Introduction to Finite Strain Theory for Continuum Elasto-Plasticity

Koichi Hashiguchi, Yuki Yamakawa

• Publisher: Wiley
• Year: 2012
• ISBN:
  9781118437735
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Mechanics

Comprehensive introduction to finite elastoplasticity, addressing various analytical and numerical analyses & including state-of-the-art theories

Introduction to Finite Elastoplasticity presents introductory explanations that can be readily understood by readers with only a basic knowledge of elastoplasticity, showing physical backgrounds of concepts in detail and derivation processes of almost all equations. The authors address various analytical and numerical finite strain analyses, including new theories developed in recent years, and explain fundamentals including the push-forward and pull-back operations and the Lie derivatives of tensors.

As a foundation to finite strain theory, the authors begin by addressing the advanced mathematical and physical properties of continuum mechanics. They progress to explain a finite elastoplastic constitutive model, discuss numerical issues on stress computation, implement the numerical algorithms for stress computation into large-deformation finite element analysis and illustrate several numerical examples of boundary-value problems. Programs for the stress computation of finite elastoplastic models explained in this book are included in an appendix, and the code can be downloaded from an accompanying website.

Table of contents

• INTRODUCTION TO FINITE STRAIN THEORY FOR CONTINUUM ELASTO-PLASTICITY
• Contents
• Preface
• Series Preface
• Introduction
• 1 Mathematical Preliminaries
• 2 General (Curvilinear) Coordinate System
• 3 Description of Physical Quantities in Convected Coordinate System
• 4 Strain and Strain Rate Tensors
• 5 Convected Derivative
• 6 Conservation Laws and Stress (Rate) Tensors
• 7 Hyperelasticity
• 8 Finite Elasto-Plastic Constitutive Equation
• 9 Computational Methods for Finite Strain Elasto-Plasticity
• 10 Computer Programs
• A Projection of Area
• B Geometrical Interpretation of Strain Rate and Spin Tensors
• C Proof for Derivative of Second Invariant of Logarithmic-Deviatoric Deformation Tensor
• D Numerical Computation of Tensor Exponential Function and Its Derivative
• References
• Index