Continuum mechanics: constitutive equations and applications

In the previous chapters we've learned about the definition and meaning of the concepts of stress and strain. One is an objective measure of load and the other is an objective measure of deformation. In fluids, one talks about the rate of deformation as opposed to simply strain (i.e., deformation by itself). We all know, though, that deformation is caused by loads (i.e., there must be a relationship between stress and strain). A relationship between stress and strain (or rate-of-deformation tensor) is simply called a "constitutive equation." Below we will describe how such equations are formulated. Read more…
Abstract: In the previous chapters we've learned about the definition and meaning of the concepts of stress and strain. One is an objective measure of load and the other is an objective measure of deformation. In fluids, one talks about the rate of deformation as opposed to simply strain (i.e., deformation by itself). We all know, though, that deformation is caused by loads (i.e., there must be a relationship between stress and strain). A relationship between stress and strain (or rate-of-deformation tensor) is simply called a "constitutive equation." Below we will describe how such equations are formulated

Chapter 1 The Constitutive Equations of Elastic Solids and
Newtonian Fluids ……………………………………………………..1
Definition ……………………………………………………………….1
Hooken Elastic Solid …………………………………………………2
Newtonian Fluid …………………………………………………….20
Chapter 2 Introduction to the Equations for Conservation of
Mass and the Navier-Stokes Equations ……………………….25
Defintion ………………………………………………………………25
The Equation of Continuity (Conservation of Mass) …….25
The Navier-Stokes Equations…………………………………….28
Chapter 3 Torsion of Circular Shafts ………………………………………..35
Torsion of a Circular Shaft: A Classic Problem …………….35
Saint-Venant’s Theory of Torsion ……………………………….39
Chapter 4 Equations for Analysis of Beams
Under Bending Load ……………………………………………….51
Comparability Equations for Stresses …………………………51
Bending Under Terminal Couples ……………………………..53
Bending by Transverse Loading …………………………………55
Chapter 5 Analysis of Elasticity of a Plane Under Stress ……………….63
Plane strain ……………………………………………………………63
Generalized Plane Stress …………………………………………..65
Compatibility Equations Implied by Fundamental
2D Systems …………………………………………………………68
Solution of 2D problems Using Airy Stress Functions …..69
Solution by Polynomials …………………………………………..71
Plane Elasticity in Polar Coordinates ………………………….74
Axially Symmetric Problems ……………………………………..78
Stress Concentration Near a Circular Hole ………………….80
Index ………………………………………………………………………………………87
Contents

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