Nonlinear Continuum Mechanics for Finite Elasticity-Plasticity

Multiplicative Decomposition with Subloading Surface Model

Koichi Hashiguchi

• Publisher: Elsevier
• Year: 2020
• Print ISBN:
  9780128194287
• eBook ISBN:
  9780128194294
• Topic: Technology & Engineering
• Subtopic: Mechanical Engineering
• Index: Technology & Engineering

Nonlinear Continuum Mechanics for Finite Elasticity-Plasticity empowers readers to fully understand the constitutive equation of finite strain, an essential piece in assessing the deformation/strength of materials and safety of structures. The book starts by providing a foundational overview of continuum mechanics, elasticity and plasticity, then segues into more sophisticated topics such as multiplicative decomposition of deformation gradient tensor with the isoclinic concept and the underlying subloading surface concept. The subloading surface concept insists that the plastic strain rate is not induced suddenly at the moment when the stress reaches the yield surface but it develops continuously as the stress approaches the yield surface, which is crucially important for the precise description of cyclic loading behavior. Then, the exact formulations of the elastoplastic and viscoplastic constitutive equations based on the multiplicative decomposition are expounded in great detail. The book concludes with examples of these concepts and modeling techniques being deployed in real-world applications. Table of Contents:1. Mathematical Basics2. General (Curvilinear) Coordinate System3. Description of Deformation/Rotation in Convected Coordinate System4. Deformation/Rotation (Rate) Tensors5. Conservation Laws and Stress Tensors6. Hyperelastic Equations7. Development of Elastoplastic Constitutive Equations8. Multiplicative Decomposition of Deformation Gradient Tensor9. Multiplicative Hyperelastic-based Plastic and Viscoplastic Constitutive Equations10. Friction Model: Finite Sliding Theory - Covers both the fundamentals of continuum mechanics and elastoplasticity while also introducing readers to more advanced topics such as the subloading surface model and the multiplicative decomposition among others - Approaches finite elastoplasticity and viscoplasticty theory based on multiplicative decomposition and the subloading surface model - Provides a thorough introduction to the general tensor formulation details for the embedded curvilinear coordinate system and the multiplicative decomposition of the deformation gradient

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Preface
• Chapter 1. Mathematical fundamentals
• Chapter 2. Curvilinear coordinate system
• Chapter 3. Tensor operations in convected coordinate system
• Chapter 4. Deformation/rotation (rate) tensors
• Chapter 5. Conservation laws and stress tensors
• Chapter 6. Hyperelastic equations
• Chapter 7. Development of elastoplastic and viscoplastic constitutive equations
• Chapter 8. Multiplicative decomposition of deformation gradient tensor
• Chapter 9. Subloading-multiplicative hyperelastic-based plastic and viscoplastic constitutive equations
• Chapter 10. Subloading-friction model: finite sliding theory
• Chapter 11. Comments on formulations for irreversible mechanical phenomena
• Appendix 1. Proofs for formula of scalar triple products with invariants
• Appendix 2. Convective stress rate tensors
• Appendix 3. Cauchy elastic and hypoelastic equations
• Bibliography
• Index