELD et al 246 p- Automorphisms of finite /^-groups, E.I. KHUKHRO 247 Analytic number theory, Y. MOTOHASHI (ed) 248 Tame topology and o-minimal structures, LOU VAN DEN DRIES 249 The atlas of finite groups: ten years on, ROBERT CURTIS & ROBERT WILSON (eds) 250 Characters and blocks of finite groups, G. NAVARRO 251 Grobner bases and applications, B. BUCHBERGER & F. WINKLER (eds) 252 Geometry and cohomology in group theory, P. KROPHOLLER, G. NIBLO, R. STOHR (eds) 253 The ^-Schur algebra, S.DONKIN 254 Galois representations in arithmetic algebraic geometry, A.J. SCHOLL & R.L. TAYLOR (eds) 255 Symmetries and integrability of difference equations, P.A. CLARKSON & F.W. NIJHOFF (eds) 256 Aspects of Galois theory, HELMUT VOLKLEIN et al 257 An introduction to noncommutative differential geometry and its physical applications 2ed, J. MADORE 258 Sets and proofs, S.B. COOPER & J. TRUSS (eds) 259 Models and computability, S.B. COOPER & J. TRUSS (eds) 260 Groups St Andrews 1997 in Bath, I, CM. CAMPBELL et al 261 Groups St Andrews 1997 in Bath, II, CM. CAMPBELL et al 263 Singularity theory, BILL BRUCE & DAVID MOND (eds) 264 New trends in algebraic geometry, K. HULEK, F. CATANESE, C PETERS & M. REID (eds) 265 Elliptic curves in cryptography, I. BLAKE, G. SEROUSSI & N. SMART 267 Surveys in combinatorics, 1999, J.D. LAMB & D.A. PREECE (eds) 268 Spectral asymptotics in the semi-classical limit, M. DIMASSI & J. SJOSTRAND 269 Ergodic theory and topological dynamics, M.B. BEKKA & M. MAYER 270 Analysis on Lie Groups, N.T. VAROPOULOS & S. MUSTAPHA 271 Singular perturbations of differential operators, S. ALBEVERIO & P. KURASOV 272 Character theory for the odd order function, T. PETERFALVI 273 Spectral theory and geometry, E.B. DAVIES & Y. SAFAROV (eds) 274 The Mandelbrot set, theme and variations, TAN LEI (ed) 275 Computatoinal and geometric aspects of modern algebra, M. D. ATKINSON et al (eds) 276 Singularities of plane curves, E. CASAS-ALVERO 277 Descriptive set theory and dynamical systems, M. FOREMAN et al (eds) 278 Global attractors in abstract parabolic problems, J.W. CHOLEWA & T. DLOTKO 279 Topics in symbolic dynamics and applications, F. BLANCHARD, A. MAASS & A. NOGUEIRA (eds) 280 Characters and Automorphism Groups of Compact Riemann Surfaces, T. BREUER 281 Explicit birational geometry of 3-folds, ALESSIO CORTI & MILES REID (eds) 282 Auslander-Buchweitz approximations of equivariant modules, M.HASHIMOTO 283 Nonlinear elasticity, R. OGDEN & Y. FU (eds)
- 8. London Mathematical Society Lecture Note Series. 283 Nonlinear Elasticity: Theory and Applications Edited by Y. B. Fu University ofKeele R. W. Ogden University ofGlasgow | CAMBRIDGE UNIVERSITY PRESS
- 9. PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE The Pitt Building, Trumpington Street, Cambridge, United Kingdom CAMBRIDGE UNIVERSITY PRESS The Edinburgh Building, Cambridge, CB2 2RU, UK 40 West 20th Street, New York, NY 10011-4211, USA 10 Stamford Road, Oakleigh, VIC 3166, Australia Ruiz de Alarcon 13,28014 Madrid, Spain Dock House, The Waterfront, Cape Town 8001, South Africa http://www.cambridge.org © Cambridge University Press 2001 This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2001 A catalogue recordfor this book is available from the British Library ISBN 0 521 79695 4 paperback Transferred to digital printing 2002
- 10. Contents 1 Elements of the Theory of Finite Elasticity R. W. Ogden 1 1.1 Introduction 1 1.2 Elastostatics 3 1.3 Examples of boundary-value problems 27 1.4 Incremental equations 34 1.5 Incremental boundary-value problems 42 1.6 Elastodynamics 47 2 Hyperelastic Bell Materials: Retrospection, Experiment, Theory Af. F. Beatty 58 2.1 Introduction 58 2.2 Retrospection 59 2.3 Experiment 64 2.4 Theory 70 2.5 Isotropic, hyperelastic Bell materials 84 2.6 Concluding remarks: Bell's incremental theory 90 3 Universal Results in Finite Elasticity G. Saccomandi 97 3.1 Introduction 97 3.2 Isotropic unconstrained elasticity 100 3.3 Universal solutions for isotropic constrained elasticity 106 3.4 Details for essentially plane deformations 114 3.5 Incompressible materials 119 3.6 The universal manifold 123 3.7 Relative universal deformations 126 3.8 Concluding remarks 130 4 Equilibrium Solutions for Compressible Nonlinearly Elastic Materials C. 0. Horgan 135 4.1 Introduction 135 4.2 Axisymmetric deformations of homogeneous isotropic compressible elastic solids 136 4.3 Transformation to a pair of first-order differential equations ... 138 4.4 An alternative transformation 139 4.5 Spherically and cylindrically symmetric deformations for
- 11. vi Contents special classes of compressible materials 140 4.6 The Blatz-Ko material 145 4.7 Other equilibrium solutions 147 4.8 The generalized Blatz-Ko material and its various specializations 147 4.9 Ellipticity of the governing equilibrium equations 150 4.10 Isochoric deformations 153 5 Exact Integrals and Solutions for Finite Deformations of the Incompressible Varga Elastic Materials J.M. Hill 160 5.1 Introduction 160 5.2 General equations for plane strain and axiaJly symmetric deformations 166 5.3 Exact integrals and solutions for plane strain deformations 170 5.4 Exact integrals and solutions for axially symmetric deformations 175 5.5 A further plane strain deformation 180 5.6 A further axially symmetric deformation 184 5.7 Small superimposed deformations 188 5.8 Further general integrals 194 6 Shear Ph. Boulanger and M. Hayes 201 6.1 Introduction 201 6.2 Basic equations 205 6.3 Properties of the planes of central circular section of the C-ellipsoid 208 6.4 Unsheared pairs in a given plane 211 6.5 Maximum shear in a given plane for given 0 218 6.6 Global extremal shear for given 0 219 6.7 Maximum shear in a given plane. Global maximum 220 6.8 Pairs of unsheared material elements 224 6.9 Unsheared triads 226 6.10 Shear of planar elements 229 7 Elastic Membranes D.M. Haughton 233 7.1 Introduction 233 7.2 The general theory 234 7.3 Incremental equations 248 7.4 Wrinkling theory 257
- 12. Contents vii 7.5 Exact solutions 262 8 Elements of the Theory of Elastic Surfaces D. J. Steigmann ... 268 8.1 Introduction 268 8.2 The relationship between the Cosserat and Kirchhoff-Love theories of elastic shells .. 271 8.3 Cosserat theory 272 8.4 Constraints 275 8.5 Invariance and the reduced constitutive equations 278 8.6 Equations of motion and the Kirchhoff edge conditions 279 8.7 Moment of momentum 282 8.8 Summary of the Kirchhoff-Love theory 283 8.9 Material symmetry 286 8.10 Energy minimizers 297 9 Singularity Theory and Nonlinear Bifurcation Analysis Y.-C. Chen 305 9.1 Introduction 305 9.2 Bifurcation equation and Liapunov-Schmidt reduction 309 9.3 The recognition problem 316 9.4 Bifurcation of pure homogeneous deformations with Z<i symmetry 325 9.5 Bifurcation of pure homogeneous deformations with D$ symmetry 330 9.6 Bifurcation of inflation of spherical membranes 336 10 Perturbation Methods and Nonlinear Stability Analysis Y.B. Fu 345 10.1 Introduction 345 10.2 Bifurcation at a non-zero mode number 349 10.3 Bifurcation at a zero mode number 360 10.4 Necking of an elastic plate under stretching 367 10.5 Conclusion 378 Appendix A: Incremental equations in cylindrical and spherical polar coordinates 382 Appendix B: Contributions to linear stability analysis in Finite Elasticity 387 11 Nonlinear Dispersive Waves in a Circular Rod Composed of a Mooney-Rivlin Material H.-H. Dai 392 11.1 Introduction 392
