Influence of Anisotropy of Linear Compression Modules on the Process of Deformation of Anisotropic Materials

The possibility of modeling elastoplastic deformations in materials characterized by anisotropy of elastic and plastic properties without restrictions on the anisotropy magnitude of linear compressibility of the material is shown. The mathematical model of elastoplastic deformation of anisotropic materials is applicable for symmetry cases when it is possible to decompose the elastic deformation energy into the volume change energy and the shape change energy. To simulate the processes of deformation of anisotropic materials by the dynamic finite element method, the anisotropic pressure caused by uniform volumetric deformation is introduced into the difference scheme instead of the isotropic pressure. In this case, the total stress tensor is uniquely decomposed into the anisotropic pressure tensor and the total stress tensor deviator. A criterion is given for the possibility of using the anisotropic pressure when modeling the elastic-plastic deformation in anisotropic materials instead of the spherical part of the stress tensor within the framework of the model of a volume-isotropic material.