(BQ) Part 2 book "Introduction to continuum mechanics" has contents: The elastic solid (linear isotropic elastic solid; constitutive equation for isotropic elastic solid under large deformation), newtonian viscous fluid, integral formulation of general principles, non newtonian fluids. | 5 The Elastic Solid So far we have studied the kinematics of deformation, the description of the state of stress and four basic principles of continuum physics: the principle of conservation of mass [Eq. ()], the principle of linear momentum [Eq. ()], the principle of moment of momentum [Eq. ()] and the principle of conservation of energy [Eq. ()]. All these relations are valid for every continuum, indeed no mention was made of any material in the derivations. These equations are however not sufficient to describe the response of a specific material due to a given loading. We know froiu experience that under the same loading conditions, the response of steel is different from that of water. Furthermore, for a given material, it varies with different loading conditions. For example, for moderate loadings, the deformation in steel caused by the application of loads disappears with the removal of the loads. This aspect of the material behavior is known as elasticity. Beyond a certain level of loading, there will be permanent deformations, or even fracture exhibiting behavior quite different from that of elasticity. In this chapter, we shall study idealized materials which model the elastic behavior of real solids. The linear isotropic elastic model will be presented in part A, followed by the linear anisotropic elastic model in part B and an incompressible isotropic nonlinear elastic model in part C. Mechanical Properties We want to establish some appreciation of the mechanical behavior of solid materials. To do this, we perform some thought experiments modeled after real laboratory experiments. Suppose from a block of material, we cut out a slender cylindrical test specimen of cross-sectional area^t The bar is now statically tensed by an axially applied load /*, and the elongation A/, over some axial gage length/, is measured. A typical plot of tensile force against elongation is shown in Fig. . Within the linear portion OA .