- 13. viii Contents 11.2 Basic equations 394 11.3 Traveling waves 398 11.4 Phase plane analysis 399 11.5 Physically acceptable solutions 404 11.6 Linearization 408 11.7 Solitary waves of plane expansion 410 11.8 Solitary cusp waves of radial expansion 415 11.9 Periodic cusp waves of radial expansion 417 11.10 Periodic waves of type I 422 11.11 Solitary waves of radial contraction 423 11.12 Solitary cusp waves of radial contraction 426 11.13 Periodic cusp waves of radial contraction 427 11.14 Periodic waves of type II 429 11.15 Summary 430 12 Strain-energy Functions with Multiple Local Minima: Modeling Phase Transformations Using Finite Thermo-elasticity R. Abeyaratne, K. Bhattacharya and J. K. Knowles 433 12.1 Introduction 433 12.2 Strain-energy functions with multiple local minima: motivation from the lattice theory of martensitic transformations 435 12.3 A strain-energy function with multiple local minima: a material with cubic and tetragonal phases 444 12.4 Uniaxial motion of a slab. Formulation 449 12.5 A static problem and the role of energy minimization 454 12.6 A dynamic problem and the role of kinetics and nucleation .. 464 12.7 Nonequilibrium thermodynamic processes. Kinetics 476 12.8 Higher dimensional static problems. The issue of geometric compatibility 480 13 Pseudo-elasticity and Stress Softening R. W. Ogden 491 13.1 Introduction 491 13.2 Pseudo-elasticity 494 13.3 A model for stress softening 503 13.4 Azimuthal shear 509 13.5 Inflation and deflation of a spherical shell 516 13.6 Discontinuous changes in material properties 520 Subject Index 523
- 14. Preface The subject of Finite Elasticity (or Nonlinear Elasticity), although many of its ingredients were available much earlier, really came into its own as a discipline distinct from the classical theory of linear elasticity as a result of the impor- tant developments in the theory from the late 1940s associated with Rivlin and the collateral developments in general Continuum Mechanics associated with the Truesdell school during the 1950s and 1960s. Much of the impetus for the theoretical developments in Finite Elasticity came from the rubber industry be- cause of the importance of (natural) rubber in many engineering components, not least car tyres and bridge and engine mountings. This impetus is main- tained today with an ever increasing use of rubber (natural and synthetic) and other polymeric materials in a broader and broader range of engineering prod- ucts. The importance of gaining a sound theoretically-based understanding of the thermomechanical behaviour of rubber was only too graphically illustrated by the role of the rubber O-ring seals in the Challenger shuttle disaster. This extreme example serves to underline the need for detailed characterization of the mechanical properties of different rubberlike materials, and this requires not just appropriate experimental data but also the rigorous theoretical frame- work for analyzing those data. This involves both elasticity theory per se and extensions of the theory to account for inelastic effects. Over the last few years the applications of the theory have extended beyond the traditional regime of rubber mechanics and they now embrace other ma- terials capable of large elastic strains. These include, in particular, biological tissue such as skin, arterial walls and the heart. This is an important new development and it is increasingly recognized by medical researchers and clin- icians that understanding of the mechanics of such tissue is of fundamental importance in developing improved intervention treatments (such as balloon angioplasty) and artificial replacement parts. While understanding of Finite Elasticity is in itself important the theory also provides a gateway towards the understanding of more complex (non-elastic) material behaviour in the large deformation regime, such as finite deformation plasticity and nonlinear viscoelasticity, and it has an underpinning role in such theories. Additionally, because of its intrinsic nonlinearity, the equations of Finite Elasticity provide a rich basis for purely mathematical studies in, for example, IX
- 15. x Preface nonlinear analysis. Indeed, developments, in particular in the theory of partial differential equations, have been stimulated by work in Finite Elasticity, and these mathematical developments in turn have had an influence on research in the mechanical aspects of Finite Elasticity. Thus, the subject is wide ranging in both its theoretical and application perspectives. The turn of the century is an appropriate time to assess the state of develop- ment of the subject of Finite Elasticity and its potential for further applications and further theoretical development. With this in mind this volume aims to provide an overview of the theory from the perspectives of twelve researchers who have contributed to the subject over the last few years. It is hoped that it will provide a foundation and springboard for possible future developments. The material covered in this volume is necessarily selective and not by any means exhaustive. Thus, some important topics (such as fracture mechanics and the mechanics of composite materials) are not addressed. Nevertheless, there is nothing presently available in the literature that covers such a broad range of topics within the general framework of Finite/Nonlinear Elasticity as that presented here. The various chapters combine concise theory with a number of important applications, and the emphasis is directed more towards understanding of mechanical phenomena and problem solving rather than de- velopment of the theory for its own sake. Different chapters deal with, on the one hand, a number of classical research directions concerned with, for example, exact solutions, universal relations and the effect of internal constraints, and, on the other hand, with recent devel- opments associated with phase transitions and pseudo-elasticity. New ideas from nonlinear analysis, such as nonlinear bifurcation analysis and dynamical systems theory are also featured. Chapter 1 provides the basic theory required for use in the other chapters. Chapters 2-6 deal with different aspects of the solution of boundary-value prob- lems for unconstrained and internally constrained materials, while Chapters 7 and 8 are concerned with the related topics of membrane theory and the theory of elastic surfaces. Chapter 9 deals with the important topic of non-uniqueness of solution using the tools of singularity theory and bifurcation theory and Chapter 10 examines some related aspects concerned with nonlinear stabil- ity analysis based on methods of perturbation theory. Nonlinear dynamics is discussed in Chapter 11, which is concerned with nonlinear wave propaga- tion in an elastic rod. Chapters 12 and 13 are based on different notions of pseudo-elasticity theory: Chapter 12 develops a theory of phase transitions us- ing non-convex strain-energy functions, while Chapter 13 is concerned with the effect of changing the (elastic) constitutive law during the deformation process. Most of the contributors to this volume participated in an International
