ABSTRACT

An isotropic material has the same properties in all directions. An anisotropic material may have different properties in different directions. There are many materials that have anisotropic material behavior. These materials may follow linear elasticity. If infinitesimal strain measure is assumed, there are six independent components of strain. In the absence of body moment, there are six stress components. If stress and strain components are linearly related, 36 coefficients are needed to express stress components in terms of the strain components. However, using the first law of thermodynamics and assuming the existence of a strain energy density function, it can be shown that there are only 21 distinct coefficients (Boresi et al. 1993). The elastic anisotropy is well described in many elasticity books such as Boresi et al. (1993). It will not be described in this chapter. The scope of this chapter is plastic anisotropy.