A local constitutive model with anisotropy for various homogeneous 2D biaxial deformation modes

A local constitutive model for granular materials with anisotropy is proposed and applied to different biaxial box deformation modes. The simplified version of the model (in the coordinate system of the biaxial box) involves only scalar values for hydrostatic and shear stresses, for the isotropic and shear strains as well as the new parameter, the (scalar) anisotropy modulus. A non-linear constitutive evolution equation, for both shear stress and anisotropy, during deviatoric (shear) deformation is based on observations gained from Discrete Element Method (DEM) simulations. While parameters like the bulk modulus are set to constant, for the sake of simplicity, the model involves a yield stress and a maximal anisotropy as well as the corresponding deviatoric shear-rate pre-factors for incremental stress and incremental anisotropy modulus. In this study, the self-consistency of the simple-most model is discussed before it is applied to various bi-axial deformation modes. Constant anisotropy is compared to evolving anisotropy, where the sign accounts for the direction (tension or compression corresponds to positive or negative strain, respectively). Generalization to arbitrary orientation and possible non-coaxial strain, stress and fabric tensors is not yet attempted in this study.