Applied Mechanics of Solids
Applied Mechanics of Solids
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DOI：
10.1201/9781439802489
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发表时间：
2009-10
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影响因子：
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通讯作者：
A. Bower
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文献类型：
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作者：
A. Bower
1固体力学概述定义固体力学中的一个问题2控制方程固体形状变化的数学描述固体中作用力的数学描述可变形固体的运动方程和平衡方程应力做功：虚功原理3本构模型：应力和应变之间的关系本构方程的一般要求线性弹性材料行为亚弹性：在小变形下具有非线性应力-应变关系的弹性材料广义虎克定律：承受小拉伸但大旋转的弹性材料超弹性：承受大应变的橡胶和泡沫的时间依赖性行为线性粘弹性材料：聚合物在小应变下的时间依赖性行为小应变，速率依赖性塑性：加载金属超过屈服小应变粘塑性：晶体的蠕变和高应变率变形大应变，费率-相关塑性大应变粘弹性临界状态模型金属单晶本构模型固体接触面和界面本构模型4简单边界的解拟静力线性弹性问题的轴对称解和球对称解拟静力弹塑性问题的轴对称解和球对称解拟静力弹塑性问题的球对称解线弹性材料静态大应变问题的简单动力学解线弹性固体的5种解一般原理平面应力应变的Airy函数解静态线弹性问题的复解平面应变静态线弹性问题的变元解三维静态线弹性问题的解各向异性线弹性固体广义平面问题的解各向同性线弹性固体动力问题的解解静态线弹性问题的能量法互易定理及其应用弹性固体位错几何弹性固体固有频率估计的里兹方法6塑性固体的解滑移线场理论塑性中的边界定理及其应用7有限元分析：简介有限元软件使用指南一个简单的有限元8有限元分析：静力线性弹性广义有限元法的理论与实现动力线性弹性有限元法非线性有限元法（亚弹性）材料大变形有限元法：超弹性材料粘塑性有限元法高级单元公式：不兼容模式，集成度降低，示例FEA程序和输入文件的混合元素列表9静态和循环载荷下断裂和疲劳机制的建模材料失效总结基于应力和应变的断裂和疲劳准则模拟裂纹扩展的失效：线性弹性断裂力学断裂力学能量方法塑性断裂力学界面的线性弹性断裂力学杆、梁、膜、板和壳的10种解决方案简介：细长杆运动和变形的矢量和张量的并矢记法--变形杆精确一般理论的简化弹性杆运动和薄壳变形的简单问题的解：一般理论一般壳理论的简化版本：平板和薄膜简单问题的解涉及薄膜、板和壳附录A：矢量和矩阵的复习A.1. A.2.矢量矢量场和矢量计算A.3.附录B：张量及其性质简介张量的基本性质B.2.二阶张量上的运算B.3.特殊张量附录C：向量和张量运算的索引符号C.1。向量和张量分量C.2.索引符号的约定和特殊符号C.3.索引符号规则C.4.使用索引符号表示的向量运算C.5.用指数表示法表示的张量运算C.6.使用索引符号计算C.7.附录D：极坐标系中的向量和张量运算D.1.球极坐标D.2.圆柱极坐标附录E：其他推导E.1。四面体各面面积之间的关系E.2.变形前后面积元素之间的关系E.3.变形固体中体积积分的时间导数E.4.变形杆曲率向量的时间导数参考文献
1 Overview of Solid Mechanics DEFINING A PROBLEM IN SOLID MECHANICS 2 Governing Equations MATHEMATICAL DESCRIPTION OF SHAPE CHANGES IN SOLIDS MATHEMATICAL DESCRIPTION OF INTERNAL FORCES IN SOLIDS EQUATIONS OF MOTION AND EQUILIBRIUM FOR DEFORMABLE SOLIDS WORK DONE BY STRESSES: PRINCIPLE OF VIRTUAL WORK 3 Constitutive Models: Relations between Stress and Strain GENERAL REQUIREMENTS FOR CONSTITUTIVE EQUATIONS LINEAR ELASTIC MATERIAL BEHAVIORSY HYPOELASTICITY: ELASTIC MATERIALS WITH A NONLINEAR STRESS-STRAIN RELATION UNDER SMALL DEFORMATION GENERALIZED HOOKE'S LAW: ELASTIC MATERIALS SUBJECTED TO SMALL STRETCHES BUT LARGE ROTATIONS HYPERELASTICITY: TIME-INDEPENDENT BEHAVIOR OF RUBBERS AND FOAMS SUBJECTED TO LARGE STRAINS LINEAR VISCOELASTIC MATERIALS: TIME-DEPENDENT BEHAVIOR OF POLYMERS AT SMALL STRAINS SMALL STRAIN, RATE-INDEPENDENT PLASTICITY: METALS LOADED BEYOND YIELD SMALL-STRAIN VISCOPLASTICITY: CREEP AND HIGH STRAIN RATE DEFORMATION OF CRYSTALLINE SOLIDS LARGE STRAIN, RATE-DEPENDENT PLASTICITY LARGE STRAIN VISCOELASTICITY CRITICAL STATE MODELS FOR SOILS CONSTITUTIVE MODELS FOR METAL SINGLE CRYSTALS CONSTITUTIVE MODELS FOR CONTACTING SURFACES AND INTERFACES IN SOLIDS 4 Solutions to Simple Boundary and Initial Value Problems AXIALLY AND SPHERICALLY SYMMETRIC SOLUTIONS TO QUASI-STATIC LINEAR ELASTIC PROBLEMS AXIALLY AND SPHERICALLY SYMMETRIC SOLUTIONS TO QUASI-STATIC ELASTIC-PLASTIC PROBLEMS SPHERICALLY SYMMETRIC SOLUTION TO QUASI-STATIC LARGE STRAIN ELASTICITY PROBLEMS SIMPLE DYNAMIC SOLUTIONS FOR LINEAR ELASTIC MATERIALS 5 