Front Cover -- The Mechanics of Constitutive Modeling -- Copyright Page -- Contents -- Preface -- Chapter 1. Notations and Cartesian tensors -- 1.1 Matrix notation -- 1.2 Cartesian coordinate system -- 1.3 Index notation -- 1.4 Change of coordinate system -- 1.5 Cartesian tensors -- 1.6 Example of tensors - Isotropic tensors -- Chapter 2. Strain tensor -- 2.1 Introduction -- 2.2 Small strain tensor -- 2.3 Rigid-body motions -- 2.4 Physical significance of the strain tensor -- 2.5 Change of coordinate system -- 2.6 Principal strains and principal directions - Invariants -- 2.7 Extremum values of the normal strain -- 2.8 Cayley-Hamilton's theorem -- 2.9 Deviatoric strains -- 2.10 Important strain invariants -- 2.11 Change of coordinate system - Mohr's circle -- 2.12 Special states of strain -- Chapter 3. Stress tensor -- 3.1 Introduction -- 3.2 Change of coordinate system -- 3.3 Principal stresses and principal directions - Invariants -- 3.4 Stress deviator tensor -- 3.5 Change of coordinate system - Mohr's circle -- 3.6 Special states of stress -- 3.7 Equations of motion -- 3.8 Weak formulation - Principle of virtual work -- Chapter 4. Hyper-elasticity -- 4.1 Strain energy and hyper-elasticity -- 4.2 Complementary energy and hyper-elasticity -- 4.3 Linear hyper-elasticity Anisotropy -- 4.4 Linear elasticity - Matrix formulation -- 4.5 Change of coordinate system when using matrix format -- 4.6 Anisotropy in linear hyper-elasticity -- 4.7 Initial strains - Thermoelasticity -- 4.8 Most general isotropic hyper-elasticity -- 4.9 Isotropic linear elasticity -- 4.10 Nonlinear isotropic Hooke formulation -- 4.11 Plane strain -- 4.12 Plane stress -- 4.13 Incompressible linear hyper-elasticity -- Chapter 5. Cauchy-elasticity -- 5.1 Response function, principle of coordinate invariance and isotropic tensor function.

5.2 Most general isotropic Cauchy-elasticity -- 5.3 Proof of most general form of isotropic Cauchy-elasticity -- 5.4 Nonlinear isotropic Hooke formulation -- Chapter 6. Representation theorems -- 6.1 Scalar functions -- 6.2 Second-order tensor functions -- 6.3 Thermoelasticity -- 6.4 Viscoelasticity -- 6.5 Orthotropic linear elasticity -- 6.6 Transverse isotropic linear elasticity -- Chspter 7. Hypo - elasticity -- 7.1 Time-independent response -- Chapter 8. Failure and initial yield criteria -- 8.1 Haigh-Westergaard coordinate system - Geometrical interpretation of stress invariants -- 8.2 Symmetry properties of the failure or initial yield curve in the deviatoric plane -- 8.3 von Mises criterion -- 8.4 Drucker-Prager criterion -- 8.5 Coulomb criterion -- 8.6 Mohr's failure mode criterion -- 8.7 Tresca criterion -- 8.8 Experimental results for metals and steel - von Mises versusTresca -- 8.9 Rankine criterion and modified Coulomb criterion -- 8.10 Experimental results for concrete versus the modified Coulomb criterion -- 8.11 4-parameter criterion -- 8.12 Experimental results for concrete versus the 4-parameter criterion -- 8.13 Anisotropic criteria -- Chapter 9. Introduction to plasticity theory -- 9.1 Change of yield surface due to loading - Hardening rules -- 9.2 Development of plastic strains - Introductory remarks -- 9.3 Drucker's postulate and its consequences -- 9.4 Consistency relation and evolution laws -- 9.5 Preliminary loading and unloading criteria -- 9.6 Isotropic hardening of a von Mises material -- 9.7 Proportional loading of isotropic hardening von Mises material -- 9.8 Conditions for plastic incompressibility -- Chapter 10. General plasticity theory -- 10.1 Fundamental equations -- 10.2 Generalized plastic modulus - Relation between stress rates and total strain rates -- 10.3 Evaluation of plastic modulus H.

