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Book Cover
E-book
Author Anand, Lallit author

Title Continuum mechanics of solids / Lallit anand, Sanjay Govindjee
Edition First edition
Published Oxford, United Kingdom Oxford University Press 2020

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Description 1 online resource illustrations
Series Oxford graduate texts
Oxford graduate texts.
Contents Cover -- Continuum Mechanics of Solids -- Copyright -- Preface -- Acknowledgments -- Contents -- PART I: Vectors and tensors -- 1: Vectors and tensors: Algebra -- 1.1 Cartesian coordinate frames. Kronecker delta. Alternating symbol -- 1.1.1 Summation convention -- 1.2 Tensors -- 1.2.1 What is a tensor? -- 1.2.2 Zero and identity tensors -- 1.2.3 Tensor product -- 1.2.4 Components of a tensor -- 1.2.5 Transpose of a tensor -- 1.2.6 Symmetric and skew tensors -- 1.2.7 Axial vector of a skew tensor -- 1.2.8 Product of tensors -- 1.2.9 Trace of a tensor. Deviatoric tensors
1.2.10 Positive definite tensors -- 1.2.11 Inner product of tensors. Magnitude of a tensor -- 1.2.12 Matrix representation of tensors and vectors -- 1.2.13 Determinant of a tensor -- 1.2.14 Invertible tensors -- 1.2.15 Cofactor of a tensor -- 1.2.16 Orthogonal tensors -- 1.2.17 Transformation relations for components of a vector and a tensor under a change in basis -- Transformation relation for vectors -- Transformation relation for tensors -- 1.2.18 Eigenvalues and eigenvectors of a tensor. Spectral theorem -- Eigenvalues of symmetric tensors -- Other invariants and eigenvalues
1.2.19 Fourth-order tensors -- Transformation rules for fourth-order tensors -- 2: Vectors and tensors: Analysis -- 2.1 Directional derivatives and gradients -- 2.2 Component expressions for differential operators -- 2.2.1 Divergence, curl, and Laplacian -- 2.3 Generalized derivatives -- 2.4 Integral theorems -- 2.4.1 Localization theorem -- 2.4.2 Divergence theorem -- 2.4.3 Stokes theorem -- PART II: Kinematics -- 3: Kinematics -- 3.1 Motion: Displacement, velocity, and acceleration -- 3.1.1 Examplemotions -- Simple shear -- Elementary elongation -- Rigid motion -- Bending deformation
3.2 Deformation and displacement gradients -- 3.2.1 Transformation of material line elements -- 3.2.2 Transformation of material volume elements -- 3.2.3 Transformation of material area elements -- 3.3 Stretch and rotation -- 3.3.1 Polar decomposition theorem -- 3.3.2 Properties of the tensorsUand C -- 3.4 Strain -- 3.4.1 Biot strain -- 3.4.2 Green finite strain tensor -- 3.4.3 Hencky's logarithmic strain tensors -- 3.5 Infinitesimal deformation -- 3.5.1 Infinitesimal strain tensor -- 3.5.2 Infinitesimal rotation tensor -- 3.6 Example infinitesimal homogeneous strain states
3.6.1 Uniaxial compression -- 3.6.2 Simple shear -- 3.6.3 Pure shear -- 3.6.4 Uniform compaction (dilatation) -- 3.6.5 Infinitesimal rigid displacement -- 3.7 Volumetric deviatoric split -- 3.7.1 Volume changes -- 3.7.2 Strain deviator -- 3.8 Summary ofmajor kinematical concepts related to infinitesimal strains -- Appendices -- 3.A Linearization -- 3.B Compatibility conditions -- 3.B.1 Proof of the compatibility theorem -- PART III: Balance laws -- 4: Balance laws for mass, forces, and moments -- 4.1 Balance of mass -- 4.2 Balance of forces and moments. Stress tensor. Equation of motion
Summary This introductory graduate text is a unified treatment of the major concepts of Solid Mechanics for beginning graduate students in the many branches of engineering. Major topics are elasticity, viscoelasticity, plasticity, fracture, and fatigue. The book also has chapters on thermoelasticity, chemoelasticity, poroelasticity and piezoelectricity
Bibliography Includes bibliographical references and index
Notes Print version record
Subject Continuum mechanics.
Continuum mechanics
Form Electronic book
Author Govindjee, Sanjay author
ISBN 9780192633699
0192633694
9780191896767
0191896764