Solutions for Linear Elastic Solids GENERAL PRINCIPLES AIRY FUNCTION SOLUTION TO PLANE STRESS AND STRAIN STATIC LINEAR ELASTIC PROBLEMS COMPLEX VARIABLE SOLUTION TO PLANE STRAIN STATIC LINEAR ELASTIC PROBLEMS SOLUTIONS TO 3D STATIC PROBLEMS IN LINEAR ELASTICITY SOLUTIONS TO GENERALIZED PLANE PROBLEMS FOR ANISOTROPIC LINEAR ELASTIC SOLIDS SOLUTIONS TO DYNAMIC PROBLEMS FOR ISOTROPIC LINEAR ELASTIC SOLIDS ENERGY METHODS FOR SOLVING STATIC LINEAR ELASTICITY PROBLEMS THE RECIPROCAL THEOREM AND APPLICATIONS ENERGETICS OF DISLOCATIONS IN ELASTIC SOLIDS RAYLEIGH-RITZ METHOD FOR ESTIMATING NATURAL FREQUENCY OF AN ELASTIC SOLID 6 Solutions for Plastic Solids SLIP-LINE FIELD THEORY BOUNDING THEOREMS IN PLASTICITY AND THEIR APPLICATIONS 7 Finite Element Analysis: An Introduction A GUIDE TO USING FINITE ELEMENT SOFTWARE A SIMPLE FINITE ELEMENT PROGRAM 8 Finite Element Analysis: Theory and Implementation GENERALIZED FEM FOR STATIC LINEAR ELASTICITY THE FEM FOR DYNAMIC LINEAR ELASTICITY FEM FOR NONLINEAR (HYPOELASTIC) MATERIALS FEM FOR LARGE DEFORMATIONS: HYPERELASTIC MATERIALS THE FEM FOR VISCOPLASTICITY ADVANCED ELEMENT FORMULATIONS: INCOMPATIBLE MODES, REDUCED INTEGRATION, AND HYBRID ELEMENTS LIST OF EXAMPLE FEA PROGRAMS AND INPUT FILES 9 Modeling Material Failure SUMMARY OF MECHANISMS OF FRACTURE AND FATIGUE UNDER STATIC AND CYCLIC LOADING STRESS- AND STRAIN-BASED FRACTURE AND FATIGUE CRITERIA MODELING FAILURE BY CRACK GROWTH: LINEAR ELASTIC FRACTURE MECHANICS ENERGY METHODS IN FRACTURE MECHANICS PLASTIC FRACTURE MECHANICS LINEAR ELASTIC FRACTURE MECHANICS OF INTERFACES 10 Solutions for Rods, Beams, Membranes, Plates, and Shells PRELIMINARIES: DYADIC NOTATION FOR VECTORS AND TENSORS MOTION AND DEFORMATION OF SLENDER RODS SIMPLIFIED VERSIONS OF THE GENERAL THEORY OF DEFORMABLE ROD EXACT SOLUTIONS TO SIMPLE PROBLEMS INVOLVING ELASTIC RODS MOTION AND DEFORMATION OF THIN SHELLS: GENERAL THEORY SIMPLIFIED VERSIONS OF GENERAL SHELL THEORY: FLAT PLATES AND MEMBRANES SOLUTIONS TO SIMPLE PROBLEMS INVOLVING MEMBRANES, PLATES, AND SHELLS Appendix A: Review of Vectors and Matrices A.1. VECTORS A.2. VECTOR FIELDS AND VECTOR CALCULUS A.3. MATRICES Appendix B: Introduction to Tensors and Their Properties B.1. BASIC PROPERTIES OF TENSORS B.2. OPERATIONS ON SECOND-ORDER TENSORS B.3. SPECIAL TENSORS Appendix C: Index Notation for Vector and Tensor Operations C.1. VECTOR AND TENSOR COMPONENTS C.2. CONVENTIONS AND SPECIAL SYMBOLS FOR INDEX NOTATION C.3. RULES OF INDEX NOTATION C.4. VECTOR OPERATIONS EXPRESSED USING INDEX NOTATION C.5. TENSOR OPERATIONS EXPRESSED USING INDEX NOTATION C.6. CALCULUS USING INDEX NOTATION C.7. EXAMPLES OF ALGEBRAIC MANIPULATIONS USING INDEX NOTATION Appendix D: Vectors and Tensor Operations in Polar Coordinates D.1. SPHERICAL-POLAR COORDINATES D.2. CYLINDRICAL-POLAR COORDINATES Appendix E: Miscellaneous Derivations E.1. RELATION BETWEEN THE AREAS OF THE FACES OF A TETRAHEDRON E.2. RELATION BETWEEN AREA ELEMENTS BEFORE AND AFTER DEFORMATION E.3. TIME DERIVATIVES OF INTEGRALS OVER VOLUMES WITHIN A DEFORMING SOLID E.4. TIME DERIVATIVES OF THE CURVATURE VECTOR FOR A DEFORMING ROD References