10.4 General loading and unloading criteria -- 10.5 Plane strain -- 10.6 Plane stress -- Chapter 11. Plastic collapse theorems -- 11.1 Lower bound theorem -- 11.2 Upper bound theorem -- 11.3 Simple example -- 11.4 Nonassociated plasticity -- Chapter 12. Common plasticity models -- 12.1 Experimental characteristics -- 12.2 Isotropic von Mises hardening -- 12.3 Kinematic von Mises hardening -- 12.4 Mixed von Mises hardening -- 12.5 Melan-Prager's evolution law versus Ziegler's evolution law -- 12.6 Orthotropic Hill plasticity -- 12.7 Drucker-Prager plasticity. Frictional materials -- Chapter 13. Nonlinear kinematic hardening laws -- 13.1 Mro'z model -- 13.2 Bounding surface models -- 13.3 Armstrong and Frederick model -- Chapter 14. Introduction to time-dependent material behavior -- 14.1 Viscoelasticity -- 14.2 Differential equation approach -- 14.3 Hereditary approach -- Chapter 15. Creep and viscoplasticity -- 15.1 Results based on the standard creep test -- 15.2 Uniaxial stress changes - Classical hardening rules -- 15.3 Multiaxial stress states -- 15.4 Viscoplasticity -- Chapter 16. Nonlinear finite element method -- 16.1 Equations of motion -- 16.2 Static conditions -- Chapter 17. Solution of nonlinear equilibrium equations -- 17.1 Euler forward scheme -- 17.2 General iteration format -- 17.3 Standard iteration format for equilibrium iterations . Iteration matrix -- 17.4 Newton-Raphson scheme -- 17.5 Initial stiffness and modified Newton-Raphson schemes -- 17.6 Consideration of boundary condtions -- 17.7 Convergence criteria -- 17.8 Quasi-Newton methods -- 17.9 Line search -- 17.10 Limit points -- 17.11 Bergan's minimum residual force method -- Chapter 18. Integration of constitutive equations -- 18.1 Elasto-plasticity -- 18.2 Viscoplasticity -- Chapter 19. Solution of dynamic finite element equations -- 19.1 Introduction -- 19.2 Explicitscheme.

19.3 Implicit schemes -- Chapter 20. Basic principles of thermodynamics -- 20.1 Temperature - Absolute temperature -- 20.2 Heat and heat flow -- 20.3 State variables and state functions . Introduction to the first law -- 20.4 First law of thermodynamics -- 20.5 Ideal gases -- 20.6 Reversible and irreversible processes -- 20.7 Introduction to the second law -- 20.8 Efficiency of various heat engines -- 20.9 The Carnot process -- 20.10 Thermodynamic temperature scale -- 20.11 Entropy - Clausius's inequality -- 20.12 Maximum entropy at thermodynamic equilibrium -- 20.13 The second law and the Clausius-Duhem inequality -- 20.14 Various approaches to thermodynamics -- Chapter 21. Thermodynamic framework for constitutive modeling -- 21.1 Thermo-elastic materials -- 21.2 Inelastic materials - Internal variables -- 21.3 Choice of evolution laws - Fulfillment of the mechanical dissipation inequality -- 21.4 Heat equation -- 21.5 Properties of state functions at thermodynamical equilibrium -- Chapter 22. Plasticity, viscoplasticity and viscoeasticity -- 22.1 Fundamental equations of plasticity -- 22.2 Further discussion of the postulate of maximum dissipation -- 22.3 Examples of typical plasticity models -- 22.4 Use of plastic work as internal variable -- 22.5 Corner plasticity -- 22.6 Viscoplasticity -- 22.7 Viscoelasticity -- Chapter 23. Thermo-plasticity -- 23.1 Change of material parameters with temperature -- 23.2 Equations of thermo-plasticity -- 23.3 Isotropic hardening von Uses plasticity -- 23.4 Field equations - Finite element formulation -- 23.5 Solution of uncoupled thermo-plasticity -- 23.6 Solution of coupled thermo-plasticity -- 23.7 Adiabatic heating -- 23.8 Staggered solution scheme -- Chapter 24. Uniqueness and discontinuous bifurcations -- 24.1 Simple illustration - Tension bar -- 24.2 Equations of plasticity theory.

24.3 Uniqueness of elasto-plastic materials -- 24.4 Discontinuous bifurcations -- 24.5 Acceleration waves -- A Convexity - Minimiza tion of function subject to constraints -- A.l Convexfunction -- A.2 Unconstrained minimum -- A.3 Inequality constrained minimum . Kuhn-Tucker relations -- Bibliography -- Index.