Modern computer simulations make stress analysis easy. As they continue to replace classical mathematical methods of analysis, these software programs require users to have a solid understanding of the fundamental principles on which they are based.
Develop Intuitive Ability to Identify and Avoid Physically Meaningless Predictions
Applied Mechanics of Solids is a powerful tool for understanding how to take advantage of these revolutionary computer advances in the field of solid mechanics. Beginning with a description of the physical and mathematical laws that govern deformation in solids, the text presents modern constitutive equations, as well as analytical and computational methods of stress analysis and fracture mechanics. It also addresses the nonlinear theory of deformable rods, membranes, plates, and shells, and solutions to important boundary and initial value problems in solid mechanics.
The author uses the step-by-step manner of a blackboard lecture to explain problem solving methods, often providing the solution to a problem before its derivation is presented. This format will be useful for practicing engineers and scientists who need a quick review of some aspect of solid mechanics, as well as for instructors and students.
Select and Combine Topics Using Self-Contained Modules and Subsections
Borrowing from the classical literature on linear elasticity, plasticity, and structural mechanics, this book:
- Introduces concepts, analytical techniques, and numerical methods used to analyze deformation, stress, and failure in materials or components
- Discusses the use of finite element software for stress analysis
- Assesses simple analytical solutions to explain how to set up properly posed boundary and initial-value problems
- Provides an understanding of algorithms implemented in software code
Complemented by the author’s website, which features problem sets and sample code for self study, this book offers a crucial overview of problem solving for solid mechanics. It will help readers make optimal use of commercial finite element programs to achieve the most accurate prediction results possible.
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
Biography
Allan Bower is a professor of engineering at Brown University, where he teaches in the undergraduate mechanical engineering program and the graduate program in mechanics of solids. He earned undergraduate and graduate degrees from the University of Cambridge and spent a short period on the faculty at Cambridge before joining Brown in 1992. His research involves developing and using computer simulations to model deformation and failure in materials. Applications of interest include modeling wear, plasticity, and contact fatigue between contacting surfaces; fracture in composites and ceramics; and mechanical failure processes in microelectronic circuits.
"It’s an impressive piece of work. It covers an immense amount of material and is well written."
—James R. Barber, University of Michigan, Ann Arbor, USA"A valuable treatise in mechanics of solids."
—David L. McDowell, Georgia Institute of Technology, Atlanta, USA"This book is great for materials science and engineering students who are interested in both classic and state-of-the-art materials research. With both in-depth discussion and authoritative summary, it will be widely used in teaching and research in theoretical and computational mechanics of materials."
—Yanfei Gao, University of Tennessee, Knoxville, USA