- 16. Preface xi Workshop on Nonlinear Elasticity held at City University, Hong Kong, in April 2000. Whilst the chapters in this volume do not form the proceedings of that Workshop it is important to emphasize that this volume and the Workshop were planned in parallel and that the Workshop served to focus ideas for the volume. We are pleased to acknowledge the generous support for the Workshop from the Liu Bie Ju Centre for Mathematical Sciences, City University of Hong Kong, and the personal support and encouragement of Professor Roderick S. C. Wong, Director of the Centre. We are very grateful to all the contributors for their enthusiastic response to this project and for the timely production of their chapters. Y.B. Fu R.W. Ogden December 2000
- 18. Elements of the theory of finite elasticity R.W. Ogden Department of Mathematics University of Glasgow, Glasgow G12 8QW, U.K. Email: rwo@maths.gla.ac.uk In this chapter we provide a brief overview of the main ingredients of the nonlinear theory of elasticity in order to establish the basic background material as a reference source for the other, more specialized, chapters in this volume. 1.1 Introduction In this introductory chapter we summarize the basic equations of nonlinear elasticity theory as a point of departure and as a reference source for the other articles in this volume which are concerned with more specific topics. There are several texts and monographs which deal with the subject of non- linear elasticity in some detail and from different standpoints. The most impor- tant of these are, in chronological order of the publication of the first edition, Green and Zerna (1954, 1968, 1992), Green and Adkins (1960, 1970), Truesdell and Noll (1965), Wang and Truesdell (1973), Chadwick (1976, 1999), Marsden and Hughes (1983, 1994), Ogden (1984a, 1997), Ciarlet (1988) and Antman (1995). See also the textbook by Holzapfel (2000), which deals with viscoelas- ticity and other aspects of nonlinear solid mechanics as well as containing an extensive treatment of nonlinear elasticity. These books may be referred to for more detailed study. Subsequently in this chapter we shall refer to the most re- cent editions of these works. The review articles by Spencer (1970) and Beatty (1987) are also valuable sources of reference. Section 1.2 of this chapter is concerned with laying down the basic equa- tions of elastostatics and it includes a summary of the relevant geometry of deformation and strain, an account of stress and stress tensors, the equilibrium equations and boundary conditions and an introduction to the formulation of constitutive laws for elastic materials, with discussion of the important notions of objectivity and material symmetry. Some emphasis is placed on the spe- cial case of isotropic elastic materials, and the constitutive laws for anisotropic
- 19. 2 R.W. Ogden material consisting of one or two families of fibres are also discussed. The mod- ifications to the constitutive laws when internal constraints such as incompress- ibility and inextensibility are present are provided. The general boundary-value problem of nonlinear elasticity is then formulated and the circumstances when this can be cast in a variational structure are discussed briefly. In Section 1.3 some basic examples of boundary-value problems are given. Specifically, the equations governing some homogeneous deformations are high- lighted, with the emphasis on incompressible materials. Other chapters in this volume will discuss a range of different boundary-value problems involving non- homogeneous deformations so here we focus attention on just one problem as an exemplar. This is the problem of extension and inflation of a thick-walled circular cylindrical tube. The analysis is given for an incompressible isotropic elastic solid and also for a material with two mechanically equivalent symmet- rically disposed families of fibres in order to illustrate some differences between isotropic and anisotropic response. The (linearized) equations of incremental elasticity associated with small de- formations superimposed on a finite deformation are summarized in Section 1.4. The incremental constitutive law for an elastic material is used to iden- tify the (fourth-order) tensor of elastic moduli associated with the stress and deformation variables used in the formulation of the governing equations, and explicit expressions for the components of this tensor are given in the case of an isotropic material. For the two-dimensional specialization, necessary and sufficient conditions on these components for the strong ellipticity inequalities to hold are given for both unconstrained and incompressible materials. A brief discussion of incremental uniqueness and stability is then given in the context of the dead-load boundary-value problem and the associated local inequalities are given explicit form for an isotropic material, again for both unconstrained and incompressible materials. A short discussion of global aspects of non- uniqueness for an isotropic material sets the incremental results in a broader context. In Section 1.5 the equations of incremental deformations and equilibrium given in Section 1.4 are specialized to the plane strain context in order to provide a formulation for the analysis of incremental plane strain boundary- value problems. Specifically, we provide an example of a typical incremental boundary-value problem by considering bifurcation of a uniformly deformed half-space from a homogeneously deformed configuration into a non-homogene- ous local mode of deformation. An explicit bifurcation condition is given for this problem and the results are illustrated for two forms of strain-energy function. Finally, in Section 1.6 we summarize the equations associated with the (non- linear) dynamics of an elastic body at finite strain. The (linearized) equations
