Cover -- Title Page -- Copyright -- Contents -- Preface -- Notations -- Chapter 1 : Introduction -- 1.1 Introduction to material modelling -- 1.2 Complexity of material response in engineering -- 1.3 Classification of modelling of material response -- 1.3.1 Empirical models -- 1.3.2 Micromechanical models -- 1.3.3 Phenomenological models -- 1.4 Limitations of the continuum hypothesis -- 1.5 Focus of this book -- Chapter 2 : Preliminary Concepts -- 2.1 Introduction -- 2.2 Coordinate frame and system -- 2.3 Tensors -- 2.3.1 Tensors of different orders -- 2.3.2 Notations for tensors -- 2.4 Derivative operators -- Summary -- Exercise -- Chapter 3 : Continuum Mechanics Concepts -- 3.1 Introduction -- 3.2 Kinematics -- 3.2.1 Transformations -- 3.2.1.1 Transformation of line elements -- 3.2.1.2 Transformation of volume elements -- 3.2.1.3 Transformation of area elements -- 3.2.2 Important types of motions -- 3.2.2.1 Isochoric deformations -- 3.2.2.2 Rigid body motion -- 3.2.2.3 Homogeneous deformations -- 3.2.3 Decomposition of deformation gradient -- 3.2.3.1 Polar decomposition theorem -- 3.2.3.2 Stretches -- 3.2.4 Strain measures -- 3.2.4.1 Displacements -- 3.2.4.2 Infinitismal strains -- 3.2.5 Motions -- 3.2.5.1 Velocity gradient -- 3.2.6 Relative deformation gradient -- 3.2.7 Time derivatives viewed from different coordinates -- 3.2.7.1 Co-rotational derivatives -- 3.2.7.2 Convected derivatives -- 3.3 Balance laws -- 3.3.1 Transport theorem -- 3.3.2 Balance of mass -- 3.3.3 Balance of linear momentum -- 3.3.4 Balance of angular momentum -- 3.3.5 Work energy identity -- 3.3.6 Thermodynamic principles -- 3.3.6.1 First law of thermodynamics -- 3.3.6.2 Second law of thermodynamics -- 3.3.6.3 Alternate energy measures in thermodynamics -- 3.3.7 Referential description of balance laws.

3.3.7.1 Relations between variables in deformed and undeformed configurations -- 3.3.7.2 Statement of the balance laws in reference configuration -- 3.3.8 Indeterminate nature of the balance laws -- 3.3.9 A note on multiphase and multi-component materials -- 3.3.9.1 Chemical potential -- 3.4 Constitutive relations -- 3.4.1 Transformations -- 3.4.1.1 Euclidean transformations -- 3.4.1.2 Galilean transformations -- 3.4.2 Objectivity of mathematical quantities -- 3.4.3 Invariance of motions and balance equations -- 3.4.4 Invariance of constitutive relations -- 3.4.4.1 Frame invariance in a thermoelastic material -- 3.4.4.2 Constitutive relations for thermoelastic materials -- 3.4.4.3 Frame invariance and constitutive relations for a thermoviscous fluid -- 3.4.5 Frame invariance of derivatives -- Summary -- Exercise -- Chapter 4 : Linear Mechanical Models of Material Deformation -- 4.1 Introduction -- 4.2 Linear elastic solid models -- 4.2.1 Small strain assumption of linear elasticity -- 4.2.2 Classes of elastic constants -- 4.2.2.1 General anisotropic linear elastic solid -- 4.2.2.2 Materials with single plane of elastic symmetry -- 4.2.2.3 Materials with two planes of elastic symmetry -- 4.2.2.4 Materials with symmetry about an axis of rotation -- 4.2.2.5 Isotropic materials -- 4.3 Linear viscous fluid models -- 4.3.1 General anisotropic viscous fluid -- 4.3.2 Isotropic viscous fluid -- 4.4 Viscoelastic models -- 4.4.1 Useful definitions for description of viscoelastic behaviour -- 4.4.1.1 Creep compliance and relaxation modulus -- 4.4.1.2 Phase lag, storage modulus and loss modulus -- 4.4.2 Simplistic models of viscoelasticity -- 4.4.2.1 Maxwell model -- 4.4.2.2 Kelvin-Voigt model -- 4.4.2.3 Mechanical analogs for viscoelastic models -- 4.4.3 Time temperature superposition -- Summary -- Exercise.

