Linear elasticity

About: Linear elasticity is a research topic. Over the lifetime, 9080 publications have been published within this topic receiving 258684 citations.

Continuum mechanics for engineers

Abstract: Continuum Theory Continuum Mechanics Starting Over Notation Essential Mathematics Scalars, Vectors and Cartesian Tensors Tensor Algebra in Symbolic Notation - Summation Convention Indicial Notation Matrices and Determinants Transformations of Cartesian Tensors Principal Values and Principal Directions Tensor Fields, Tensor Calculus Integral Theorems of Gauss and Stokes Stress Principles Body and Surface Forces, Mass Density Cauchy Stress Principle The Stress Tensor Force and Moment Equilibrium Stress Tensor Symmetry Stress Transformation Laws Principal Stresses Principal Stress Directions Maximum and Minimum Stress Values Mohr's Circles For Stress Plane Stress Deviator and Spherical Stress States Octahedral Shear Stress Kinematics of Deformation and Motion Particles, Configurations, Deformations and Motion Material and Spatial Coordinates Langrangian and Eulerian Descriptions The Displacement Field The Material Derivative Deformation Gradients, Finite Strain Tensors Infinitesimal Deformation Theory Compatibility Equations Stretch Ratios Rotation Tensor, Stretch Tensors Velocity Gradient, Rate of Deformation, Vorticity Material Derivative of Line Elements, Areas, Volumes Fundamental Laws and Equations Material Derivatives of Line, Surface, and Volume Integrals Conservation of Mass, Continuity Equation Linear Momentum Principle, Equations of Motion Piola-Kirchhoff Stress Tensors, Lagrangian Equations of Motion Moment of Momentum (Angular Momentum) Principle Law of Conservation of Energy, The Energy Equation Entropy and the Clausius-Duhem Equation The General Balance Law Restrictions on Elastic Materials by the Second Law of Thermodynamics Invariance Restrictions on Constitutive Equations from Invariance Constitutive Equations Linear Elasticity Elasticity, Hooke's Law, Strain Energy Hooke's Law for Isotropic Media, Elastic Constants Elastic Symmetry Hooke's Law for Anisotropic Media Isotropic Elastostatics and Elastodynamics, Superposition Principle Saint-Venant Problem Plane Elasticity Airy Stress Function Linear Thermoelasticity Three-Dimensional Elasticity Classical Fluids Viscous Stress Tensor, Stokesian, and Newtonian Fluids Basic Equations of Viscous Flow, Navier-Stokes Equations Specialized Fluids Steady Flow, Irrotational Flow, Potential Flow The Bernoulli Equation, Kelvin's Theorem Nonlinear Elasticity Molecular Approach to Rubber Elasticity A Strain Energy Theory for Nonlinear Elasticity Specific Forms of the Strain Energy Exact Solution for an Incompressible, Neo-Hookean Material Linear Viscoelasticity Viscoelastic Constitutive Equations in Linear Differential Operator Form One-Dimensional Theory, Mechanical Models Creep and Relaxation Superposition Principle, Hereditary Integrals Harmonic Loadings, Complex Modulus, and Complex Compliance Three-Dimensional Problems, The Correspondence Principle Appendices Index

Hydraulic fracture mechanics

Abstract: Hydraulically Induced Fractures in the Petroleum and Related Industries. Linear Elasticity, Fracture Shapes and Induced Stresses. Stresses in Formations. Fracture Geometry. Rheology and Laminar Flow. Non-Laminar Flow and Solids Transport. Advanced Topics of Rheology and Fluid Mechanics. Material Balance. Coupling of Elasticity, Flow and Material Balance. Fracture Propagation. Fracture Height Growth (3D and P-3D Geometries). Appendix. References. Index.

