PRINCIPLES FOR CONSTITUTIVE EQUATIONS AND EXPRESSIONS OF ANISOTROPY IN SOIL MATERIALS

Abstract

Much attention has been paid to anisotropic behavior of soils, such as the inherent anisotropy and the stress induced anisotropy. Nevertheless, they often appear in the literature without any clear definitions. In the theory of finite deformations, the concept of isotropy is well established and is clearly distinguishable from the objectivity. However, in the infinitesimal theory, which is usually assumed in soil mechanics, they seem to be in confusion and, as a result, even simple anisotropy is not clearly defined. In this paper, we therefore first discuss the general principles of constitutive equations in finite theories and in infinitesimal theories to make a clear distinction between the objectivity and the isotropy. One of our most important results is that, if reference vectors or tensors are employed, in infinitesimal theories, the objectivity requires that anisotropic materials can be represented by isotropic functions. Using a reference tensor, we finally give a clear definition of the inherent anisotropy and the stress induced anisotropy. We then examine their difinitions employing a concrete example and show how the principles derived are useful, including the failure condition and the materials of differential type.