应用固体力学

　　This book is the result of a similar process. Some 15 years ago， I joined the faculty in thesolid mechanics group in the Division of Engineering at Brown University. I am a proudgraduate of an institution that considers inhaling the air once breathed by Isaac Newtonto be more educational than taking graduate courses. Consequently， I started at Brownwith lungs and head filled with erudite air but knowing far less about solid mechanics thanthe students in my classes. I have spent the intervening years attempting to remedy thissituation， principally by eavesdropping on the conversations of my colleagues， who are allgenuine and highly respected experts in solid mechanics. This book summarizes what Ihave learned.

　　Allan F. Bower，毕业于剑桥大学，目前就职于布朗大学。在1991年加入布朗担任助理教授之前，他是剑桥大学工程系的大学讲师。他目前担任布朗/通用汽车公司计算材料研究合作研究实验室的联合主任（与通用汽车公司的马克·韦布鲁奇博士）。

Preface， xxiii
Author， xxv
CHAPTER 1 Overview of Solid Mechanics
1．1 DEFINING A PROBLEM IN SOLID MECHANICS
1．1．1 Deciding What to Calculate
1．1．2 Defining the Geometry of the Solid
1．1．3 Defining Loading
1．1．4 Deciding What Physics to Include in the Model
1．1．5 Defining Material Behavior
1．1．6 A Representative Initial Value Problem in Solid Mechanics
1．1．7 Choosing a Method of Analysis
CHAPTER 2 Governin~ Equations
2．1 MATHEMATICAL DESCRIPTION OF SHAPE CHANGES IN SOLIDS
2．1．1 Displacement and Velocity Fields
2．1．2 Displacement Gradient and Deformation Gradient Tensors
2．1．3 Deformation Gradient Resulting from Two Successive Deformations
2．1．4 The Jacobian of the Deformation Gradient
2．1．5 Lagrange Strain Tensor
2．1．6 Eulerian Strain Tensor
2．1．7 Infinitesimal Strain Tensor
2．1．8 Engineering Shear Strains
2．1．9 Decomposition of Infinitesimal Strain into Volumetric and Deviatoric Parts
2．1．10 Infinitesimal Rotation Tensor
2．1．11 Principal Values and Directions of the Infinitesimal Strain Tensor
2．1．12 Cauchy-Green Deformation Tensors
2．1．13 Rotation Tensor and Left and Right Stretch Tensors
2．1．14 Principal Stretches
2．1．15 Generalized Strain Measures
2．1．16 The Velocity Gradient
2．1．17 Stretch Rate and Spin Tensors
2．1．18 Infinitesimal Strain Rate and Rotation Rate
2．1．19 Other Deformation Rate Measures
2．1．20 Strain Equations of Compatibility for Infinitesimal Strains
2．2 MATHEMATICAL DESCRIPTION OF INTERNAL FORCES IN SOLIDS
2．2．1 Surface Traction and Internal Body Force
2．2．2 Traction Acting on Planes within a Solid
2．2．3 Cauchy （True） Stress Tensor
2．2．4 Other Stress Measures： Kirchhoff， Nominal， and Material Stress Tensors
2．2．5 Stress Measures for Infinitesimal Deformations
2．2．6 Principal Stresses and Directions
2．2．7 Hydrostatic， Deviatoric， and yon Mises Effective Stress
2．2．8 Stresses near an External Surface or Edge： Boundary Conditions on Stresses
2．3 EQUATIONS OF MOTION AND EQUILIBRIUM FOR DEFORMABLE SOLIDS
2．3．1 Linear Momentum Balance in Terms of Cauchy Stress
2．3．2 Angular Momentum Balance in Terms of Cauchy Stress
2．3．3 Equations of Motion in Terms of Other Stress Measures
2．4 WORK DONE BY STRESSES： PRINCIPLE OF VIRTUAL WORK
2．4．1 Work Done by Cauchy Stresses
2．4．2 Rate of Mechanical Work in Terms of Other Stress Measures
2．4．3 Rate of Mechanical Work for Infinitesimal Deformations
2．4．4 The Principle of Virtual Work
2．4．5 The Virtual Work Equation in Terms of Other Stress Measures
2．4．6 The Virtual Work Equation for Infinitesimal Deformations
CHAPTER 3 Constitutive Models： Relations between Stress and Strain
3．1 GENERAL REQUIREMENTS FOR CONSTITUTIVE EQUATIONS
3．1．1 Thermodynamic Restrictions
3．1．2 Objectivity
3．1．3 Drucker Stability
3．2 LINEAR ELASTIC MATERIAL BEHAVIOR
3．2．1 Isotropic， Linear Elastic Material Behavior
3．2．2 Stress-Strain Relations for Isotropic， Linear Elastic Materials： Young's Modulus， Poisson's Ratio， and the Thermal Expansion Coefficient
3．2．3 Reduced Stress-Strain Equations for Plane Deformation of Isotropic Solids
3．2．4 Representative Values for Density and Elastic Constants of Isotropic Solids
3．2．5 Other Elastic Constants： Bulk， Shear， and Lame Modulus
3．2．6 Physical Interpretation of Elastic Constants for Isotropic Solids
3．2．7 Strain Energy Density for Isotropic Solids
3．2．8 Stress-Strain Relation for a General Anisotropic Linear Elastic Material： Elastic Stiffness and Compliance Tensors
3．2．9 Physical Interpretation of the Anisotropic Elastic Constants
3．2．10 Strain Energy Density for Anisotropic， Linear Elastic Solids
3．2．11 Basis Change Formulas for Anisotropic Elastic Constants
3．2．12 The Effect of Material Symmetry on Stress-Strain Relations for Anisotropic Materials
3．2．13 Stress-Strain Relations for Linear Elastic Orthotropic Materials
3．2．14 Stress-Strain Relations for Linear Elastic Transversely Isotropic Material
3．2．15 Representative Values for Elastic Constants of Transversely
Isotropic Hexagonal Close-Packed Crystals
3．2．16 Linear Elastic Stress-Strain Relations for Cubic Materials
3．2．17 Representative Values for Elastic Properties of Cubic Crystals and Compounds
3．3 HYPOELASTICITY： ELASTIC MATERIALS WITH A NONLINEAR STRESS-STRAIN RELATION UNDER SMALL DEFORMATION
3．4 GENERALIZED HOOKE'S LAW： ELASTIC MATERIALS SUBJECTED TO SMALL STRETCHES BUT LARGE ROTATIONS
3．5 HYPERELASTICITY： TIME-INDEPENDENT BEHAVIOR OF RUBBERS
AND FOAMS SUBJECTED TO LARGE STRAINS
3．5．1 Deformation Measures Used in Finite Elasticity
3．5．2 Stress Measures Used in Finite Elasticity
3．5．3 Calculating Stress-Strain Relations from the Strain Energy Density
3．5．4 A Note on Perfectly Incompressible Materials
……
CHAPTER 4 Solutions to Simple Boundary and Initial Value Problems
CHAPTER 5 Solutions for Linear Elastic Solids
CHAPTER 6 Solutions for Plastic Solids
CHAPTER 7 Finite Element Analysis： An Introduction
CHAPTER 8 Finite Element Analysis： Theory and Implementation
CHAPTER 9 Modeling Material Failure
CHAPTER 10 Solutions for Rods， Beams， Membranes， Plates， and Shells