Fundamentals of Micromechanics of Solids

Abstract: Preface. 1 Introduction. 1.1 Background and Motivation. 1.2 Objectives. 1.3 Organization of Book. 1.4 Notation Conventions. References. 2 Basic Equations of Continuum Mechanics. 2.1 Displacement and Deformation. 2.2 Stresses and Equilibrium. 2.3 Energy, Work, and Thermodynamic Potentials. 2.4 Constitutive Laws. 2.5 Boundary Value Problems for Small-Strain Linear Elasticity. 2.6 Integral Representations of Elasticity Solutions. Problems. Appendix 2.A. Appendix 2.B. Appendix 2.C. References. Suggested Readings. 3 Eigenstrains. 3.1 Definition of Eigenstrains. 3.2 Some Examples of Eigenstrains. 3.3 General Solutions of Eigenstrain Problems. 3.4 Examples. Problems. Appendix 3.A. Appendix 3.B. References. Suggested Readings. 4 Inclusions and Inhomogeneities. 4.1 Definitions of Inclusions and Inhomogeneities. 4.2 Interface Conditions. 4.3 Ellipsoidal Inclusion with Uniform Eigenstrains (Eshelby Solution). 4.4 Ellipsoidal Inhomogeneities. 4.5 Inhomogeneous Inhomogeneities. Problems. Appendix 4.A. Appendix 4.B. Suggested Readings. 5 Definitions of Effective Moduli of Heterogeneous Materials. 5.1 Heterogeneity and Length Scales. 5.2 Representative Volume Element. 5.3 Random Media. 5.4 Macroscopic Averages. 5.5 Hill's Lemma. 5.6 Definitions of Effective Modulus of Heterogeneous Media. 5.7 Concentration Tensors and Effective Properties. Problems. Suggested Readings. 6 Bounds for Effective Moduli. 6.1 Classical Variational Theorems in Linear Elasticity. 6.2 Voigt Upper Bound and Reuss Lower Bound. 6.3 Extensions of Classical Variational Principles. 6.4 Hashin-Shtrikman Bounds. Problems. Appendix 6.A. References. Suggested Readings. 7 Determination of Effective Moduli. 7.1 Basic Ideas of Micromechanics for Effective Properties. 7.2 Eshelby Method. 7.3 Mori-Tanaka Method. 7.4 Self-Consistent Methods for Composite Materials. 7.5 Self-Consistent Methods for Polycrystalline Materials. 7.6 Differential Schemes. 7.7 Comparison of Different Methods. Problems. Suggested Readings. 8 Determination of the Effective Moduli-Multiinclusion Approaches. 8.1 Composite-Sphere Model. 8.2 Three-Phase Model. 8.3 Four-Phase Model. 8.4 Multicoated Inclusion Problem. Problems. Appendix 8.A. Appendix 8.B. Appendix 8.C. References. Suggested Readings. 9 Effective Properties of Fiber-Reinforced Composite Laminates. 9.1 Unidirectional Fiber-Reinforced Composites. 9.2 Effective Properties of Multilayer Composites. 9.3 Effective Properties of a Lamina. 9.4 Effective Properties of a Laminated Composite Plate. Problems. Appendix 9.A. References. Suggested Readings. 10 Brittle Damage and Failure of Engineering Composites. 10.1 Imperfect Interfaces. 10.2 Fiber Bridging. 10.3 Transverse Matrix Cracks. Problems. Appendix 10.A. References. Suggested Readings. 11 Mean Field Theory for Nonlinear Behavior. 11.1 Eshelby's Solution and Kro..ner's Model. 11.2 Applications. 11.3 Time-Dependent Behavior of Polycrystalline Materials: Secant Approach. Problems. References. 12 Nonlinear Properties of Composites Materials: Thermodynamic Approaches. 12.1 Nonlinear Behavior of Constituents. 12.2 Effective Potentials. 12.3 The Secant Approach. Problems. Suggested Readings. 13 Micromechanics of Martensitic Transformation in Solids. 13.1 Phase Transformation Mechanisms at Different Scales. 13.2 Application: Thermodynamic Forces and Constitutive Equations for Single Crystals. 13.3 Overall Behavior of Polycrystalline Materials with Phase Transformation. Problems. References. Suggested Readings. Index.