- 20. Elements of the theory of finite elasticity 3 for small motions superimposed on a static finite deformation are then given and these are applied to the analysis of plane waves propagating in a homoge- neously deformed material. References are given throughout the text but these are not intended to pro- vide an exhaustive list of original sources. Where appropriate we mention papers and books where more detailed citations can be found. Also, where a topic is to be dealt with in detail in one of the other chapters of this volume the appropriate citations are included there. 1.2 Elastostatics In this section we summarize the basic equations of the static theory of non- linear elasticity, including the kinematics of deformation, the analysis of stress and the governing equations of equilibrium, and we introduce the various forms of constitutive law for an elastic material, including a discussion of isotropy and anisotropy. We then formulate the basic boundary-value problem of nonlinear elasticity. The development here is a synthesis of the essential material taken from the book by Ogden (1997) with some minor differences and additions. 1.2.1 Deformation and strain We consider a continuous body which occupies a connected open subset of a three-dimensional Euclidean point space, and we refer to such a subset as a configuration of the body. We identify an arbitrary configuration as a reference configuration and denote this by Br. Let points in Br be labelled by their position vectors X relative to an arbitrarily chosen origin and let dBr denote the boundary of Br. Now suppose that the body is deformed quasi-statically from Br so that it occupies a new configuration, B say, with boundary dB. We refer to B as the current or deformed configuration of the body. The deformation is represented by the mapping x '• Br -* B which takes points X in Br to points x in B. Thus, x = x(X), X E # r , (2.1) where x is the position vector of the point X in B. The mapping x *s called the deformation from Br to B. We require x t o be one-to-one and we write its inverse as x ~ s ° that X = x"1 (x), xGB. (2.2)
- 21. Random documents with unrelated content Scribd suggests to you:
- 25. The Project Gutenberg eBook of History of the Scottish Regiments in the British Army
- 26. This ebook is for the use of anyone anywhere in the United States and most other parts of the world at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this ebook or online at www.gutenberg.org. If you are not located in the United States, you will have to check the laws of the country where you are located before using this eBook. Title: History of the Scottish Regiments in the British Army Author: Archibald K. Murray Release date: January 30, 2016 [eBook #51087] Most recently updated: October 22, 2024 Language: English Credits: Produced by KD Weeks, Brian Coe and the Online Distributed Proofreading Team at http://www.pgdp.net (This file was produced from images generously made available by The Internet Archive/American Libraries.) *** START OF THE PROJECT GUTENBERG EBOOK HISTORY OF THE SCOTTISH REGIMENTS IN THE BRITISH ARMY ***
- 27. Transcriber’s Note The positions of the illustrative plates have been adjusted slightly to fall on paragraph breaks. The very occasional footnotes have been also moved to fall after the paragraphs in which they are referenced. Please see the transcriber’s note at the end of this text for details regarding the handling of any textual issues encountered during its preparation.
- 29. HISTORY OF THE SCOTTISH REGIMENTS IN THE BRITISH ARMY. BY ARCH. K. MURRAY, ESQ., MAJOR OF THE NINETY-SEVENTH LANARKSHIRE VOLUNTEER GUARDS. Published by Request of his Brother Officers. GLASGOW: THOMAS MURRAY AND SON. 1862.
- 30. CONTENTS. PAGE Preface, 3 Introduction, 5 Second Royal North British Dragoons, or “Scots Greys,” 13 “The Guards.” Grenadiers—Coldstreams—Scots Fusiliers, 41 The First “Royal Scots,” 78 The Twenty-First Foot, or “Royal North British Fusiliers,” 121 The Twenty-Fifth Foot. “King’s Own Borderers,” or Edinburgh Regiment, 145 The Twenty-Sixth Foot, or “Cameronians,” 169 Life Guards. Seventh Hussars—Seventeenth Light Dragoons —Seventieth Foot, 187 The Seventy-Third Foot—“Perthshire,” 191
- 31. The Seventy-Fifth Foot—“Stirlingshire,” 199 The Ninetieth Foot, or “Perthshire Volunteers,” 205 The Ninety-First Foot—“Argyleshire,” 212 The Scots Brigade, or the Old Ninety-Fourth Foot, 224 The Ninety-Ninth Foot, or “Lanarkshire,” 236 The Old Highland Brigade, 241 The Forty-Second, or “Royal Highlanders”—“Black Watch,” 250 The Seventy-First, or “Glasgow Highland Light Infantry,” 288 The Seventy-Second, or “Duke of Albany’s Highlanders,” 313 The Seventy-Fourth Highlanders, 330 The Seventy-Eighth Highlanders, or “Ross-shire Buffs,” 352 The Seventy-Ninth, or “Cameron Highlanders,” 380 The Ninety-Second, or “Gordon Highlanders,” 394 The Ninety-Third, or “Sutherland Highlanders,” 409
- 32. INDEX TO PLATES. Royal Arms, Frontispiece Scots Dragoon, Fronting page 13 Colours of the “Scots Greys,” 33 Balaklava, 39 “Scots Greys,” 1862, 40 Prince Albert, 41 Lord Clyde, 45 Napoleon, 66 Duke of Cambridge, 74 The “Guards’” Monument, 77 Gustavus Adolphus, 82 Prince de Conde, 88
- 33. Marshal Turrenne, 90 Duke de Schomberg, 95 St Sebastian, 113 The Twenty-first Royal North-British Fusiliers, 121 Blenheim, 127 Killiecrankie, 147 Ancient Badge of the Twenty-fifth, 156 Colours of the Twenty-fifth, 2 plates, 168 Marquis of Dalhousie, 184 Seringapatam, 197 Delhi, 203 Lord Lynedoch, 205 Lucknow, 211 Ancient Soldiers, Fronting page 224 Officer of Pikemen, 232
- 34. Old Highland Brigade, &c., 241 The Forty-second Royal Highlanders, 250 Sir Ralph Abercromby, 273 Sir John Moore, 280 Sebastopol, 287 The Seventy-first Glasgow Highland Light Infantry, 300 Waterloo, 310 The Seventy-second and Seventy-fourth Highlanders, 329 Duke of Wellington, 336 Wreck of the “Birkenhead,” 346 India, 373 Sir Henry Havelock, 377 Monument to the Seventy-eighth, 379 Presentation Plate to the Seventy-eighth, 379
- 35. Lochiel, 381 Duke of Richmond, 394 French Revolutionary War, 407 The Ninety-third Sutherland Highlanders, 409 Crimea, 415 Presentation of Crimean Medals, 416
- 36. PREFACE. In the present Work, the Author, without pretending to submit anything very startling or original, has endeavoured to gather from the records of the past such facts as may enable him, avoiding the tedium of detail, to present to the reader a brief and, it is hoped, at the same time, a comprehensive narrative of the origin and principal events in which our Scottish Regiments have so largely and honourably been distinguished. It is wholly foreign to the purpose of the Author in any way to overlook the valorous achievements of the English and Irish Regiments in Her Majesty’s Service, which have alike contributed to build up the military renown of the British Army; he only trusts he shall receive that same charitable indulgence, in his present undertaking, which in like circumstances he, with every right-hearted Scot, should cordially extend to brethren of either a sister land or sister isle. It is in these pages, as a Scotsman, he ventures to give expression to the nation’s gratitude and honest pride—awards, in the name of friend and foe, the meed of praise justly due to the brave soldier who has fought his country’s battles in almost every land— ofttimes victoriously—at all times honourably. The Author gratefully acknowledges the assistance freely rendered him in this compilation by many Officers of the Regiments described. He feels also considerably indebted to many very valuable works, on the same and kindred subjects, for much of his information. Unfortunately, many of these volumes are now very ancient, others nearly extinct, and nearly all so expensive as to fail in answering the purpose of the present Work, by bringing before the public, in a
