Incremental Carcass Theory of Polycrystalline Media at Large Elastic and Plastic Deformations

A two-level carcass theory as applied to media with a polycrystalline structure at large elastic and plastic deformation of crystals (crystal grains) is presented. The theory is incremental, in accordance with the incremental nature of governing equations of a crystal, which take into account the prehistory of its deformation in the medium. The theory is based on the field of carcass (macroscopic) displacements, which determines the material displacements of carcass points and carcass (macroscopic) deformations of the medium. At the macromechanical level, the equations of macroscopic deformation and motion are given in an incremental form. At the micromechanical (locally structural) level, incremental microboundary-value problems for nodal presentation blocks of the polycrystalline material are solved on the basis of carcass displacements and their increments. From the internal fields of nodal blocks and their increments found, the incremental macroscopic stresses are determined, which allow one to close the system of equations of the macromechanical level of analysis.