Nonlinear Continuum Mechanics and Large Inelastic Deformations

By Yu I. Dimitrienko

Book Overview

Preface.- Introduction. Fundamental Axioms of Continuum Mechanics.- 1. Kinematics of Continua .- 1.1. Material and Spatial Descriptions of Continuum Motion .- 1.2. Deformation Tensors and Measures.- 1.3. Polar Decomposition.- 1.4. Rate Characteristics of Continuum .- 1.5. Co-rotational Derivatives.- 2. Balance Laws.- 2.1. The Mass Conservation Law.- 2.2. The Momentum Balance Law and the Stress Tensor.- 2.3. The Angular Momentum Balance Law.- 2.4. The First Thermodynamic Law.- 2.5. The Second Thermodynamic Law .- 2.6. Deformation Compatibility Equations.- 2.7. Dynamic Compatibility Equations .- 2.8. Compatibility Equations for Deformation Rates.- 2.9. The Complete System of Continuum Mechanics.- 3. Constitutive Equations .- 3.1. Basic Principles for Derivation of Constitutive Equations.- 3.2. Energetic and Quasienergetic Couples of Tensors .- 3.3. The Principal Thermodynamic Identity.- 3.4. Principles of Thermodynamically Consistent Determinism, Equipresence and Local Action .- 3.5. Definition of Ideal Continua .- 3.6. The Principle of Material Symmetry.- 3.7. Definition of Fluids and Solids.- 3.8. Corollaries of the Principle of Material Symmetry and Constitutive Equations for Ideal Continua .- 3.9. Incompressible continua.- 3.10. The Principle of Material Indifference.- 3.11. Relationships in a Moving System.- 3.12. The Onsager Principle .- 4. Relations at Singular Surfaces .- 4.1. Relations at a Singular Surface in the Material Description.- 4.2. Relations at a Singular Surface in the Spatial Description .- 4.3. Explicit Form of Relations at a Singular Surface.- 4.4. The Main Types of Singular.- 5. Elastic Continua at Large Deformations .- 5.1. Closed Systems in the Spatial Description .- 5.2. Closed Systems in the Material Description .- 5.3. Statements of Problems for Elastic Continua at Large Deformations .- 5.4. The problem on an Elastic Beam in Tension.- 5.5. Tension of an Incompressible Beam .- 5.6. Simple Shear .- 5.7. The Lam? Problem.- 5.8. The Lam? Problem for an Incompressible Continuum.- 6. Continua of the Differential Type .- 6.1. Models An and Bn of Continua of the Differential Type .- 6.2. Models An and Bn of Fluids of the Differential Type .- 6.3. Models Cn and Dn of Continua of the Differential Type .- 6.4. The Problem on a Beam in Tension .- 7. Viscoelastic Continua at Large Deformations.- 7.1. Viscoelastic Continua of the Integral Type .- 7.2. Principal, Quadratic and Linear Models of Viscoelastic Continua .- 7.3. Models of Incompressible Viscoelastic Solids and Viscoelastic Fluids .- 7.4. Statements of Problems in Viscoelasticity Theory at Large Deformations.- 7.5. The Problem on Uniaxial Deforming of a Viscoelastic Beam .- 7.6. Dissipative Heating of a Viscoelastic Continuum under Cyclic Deforming.- 8. Plastic Continua at Large Deformations .- 8.1. Models An of Plastic Continua at Large Deformations .- 8.2. Models Bn of Plastic Continua .- 8.3. Models Cn and Dn of Plastic Continua .- 8.4. Constitutive Equations of Plasticity Theory 'in Rates' .- 8.5. Statements of Problems in Plasticity Theory .- 8.6. The Problem on All-Round Tension-Compression of a Plastic Continuum.- 8.7. The Problem on Tension of a Plastic Beam .- 8.8. Plane Waves in Plastic Continua .- 8.9. Models of Viscoplastic Continua .- References .- Basic Notation.- Subject Index.

• Format: Hardcover
• Language: English
• ISBN: 9400700334
• ISBN13: 9789400700338
• Release Date: November 2010
• Publisher: Springer
• Length: 721 Pages
• Weight: 2.68 lbs.
• Dimensions: 1.6" x 6.1" x 9.2"