- 37. cheaper and more popular form, the records of those heroic deeds, the narrative of which ought to be as “household words,” infusing a thrill of living patriotism and loyalty into the soul. It is hoped, as the grand result of the Work, that Scotsmen, considering the rich legacy of military glory bequeathed them by their heroic forefathers, specially registered in these Scottish Regiments, will be more impressed with the duty devolving on them to maintain and emulate the same. Whilst these records may afford knowledge, it is also hoped that they may awaken a larger sympathy and deeper interest on the part of the people in those, their brave countrymen, who so well represent the nation; and if circumstances preclude us from accepting the “Royal Shilling,” and so recruiting the army, let us be ready to accept, for the expression of our thoughts and feelings, that grand channel which, in our time, has been revived as the exponent of the people’s patriotism and loyalty—the Volunteer Movement—whether as active or honorary members, giving effect to our sentiments, and demonstrating, “by deeds as well as words” that we are in earnest.
- 38. INTRODUCTION. Nature has been aptly represented as a fickle goddess, scattering her bounties here and there with a partial hand. Some spots, like very Edens, are blessed with the lavish profusion of her favours—rich fertility, luxuriant vegetation, warm and delightful climates. Some, on the other hand, which have not so shared the distribution of her gifts, represent the barren wilderness, the sterile desert, the desolate places of our earth—entombed in a perpetual winter—a ceaseless winding-sheet of snow and ice seems for ever to rest upon these cold, chilly, Polar regions: or parched, fainting, dying, dead, where no friendly cloud intervenes, like the kindly hand of love and sympathy, to screen the thirsty earth from the consuming rays of a tropical sun. But, as if by “the wayside,” we gather from the analogy, that as in the world of man there is a Scripture proclaiming comfort and blessing to the poor and needy—whilst it tells the rich how hardly they shall enter into “life”—so in the world of nature there is an over-ruling, all-wise, all-just Providence, “Who moves in a mysterious way,” making ample amends in the result upon the peoples of these climes, so as yet shall cause “the wilderness to rejoice.” Thus we find that lands enriched by nature ofttimes produce a people who, rich in this world’s good things, acquired without much effort, allow their minds to become so intoxicated with present delights and indolence, as to fail in cultivating the virtues of the man. Too frequently the fruits are these—ignorance, lust, passion, infidelity, and general debility. Whilst the barren, dreary wilderness, the bleak and desolate mountain-land—like the poor and
- 39. needy upon whom Nature has frowned—enjoy the smile of Providence “in a better portion;” for there, amid a comparatively poor people, are nurtured all the sterner, the nobler, the truer, the God-like qualities of the man, the soldier, and the hero. There, too, hath been the birth-place and the abiding shrine of freedom—the bulwark and the bastion of patriotism and loyalty. Ascending higher, these—the peoples of the rejected and despised places of the earth —have ofttimes begotten and been honoured to wear the crowning attribute of piety. Turning to the history of Scotland or of Switzerland, for illustration, and taking merely a military retrospect, there it will be found. All centuries, all ages, all circumstances, are witness to the bravery and the fidelity of their mountain-soldiers. Scotland, the unendowed by Nature, has been thus largely blessed by Nature’s God, in yielding a long line of valiant and illustrious men. Perhaps no nation engrosses so large and prominent a place in the temple of military fame—none can boast so bright a page in the history of the brave. Her stern and rugged mountains, like a vast citadel, where scarce a foeman ever dared to penetrate, have been defended through centuries of war against the advancing and all but overwhelming tide of aggression; besieged, too, by the countless hosts of Tyranny, they have still remained impregnable. Her wild and desolate glens, like great arteries down which hath flowed the life- blood of the nation, in the living stream—the native and resistless valour of her clans. Her bleak and dreary heaths have written on them one dark history of blood—“the martyred children of the Covenant.” Faithful unto death; “of whom the world was not worthy.” Her crown oft crushed beneath a tyrant’s heel—her freedom trampled on—her people betrayed—all lost but honour. Unscathed, unsullied, she has triumphed, and still lives to write upon her banner, the mighty, envied, and thrice-glorious word, “Unconquered.” Armies have a very ancient history. Their origin might be traced to the very gates of Paradise. When the unbridled lust and wrathful passions of man were let loose like Furies, to wander forth upon the earth, then it was that lawless adventurers, gathering themselves together into armed bands for hostile purposes, to live and prey
- 40. upon their weaker brethren, constituted themselves armies. Passing down the stream of time, through the Feudal Age, we find one among the many greater, mightier, wealthier—a giant towering above his fellows—exercised lordship, levied tribute, military and civil, over others as over slaves. These were the days of chivalry,— the Crusades—when cavalry constituted the grand strength of an army. Here we might begin the history of cavalry as an important constituent in armies, were such our purpose. The comparative poverty of our ancient Scottish nobility prevented them contributing largely to the chivalry of the age. Almost the sole representative we have of our Scottish Cavalry, is the Second Regiment of Royal North British Dragoons, or Scots Greys—a most worthy representative. The wars of the Interregnum in Scotland—the times of Wallace and Bruce—when the feudal lords had nearly all either deserted or betrayed her, introduce us to a new force, more suited to the independent character and patriotism of the Scottish people—the formation of corps of infantry, or armed bands of free burghers. These were the fruit, to a large extent, of the Magna Charter in England, and of the struggle for liberty in Scotland. Hence the wars of Edward the Black Prince with France, distinguished by the victories of Poitiers, Agincourt, and Cressy, may be viewed not merely as the epitome of the triumphs of England over France, but more especially as illustrating the success of this new force— represented in the English yeomen, burghers, citizens, and freemen —over the old force, sustained in the chivalry, the cavalry of France. The result of these successive defeats, we find, was most disastrous to France. The jealousy and fear of the nobles and feudal lords had denied the people the use and the knowledge of arms; so that when themselves were defeated, France was ruined—since they could expect no support, as in Scotland, from an unarmed and unskilled people. They had done what they could to quench rather than foster the spirit of free patriotism, which in the nation’s extremity should have been the nation’s refuge—the soul burning to deliver their land from the yoke of the stranger. In not a few cases, the French rather sympathised with, as they sighed for the same blessings of our free- born English yeomen. Here we would mark, respectively in the
