Constitutive Models for Anisotropic Materials Susceptible to Loading Conditions

Abstract

The mechanical behavior of many structural materials displays anisotropic elastic and plastic properties in different degree. Along with anisotropy, their behavior may demonstrate the asymmetry in the mechanical properties. The simplest example of this asymmetry is the difference of the deformation characteristics or the yield limits under conditions of tension and compression in the same directions in a material. Generally the mechanical properties of materials may be expressed as the functions of direction of the applied load and some parameters of the stress state type. In some of recently proposed theories of elasticity and plasticity different from the classic isotropic theories based on the Hooke’s law and Tresca or von Mises yield criteria, the anisotropy and asymmetry of the mechanical properties in some degree are involved, but the formulation of general equations that may be easily used in engineering is still a challenged problem. In this paper, generalized constitutive equations for the description of elastic and plastic behavior of anisotropic materials with stress state dependent properties are considered.