The Mechanics Of Constitutive Modeling
Constitutive modelling is the mathematical description of how materials respond to various loadings. This is the most intensely researched field within solid mechanics because of its complexity and the importance of accurate constitutive models for practical engineering problems. \ Topics covered include:\ Elasticity - Plasticity theory - Creep theory - The nonlinear finite element method - Solution of nonlinear equilibrium equations - Integration of elastoplastic constitutive equations - The...
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Constitutive modelling is the mathematical description of how materials respond to various loadings. This is the most intensely researched field within solid mechanics because of its complexity and the importance of accurate constitutive models for practical engineering problems. Topics covered include:Elasticity - Plasticity theory - Creep theory - The nonlinear finite element method - Solution of nonlinear equilibrium equations - Integration of elastoplastic constitutive equations - The thermodynamic framework for constitutive modelling-Thermoplasticity - Uniqueness and discontinuous bifurcations• More comprehensive in scope than competitive titles, with detailed discussion of thermodynamics and numerical methods.• Offers appropriate strategies for numerical solution, illustrated by discussion of specific models.• Demonstrates each topic in a complete and self-contained framework, with extensive referencing.
1Notations and Cartesian tensors12Strain tensor213Stress tensor494Hyper-elasticity675Cauchy-elasticity1036Representation theorems1197Hypo-elasticity1398Failure and initial yield criteria1459Introduction to plasticity theory20310General plasticity theory24711Plastic collapse theorems26512Common plasticity models27913Nonlinear kinematic hardening laws32114Introduction to time-dependent material behavior35715Creep and viscoplasticity38716Nonlinear finite element method42317Solution of nonlinear equilibrium equations42918Integration of constitutive equations47519Solution of dynamic finite element equations50920Basic principles of thermodynamics51721Thermodynamic framework for constitutive modeling55122Plasticity, viscoplasticity and viscoelasticity59123Thermo-plasticity63724Uniqueness and discontinuous bifurcations673Convexity - minimization of function subject to constraints697