- 41. English and Scottish armies, the first formation of that branch of the service for which the British army has ever been specially distinguished—the Infantry. Our reader is no doubt aware of the calamitous results which flowed from the short-sighted policy of these privileged orders—the old feudal lords; whose love of a petty despotism laboured to postpone the day of reckoning “till a more convenient season”—and so refused the timely surrender of those privileges and that liberty which the growing wealth and intelligence of the people claimed. Long, bloody, and unavailing civil wars have desolated and vexed many countries as the consequence; and in France the contest attained a fearful crisis, and the people wreaked a cruel retribution in the awful horrors of the Revolution. The increasing importance of commerce, and the growing desire for wealth in preference to the uncertain and doubtful lustre of the battle-field, induced men to gather themselves together, not as formerly for war, but rather for the prosecution of trade; thus constituting themselves into trade-unions, communities, burgherates, free townships. Disowning the bondage of feudalism, as a system peculiarly adapted for war, and hostile in its spirit to a more peaceful vocation, they sought and obtained, in their earlier history at least, royal protection. Independently of their engagements and allegiance to the throne, these trading communities, aware of the restlessness, rapacity, and necessities of the old feudal lords around them, formed themselves into trained bands of free yeomen, or sort of militia, for the purpose—first, of defending their own industry, property, and lives; and, secondly, for the service of their sovereign and country in times of need. These are amongst the earliest ideas we have of a regiment. At an earlier age, we find many of the monarchs of Europe retaining in their service a body of foreign guards, specially entrusted with the defence of the royal person, so often threatened through the ambition of the nobles and the turbulence of the people. In nearly every instance these were composed of Scottish emigrants, driven from their country by the cruel and desolating wars which then
- 42. disturbed her peace, and had proscribed many of the honourable and brave. We know no exception in which these corps of guards have not maintained the Scottish character, nay, been specially distinguished for the valour and fidelity with which they fulfilled their duty. Thus originated the First Royals, or Royal Scots Regiment of the present British army. The free citizens, continuing to prosper and proportionably growing in power and influence, gradually insinuated themselves into State affairs. As they grew in wealth, so unfortunately they increased in pride and arrogance, forgetting altogether their early humility. They essayed to be a political as well as a trading community. Having overthrown the power of feudalism, they threatened to shake the foundations of the throne. These murmurings speedily awakened the royal jealousy, and broke in upon the peaceful harmony of their hitherto successful alliance. The prosperity and support of these freemen had elevated the might and majesty of the throne, with which they had been early leagued, and these together had compelled the old feudal nobility to exercise their rule in something more of a constitutional way. Gladly, therefore, did these last avail themselves of these dissensions to restore their long- lost power. Uniting with the crown, whose interests were more peculiarly their own, they called upon their still adherent tenantry to muster around them; and thus commenced the sanguinary civil wars, already in a previous paragraph referred to, between king and people, which have devastated so many lands. These tenantry, thus raised, ultimately taken into the royal pay, as regiments, have gone far to constitute the armies of their several states. In conclusion, we would remark, that the wars of the past have been as it were material contests—wars of matter rather than of mind—by which we mean that might has been understood as right; not as now, when right is acknowledged as might. Formerly it was he who excelled in physical strength and prowess that was crowned victor; now-a-days the appliances of mind, the inventive genius of man, have so improved the art of war, that upon these the result of the contest must largely depend. Skill and science, developed in a thousand ways, are the weapons with which our battles are to be
- 43. fought and won; and this, too, at a time when man has been dwarfed in his bodily might by the bloody and protracted wars of the past, and enervated by the ease and indolence found in cities, so as to be no longer able for a contest as of old; and so the providence of God steps in to supply the vacuum occasioned by decay, and from the rapid march of civilisation, and the wonderful development of the mind, represents to us a better state of things—the triumph of the mind of the present over the matter of the past. The victories of the battle-field are being superseded by the triumphs of the Cabinet. The first Napoleon conquered by the sword—the present Napoleon conquers by superior craft and intrigue, whilst we, as a nation, are sitting by to register with an occasional growl his successes. It has been the knowledge of these facts—this new system of warfare— that has aroused the nation to see its danger in time; to feel that “our glory” is but an ideal security; to know that steam and electricity have comparatively bridged the sea, and so done away with our best defence; to learn that the inventions of men comparatively equalise combatants. It has been the knowledge of these things, along with indications of a coming struggle casting its shadow before, that has called the nation, with one enthusiastic voice, to arms—in our present Volunteer force.
- 44. SCOTCH DRAGOON 1680. HISTORY OF THE SCOTTISH REGIMENTS.
