Chen / Saleeb Constitutive Equations for Engineering Materials

Elasticity and Modeling
1. Auflage 2013
ISBN: 978-1-4831-0196-5
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 37, 594 Seiten, Web PDF

Reihe: Studies in Applied Mechanics

Constitutive Equations for Engineering Materials, Volume 1: Elasticity and Modeling, Revised Edition focuses on theories on elasticity and plasticity of engineering materials. The book first discusses vectors and tensors. Coordinate systems, vector algebra, scalar products, vector products, transformation of coordinates, indicial notation and summation convention, and triple products are then discussed. The text also ponders on analysis of stress and strain and presents numerical analysis. The book then discusses elastic stress-strain relations. Basic assumptions; need for elastic models; isotropic linear stress-strain relations; principle of virtual work; strain energy and complementary energy density in elastic solids; and incremental relations grounded on secant moduli are described. The text also explains linear elasticity and failure criteria for concrete and non-linear elasticity and hypoelastic models for concrete. The selection further tackles soil elasticity and failure criteria. Mechanical behavior of soils; failure criteria of soils; and incremental stress-strain models based on modification of the isotropic linear elastic formulation are considered. The text is a good source of data for readers interested in studying the elasticity and plasticity of engineering materials.

Autoren/Hrsg.

Chen, Wai-Fah

Saleeb, Atef F.

