Possibility of Expressing Anisotropic Yield Functions of Metals using the Invariants of Stress Tensor

Abstract

Most of existing yield function have been developed base on the curve fitting of experimental data and also some theoretical effort have been done for deriving yield functions. Framework of invariant theory prepared valuable opportunity for modeling non‐linear constitutive equation that it is shown in the works of Rivlin. It has been tried using invariant theory for representation of yield function for isotropic material and it is shown that invariant theory could cover all yield functions needed for isotropic metals using a general equation. Therefore, in the present paper it has been tried to extend invariant theory for anisotropic materials. Results have shown that invariant theory have the capacity for deriving a general equation for representation of anisotropic yield function for orthotropic materials.