Thermodynamically Consistent Anisotropic Plasticity Model

The objective of the work presented in this paper is to consider the thermodynamically consistent anisotropic plasticity model based on full decomposition of stress tensor into generalised deviatoric part and generalised spherical part of stress tensor. Two fundamental tensors α_ij and β_ij which represents anisotropic material properties are defined and can be considered as generalisations of the Kronecker delta symbol which plays the main role in the theory of isotropic materials. Using two fundamental tensors, α_ij and β_ij, the concept of total generalised “pressure” and pressure corresponding to the volumetric deformation are redefined. It is shown that the formulation of anisotropic plasticity in the case of incompressible plastic flow must be considered independently from the generalised hydrostatic “pressure”. Accordingly, a modification to the anisotropic Hill criterion is introduced. Based on experimental research which has been published, the modified Hill (1948, 1950) criterion for anisotropic elasto-plasticity is validated. The results are presented, discussed and future studies are outlined.