Description
General Continuum Mechanics and Constitutive Modeling starts with a comprehensive treatment of tensor algebra that is followed by coverage of strains, stresses, and thermodynamics. General principles for constitutive modeling are presented, including objectivity, Lie-derivative, and covariance, as are issues central to configurational mechanics, such as polyconvexity and invariance principles used to establish balance equations. The book includes a chapter on hyperelasticity which analyzes isotropic and anisotropic materials, and also discusses the distinction between energetic and entropic material response.The finite element method and classic plasticity based on hypoelasticity are each covered, and the book concludes with a chapter covering plasticity based on hyperplasticity, including isotropy, anisotropy, thermoplasticity, and crystal plasticity.- Covers the fundamental concepts of polyconvexity, invariance principles, configurational mechanics, and hyperelasticity and plasticity in a clear and concise manner- Describes general continuum mechanics and constitutive modeling for large deformations and rotations, with all tensor expressions written in direct notation and component and base vectors referring to arbitrary curvilinear coordinate systems- Presents general principles for constitutive modeling, including topics such as objectivity, Lie-derivative, covariance, thermoelasticity, the differences between energetic and entropic material response, and more
Table of Contents
1. Tensor algebra in general coordinates2. Kinematics3. Stresses and balance equations4. Thermodynamics5. General principles for constitutive modeling6. Configurational mechanics7. Balance equations established using invariance principles8. Convexity of strain energy function9. Hyperelasticity10. Finite element formulation of hyperelasticity11. Plasticity based on hypo-elasticity12. Plasticity based on hyperelasticity
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