- 45. SECOND ROYAL NORTH BRITISH DRAGOONS, OR SCOTS GREYS. CHAPTER I. “Come fill up my cup, come fill up my can, Come saddle my horses, and call out my men; Unhook the west port and let us gae free; For it’s up wi’ the bonnets o’ bonnie Dundee.” EARLY HISTORY—COVENANTERS—BATTLES OF DRUMCLOG AND BOTHWELL BRIDGE—ARGYLE’S REBELLION—THE RAID OF THE MACDONALDS—FLIGHT OF JAMES II.—DUNDEE’S REBELLION—BATTLES OF KILLIECRANKIE AND CROMDALE—MASSACRE OF GLENCOE—1660–1693. The page of history presents to us many dark scenes of oppression, where one man, trampling upon the rights of another, and disregarding the heaven-born principle of charity, has sold his brother into bondage. Nay, more, (as especially illustrated in the case of Spain groaning beneath the thraldom of the Papacy), some men have even succeeded in enslaving the mind; stopping up with vile trash the avenues of knowledge, and so defacing and ruining that mirror of the intellect which reflects so much of its Creator, which originally bore the impress of divinity, and was moulded in the likeness of God. But the pride of the human heart, and the unhallowed passion of man, stay not here, but have attempted more —to subdue the soul—but in vain. It is possible to fetter or destroy
- 46. the body, nay, it is even possible to enslave, or annihilate in madness, the mind, but it is impossible for man to bind the undying soul. Nevertheless, it has been the infatuation of tyrants, deluded by false creeds, in many countries and in many ages, to seek, but in vain, to usurp the dominion of the soul. The soul, like “the bush burned but not consumed,” lives still, lives for ever, defying the fires of persecution, the wasting famine, and the devouring sword. It comes forth scatheless, purified, living; having shaken off the corruption of earth, it appears clothed in the garments of immortality. There can be no better testimony to the suitableness of the true religion to meet the wants of man than this—that whilst all others have proved themselves to be so many systems of tyranny, bereaving man of his beloved liberty, the religion of Jesus is free, and is always to be welcomed as the herald of civil and religious liberty; wherever its blessing rests, its benign influence is felt, and its glorious light shines. It was in such a time as this in Scotland, when the iron will of Charles II., already oppressing the persons and the minds of his people, aspired to the dominion of their soul and conscience, by calling upon them to introduce into their simple forms of worship a host of objectionable mummeries, savouring of Popery, and threatening thereby to corrupt the purity of the Presbyterian faith. In vain they petitioned for liberty of conscience and protested against these intrusions. Persisting in the introduction of these idle rites, and denying redress, the monarch preferred plunging the nation into all the horrors of civil war, rather than depart from his purpose. To enforce these requirements the king raised in Scotland two troops of Life Guards, afterwards disbanded; a regiment of horse, known as Claverhouse’s Troopers— “The bonnets o’ bonnie Dundee;” a regiment of Foot Guards; a regiment of foot, now the Twenty-first, North British Fusiliers; and, in 1678, two troops of dragoons, which, increased by the addition of other troops in 1681, constituted the Royal Regiment of Scots Dragoons, now known familiarly as the
- 47. Scots Greys. The corps was originally commanded by Sir Thomas Dalziel, who in 1681 was appointed the first colonel of the regiment. He was always a staunch adherent of the House of Stuart, had been taken prisoner at the battle of Worcester, but escaping from the Tower, served with distinction in the Russian army during the Tartar wars. Returning to Scotland at the Restoration, he was employed by the king in enforcing his will upon the Presbyterians, and he discharged his duty with all the scrupulous exactness of a soldier. To the Covenanters he has left a most unenviable memory—as a monster of cruelty, devoid of mercy. His eccentricities, especially in regard to dress, often excited the merriment of the Court, and created quite a sensation amongst the juveniles of the metropolis. He died in 1685. The early history of the Royal Scots Dragoons is painfully and intimately associated with the sufferings and trials of the Covenanters—a page in our history which, would the truth admit, we would gladly omit. The ignominious duty imposed upon this gallant regiment, of hunting down the Presbyterians, and the cruelties which they were called to witness, sometimes to inflict upon their unhappy brethren, must have been extremely harrowing and repulsive to the feelings of brave men. Along with a troop of horse, a troop of the corps was present in 1679, under Graham of Claverhouse, at the battle of Drumclog, where they were defeated, with the loss of twenty men, by the superior numbers and desperate valour of the Covenanters, as also from the unsuitableness of the ground for cavalry to act upon. The result of this overthrow was a general rising of the disaffected and oppressed—a motley and undisciplined army was speedily assembled, better in the use of the tongue than the sword; and as always happens where that “unruly member” is in the ascendant, proved the precursor of party division, and in the end brought ruin to the good cause in which they had embarked. Foiled in an attack upon Glasgow by the retiring royal troops, especially the Royal Scots Dragoons and Scots Foot Guards, the Covenanters took up a strong position behind the Clyde at Bothwell Bridge, and there awaited the attack of the royal army, now
- 48. advancing from Edinburgh under the Duke of Monmouth. Failing in effecting an accommodation, the battle was commenced by the Royal Scots Dragoons, supported by the Scots Foot Guards attacking the bridge, which, defended with great bravery, was only relinquished when the ammunition of the defenders was exhausted. The loss of this most important post, as well as the divisions already prevailing amongst the Covenanters, soon produced a panic which lost the battle, ruined for the present the cause of liberty of conscience, and served to add nearly ten years more to their sufferings. In the pursuit, the troopers of Claverhouse took a cruel revenge for the defeat of Drumclog, upon the broken and flying remnant. The Royal Scots Dragoons continuing to be employed in the humiliating work of persecution, were often roughly handled by the Presbyterians, especially at Ayr Moss on the 20th July, 1680, where a desperate rencontre took place. The Earl of Argyle, a nobleman of great merit, and for some time enjoying the esteem of his sovereign, being suspected of a leaning to the Nonconformists, or Covenanters, at the instigation of the Duke of York was arraigned for treason, and, accordingly, condemned to death. Escaping to France, Argyle returned in 1685, and landing with a force of 300 men in Argyleshire, summoned his clansmen, and endeavoured, with little success, to raise the Presbyterians, and so, setting up the standard of rebellion, threatened to dethrone James II., who but lately had succeeded his brother in the throne. After much fruitless manœuvring, he advanced into the Lowlands, but was met by the royal troops, including the Royal Scots Dragoons, near Dumbarton, under the Earl of Dumbarton. Attempting to retreat in the darkness of the night, his guides betrayed him, his army fell into disorder and disbanded, whilst he himself was taken prisoner and afterwards executed at Edinburgh. On the morrow, the Royal Scots Dragoons, assisted by other troops, attacked a considerable body of the rebels under Sir John Cochrane, which still remained together in the neighbourhood in a strongly fortified position. After hard fighting, in course of which