Chapter 5: Non-linear Models for Fluids -- 5.1 Introduction -- 5.2 Non-linear response of fluids -- 5.2.1 Useful definitions for non-Newtonian fluids -- 5.2.1.1 Steady shear -- 5.2.1.2 Normal stresses -- 5.2.1.3 Material functions in extensional flow -- 5.2.2 Classification of different models -- 5.3 Non-linear viscous fluid models -- 5.3.1 Power law model -- 5.3.2 Cross model -- 5.4 Non-linear viscoelastic models -- 5.4.1 Differential-type viscoelastic models -- 5.4.2 Integral -type viscoelastic models -- 5.5 Case study: rheological behaviour of asphalt -- 5.5.1 Material description -- 5.5.2 Experimental methods -- 5.5.3 Constitutive models for asphalt -- 5.5.3.1 Non-linear viscous models -- 5.5.3.2 Linear viscoelastic models -- 5.5.3.3 Non-linear viscoelastic models -- Summary -- Exercise -- Chapter 6 : Non-linear Models for Solids -- 6.1 Introduction -- 6.2 Non-linear elastic material response -- 6.2.1 Hyperelastic material models -- 6.2.2 Non-linear hyperelastic models for finite deformation -- 6.2.2.1 Network models of rubber elasticity -- 6.2.2.2 Mooney-Rivlin model for rubber elasticity -- 6.2.2.3 Ogden's model for rubber elasticity -- 6.2.2.4 Non-linear hyperelastic models in infinitismal deformation -- 6.2.3 Cauchy elastic models -- 6.2.3.1 First order Cauchy elastic models -- 6.2.3.2 Second order Cauchy elastic models -- 6.2.4 Use of non-linear elastic models -- 6.3 Non-linear inelastic models -- 6.3.1 Hypo-elastic material models -- 6.4 Plasticity models -- 6.4.1 Typical response of a plastically deforming material -- 6.4.2 Models for monotonic plastic deformation -- 6.4.3 Models for incremental plastic deformation -- 6.4.4 Material response under cyclic loading -- 6.4.5 Generalized description of plasticity models -- 6.5 Case study of cyclic deformation of soft clayey soils -- 6.5.1 Material description.

6.5.2 Experimental characterization -- 6.5.3 Constitutive model development for monotonic and cyclic behaviour -- 6.5.4 Comparison of model predictions with experimental results -- Summary -- Exercise -- Chapter 7 : Coupled Field Response of Special Materials -- 7.1 Introduction -- 7.1.1 Field variables associated with coupled field interactions -- 7.2 Electromechanical fields -- 7.2.1 Basic definitions of variables associated with electric fields -- 7.2.2 Balance laws in electricity - Maxwell's equations -- 7.2.3 Modifications to mechanical balance laws in the presence of electric fields -- 7.2.4 General constitutive relations associated with electromechanical fields -- 7.2.5 Linear constitutive relations associated with electromechanical fields -- 7.2.6 Biased piezoelectric (Tiersten's) model -- 7.3 Thermomechanical fields -- 7.3.1 Response of shape memory materials -- 7.3.1.1 Response of shape memory alloys -- 7.3.1.2 Response of shape memory polymers -- 7.3.2 Microstructural changes in shape memory materials -- 7.3.2.1 Microstructural changes associated with shape memory alloys -- 7.3.2.2 Microstructural changes associated with shape memory polymers -- 7.3.3 Constitutive modelling of shape memory materials -- 7.3.3.1 Constitutive models for shape memory alloys -- 7.3.3.2 Constitutive models for shape memory polymers -- Summary -- Exercise -- Chapter 8 : Concluding Remarks -- 8.1 Introduction -- 8.2 Features of models summarized in this book -- 8.3 Current approaches for constitutive modelling -- 8.4 Numerical simulation of system response using continuum models -- 8.5 Observations on system response -- 8.6 Challenges for the future -- Appendix -- Bibliography -- Index.