Inhaltsverzeichnis

1;Front Cover;1
2;Constitutive Equations for Engineering Materials;4
3;Copyright Page;5
4;Preface to The second Edition ;8
5;Preface;10
6;Table of Contents;12
7;Notation;14
8;Introduction;16
9;PART ONE: BASIC CONCEPTS IN ELASTICITY;22
9.1;Chapter 1. Vectors and Tensors;24
9.1.1;1.1 INTRODUCTION;25
9.1.2;1.2 COORDINATE SYSTEM;25
9.1.3;1.3 VECTOR ALGEBRA;26
9.1.4;1.4 SCALAR PRODUCT;28
9.1.5;1.5 VECTOR PRODUCT;29
9.1.6;1.6 TRIPLE PRODUCTS;31
9.1.7;1.7 SCALAR AND VECTOR FIELDS;32
9.1.8;1.8 INDICIAL NOTATION AND SUMMATION CONVENTION;35
9.1.9;1.9 THE SYMBOL dij (KRONECKER DELTA);38
9.1.10;1.10 THE SYMBOL eijk (ALTERNATING TENSOR);39
9.1.11;1.11 TRANSFORMATION OF COORDINATES;45
9.1.12;1.12 DEFINITION OF CARTESIAN TENSORS;48
9.1.13;1.13 PROPERTIES OF TENSORS;51
9.1.14;1.14 ISOTROPIC TENSORS;54
9.1.15;1.15 QUOTIENT RULE;55
9.1.16;1.16 EXAMPLES—INDICIAL NOTATIONS;56
9.1.17;1.17 SURFACE-VOLUME INTEGRAL (DIVERGENCE THEOREM);58
9.1.18;1.18 PROBLEMS;60
9.2;Chapter 2. Analysis of Stress;63
9.2.1;2.1 INTRODUCTION;63
9.2.2;2.2 STATE OF STRESS AT A POINT;65
9.2.3;2.3 CAUCHY'S FORMULAE FOR STRESSES;73
9.2.4;2.4 PRINCIPAL AXES OF STRESSES;77
9.2.5;2.5 STATIONARY VALUES OF NORMAL AND SHEAR STRESSES;85
9.2.6;2.6 PURE SHEAR STATE;90
9.2.7;2.7 OCTAHEDRAL STRESSES;92
9.2.8;2.8 STRESS DEVIATOR TENSOR;97
9.2.9;2.9 EXAMPLE—COMPARISON OF TWO STATES OF STRESSES;101
9.2.10;2.10 MOHR'S GRAPHICAL REPRESENTATION FOR STRESSES;102
9.2.11;2.11 GEOMETRIC REPRESENTATION OF STRESS;112
9.2.12;2.12 EQUATIONS OF EQUILIBRIUM;117
9.2.13;2.13 PROBLEMS;120
9.3;Chapter 3. Analysis of Strain;124
9.3.1;3.1 INTRODUCTION;124
9.3.2;3.2 STATE OF STRAIN AT A POINT;126
9.3.3;3.3 CAUCHY'S FORMULAE FOR STRAINS;132
9.3.4;3.4 PRINCIPAL STRAINS;135
9.3.5;3.5 OCTAHEDRAL STRAINS;140
9.3.6;3.6 STRAIN DEVIATOR TENSOR;141
9.3.7;3.7 MOHR'S GRAPHICAL REPRESENTATION FOR STRAINS;143
9.3.8;3.8 STRAIN-DISPLACEMENT RELATIONSHIPS;146
9.3.9;3.9 EQUATIONS OF STRAIN COMPATIBILITY;154
9.3.10;3.10 PROBLEMS;155
9.4;Chapter 4. Elastic Stress—Strain Relations;157
9.4.1;4.1 INTRODUCTION;158
9.4.2;4.2 BASIC ASSUMPTIONS (HYPOTHESES);161
9.4.3;4.3 NEED FOR ELASTIC MATERIAL MODELS;162
9.4.4;4.4 DEFINITIONS;162
9.4.5;4.5 ISOTROPIC LINEAR ELASTIC STRESS-STRAIN RELATIONS (GENERALIZED HOOKE'S LAW);165
9.4.6;4.6 PRINCIPLE OF VIRTUAL WORK;179
9.4.7;4.7 STRAIN ENERGY AND COMPLEMENTARY ENERGY DENSITY IN ELASTIC SOLIDS;185
9.4.8;4.8 ANISOTROPIC, ORTHOTROPIC, AND TRANSVERSELY ISOTROPIC LINEAR (GREEN) ELASTIC STRESS-STRAIN RELATIONS;190
9.4.9;4.9 NONLINEAR ELASTIC STRESS-STRAIN RELATIONS;197
9.4.10;4.10 UNIQUENESS, STABILITY, NORMALITY, AND CONVEXITY FOR ELASTIC SOLIDS;218
9.4.11;4.11 INCREMENTAL (HYPOELASTIC) STRESS—STRAIN RELATIONS FOR ISOTROPIC MATERIALS;232
9.4.12;4.12 AN INCREMENTAL RELATION BASED ON SECANT MODULI;237
9.4.13;4.13 VARIABLE MODULI INCREMENTAL STRESS-STRAIN MODELS;245
9.4.14;4.14 SUMMARY;254
9.4.15;4.15 PROBLEMS;257
9.4.16;4.16 REFERENCES;263
10;PART TWO: CONCRETE ELASTICITY AND FAILURE CRITERIA;264
10.1;Chapter 5. Linear Elasticity and Failure Criteria for Concrete;266
10.1.1;5.1 INTRODUCTION;267
10.1.2;5.2 MECHANICAL BEHAVIOR OF CONCRETE;268
10.1.3;5.3 FAILURE CRITERIA;280
10.1.4;5.4 MOHR-COULOMB FAILURE CRITERION WITH A TENSION CUTOFF;303
10.1.5;5.5 FIVE-PARAMETER FAILURE MODEL;309
10.1.6;5.6 LINEAR ELASTIC-FRACTURE MODELS FOR CONCRETE;318
10.1.7;5.7 FURTHER REFINEMENT FOR MODELING FRACTURED CONCRETE;339
10.1.8;5.8 INTERACTION BETWEEN CONCRETE AND REINFORCEMENT;345
10.1.9;5.9 EXAMPLES OF FINITE ELEMENT APPLICATIONS;347
10.1.10;5.10 SUMMARY;357
10.1.11;5.11 REFERENCES;358
10.2;Chapter 6. Nonlinear Elasticity and Hypoelastic Models for Concrete;363
10.2.1;6.1 INTRODUCTION;364
10.2.2;6.2 GENERAL APPROACHES FOR NONLINEAR ELASTIC STRESS-STRAIN FORMULATIONS;365
10.2.3;6.3 A TOTAL STRESS-STRAIN MODEL BASED ON DECOUPLED SECANT MODULI Ks AND Gs;372
10.2.4;6.4 A TOTAL STRESS-STRAIN MODEL BASED ON COUPLED SECANT MODULI Ks AND Gs;384
10.2.5;6.5 A TOTAL STRESS-STRAIN MODEL BASED ON DECOUPLED SECANT MODULI Es AND vs CONSIDERING SOFTENING BEHAVIOR;386
10.2.6;6.6 TOTAL STRESS-STRAIN MODELS BASED ON GENERAL CAUCHY TYPE OF FORMULATION;394
10.2.7;6.7 INCREMENTAL STRESS-STRAIN MODELS BASED ON MODIFICATION OF ISOTROPIC LINEAR ELASTIC FORMULATION;398
10.2.8;6.8 AN INCREMENTAL BIAXIAL ORTHOTROPIC MODEL FOR MONOTONIC LOADING;407
10.2.9;6.9 AN INCREMENTAL BIAXIAL ORTHOTROPIC MODEL FOR CYCLIC LOADING;412
10.2.10;6.10 AN INCREMENTAL AXISYMMETRIC ORTHOTROPIC MODEL FOR CYCLIC LOADING;419
10.2.11;6.11 A FIRST-ORDER HYPOELASTIC MODEL;427
10.2.12;6.12 EXAMPLES OF FINITE ELEMENT APPLICATIONS;436
10.2.13;6.13 SUMMARY;449
10.2.14;6.14 REFERENCES;450
11;PART THREE SOIL ELASTICITY AND FAILURE CRITERIA;454
11.1;Chapter 7. Elastic Stress—Strain Relations and Failure Criteria for Soils;456
11.1.1;7.1 INTRODUCTION;457
11.1.2;7.2 MECHANICAL BEHAVIOR OF SOILS;462
11.1.3;7.3 FAILURE CRITERIA OF SOILS;482
11.1.4;7.4 GENERAL APPROACHES FOR NONLINEAR ELASTIC STRESS-STRAIN FORMULATIONS;504
11.1.5;7.5 A TOTAL STRESS–STRAIN MODEL BASED ON SECANT MODULI Gs AND vs;508
11.1.6;7.6 A THIRD-ORDER HYPERELASTIC MODEL;512
11.1.7;7.7 INCREMENTAL STRESS-STRAIN MODELS BASED ON MODIFICATION OF THE ISOTROPIC LINEAR ELASTIC FORMULATION;530
11.1.8;7.8 INCREMENTAL STRESS-STRAIN MODELS BASED ON COUPLED TANGENTIAL MODULI Kt AND Gt;543
11.1.9;7.9 A FIRST-ORDER HYPOELASTIC MODEL;547
11.1.10;7.10 VARIABLE MODULI MODELS;556
11.1.11;7.11 EXAMPLES OF FINITE ELEMENT APPLICATIONS;557
11.1.12;7.12 SUMMARY;569
11.1.13;7.13 REFERENCES;570
12;Answers to Selected Problems;575
13;Author Index;584
14;Subject Index;588