- 49. the dragoons dismounted and fought hand to hand on foot, and after the loss of many officers, among whom were Sir Adam Blair, Sir William Wallace, and Capt. Clelland, also Lord Ross wounded, the rebels were driven back and ultimately dispersed. On the death of Lieut.-General Sir Thomas Dalziel, in 1685, Lord Charles Murray, afterwards the Earl of Dunmore, and son of the Marquis of Athole, one of the original officers of the corps, was promoted to the colonelcy. In 1688 a part of the regiment was called upon to interfere on behalf of the Government—unfortunately on the wrong side—in one of those unhappy broils which, as the dregs of feudalism, still so sorely distressed the Highlands. The Macintoshes having despoiled the Macdonald of Keppoch of his estate, during his temporary absence in the Highlands, the Macdonald, on his return, taking the law—as was usual in those days, specially amongst the clans—into his own hand, and taking an ample vengeance, redeemed his own. The Royal Scots Dragoons were sent to the assistance and for the release of the Mackintosh, who had been taken prisoner. In retaliation they were inhumanly ordered to destroy all that pertained to the Macdonald— man, woman, and child. Although such instructions were quite in keeping with the character of the Court, happily it was about the last exercise of a power ever rioting in such acts of merciless cruelty. The close of the same year brought the Prince of Orange to our shores, to deliver the land from the bondage of the Stuarts who had so grievously oppressed it. To meet this emergency, King James had drawn together to London and its neighbourhood the whole reliable forces of his kingdom. Amongst these were the troops of Scottish Life Guards; Claverhouse’s regiment of horse; Dunmore’s regiment of Royal Scots Dragoons; the regiment of Scottish Foot Guards; and two regiments of Scottish Foot—in all, 3,765 men from Scotland. After a seeming show of resistance, and much manœuvring in the vicinity of Salisbury, the monarch, dreading the wrath of an outraged people, fled to France.
- 50. “Conscience makes cowards of us all.” When the Prince of Orange, as William III., ascended the vacant throne, he found many of the troops inclined to dispute his authority, especially the regiments of Royal Scots Horse and Royal Scots Dragoons; which still remained together under the command of Viscount Dundee, and with the characteristic loyalty of Scotsmen, would still have maintained the cause of an unworthy and exiled prince, the degenerate representative of the Bruce of Bannockburn. The tact of the new monarch succeeded in winning the submission of the Royal Scots Dragoons; but the Royal Scots Horse, deserting, followed Dundee into Scotland, took part with him in his subsequent rebellion, and so, sharing his fate, have been lost to the British army. The Earl of Dunmore, declining to serve under the new king, was superseded in the colonelcy of the Royal Scots Dragoons by Sir Thomas Livingstone, afterwards Viscount Teviot—a Scottish soldier of distinction, who came over from the continent with the prince. To stem the torrent of rebellion which the return of Dundee to Scotland had excited—especially among the Highland clans, nearly all of whom were devotedly attached to the Stuarts—the Royal Scots Dragoons were ordered to return to Scotland. Throughout the succeeding campaigns the regiment behaved with signal fidelity and gallantry, with the exception of some few of its officers who were found guilty of treasonable intercourse with the rebels—having a sympathy with their old comrade in arms, Viscount Dundee. Amongst the arrested were Lieut.-Colonel Livingstone, Captains Murray, Crichton, and Livingstone. The royal forces under the command of Major-General Mackay, included, besides the Royal Scots Dragoons, many regiments since known to fame—Lord Colchester’s Horse, or the Third (Prince of Wales’) Dragoon Guards; Berkeley’s, or the Fourth (Queen’s Own Hussars) Dragoons; Sir James Leslie’s, or the Fifteenth (York, East Riding) Foot; besides a considerable body of Dutch troops under Colonel Ramsay. Dundee was joined at Inverness by Macdonald of Keppoch and his clan, thirsting for revenge because of the atrocities committed upon them
- 51. and theirs by the soldiers in the previous year. After much time spent in marching and counter-marching in search of, and pursuit of, each other, the two armies met at the Pass of Killiecrankie, when the death of Dundee, in the moment of victory, virtually ruined the Jacobite cause. The Royal Scots Dragoons, although not present at that disastrous battle, had previously distinguished themselves in a skirmish with a body of about 500 Highlanders, chiefly Macleans, who, defeating with great loss, they dispersed, and, dismounting, pursued among the rocks and crags of the mountains. In the following year, the rebels still continuing in arms, under General Canon—who on the death of Dundee assumed the command—and being recruited by a body of men from Ireland under General Buchan, took up a strong post and awaited the attack of the royal forces at Cromdale. Here, on the morning of the 31st April, they were suddenly attacked by Sir Thomas Livingstone, at the head of the Royal Scots Dragoons and other troops, and, amid the darkness and confusion, totally defeated and dispersed with great slaughter. The scene was one of consternation and horror, and had it not been for the merciful intervention of a mountain mist, as if to befriend her own children in their day of calamity, would have proved even more fatal to the flying enemy. In this action the Royal Scots Dragoons took a gallant part. This victory was quickly followed by the relief of the castle of Abergeldie, then besieged by the Highlanders, where two troops of the Royal Scots Dragoons utterly routed the rebels with great carnage. Unable longer to sustain such a hopeless struggle, the clans tendered their submission to King William, which was accepted. But the triumph of the Government was stained by a deed of barbarous cruelty and sin, which remains a blot on the page of British history, known as “the Massacre of Glencoe.” The Macdonalds of Glencoe having failed to tender their allegiance within the prescribed time, although they had done so a few days afterwards, the whole were treacherously murdered in cold blood, whilst peaceably sleeping, by a party of soldiers from Argyle’s regiment, who had been received and hospitably quartered among them as
- 52. friends. This inhuman action has been vainly attempted to be excused, and all authorities have alike endeavoured to escape the responsibility. We gladly record that the Royal Scots Dragoons were not called to take any part in the matter; and their colonel, Sir Thomas Livingstone, although then Commander-in-Chief in Scotland, has been fully exonerated from blame by Parliament.
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