Analysis of finite elastoplastic deformations. Kinematics and constitutive equations

The main kinematic relations and constitutive equations, which are used for creating computational methods to investigate finite elastoplastic deformations are presented in the paper. The medium kinematics is considered along with the multiplicative concept of the full deformation gradient. The constitutive equations are deduced using the theory of flow and the second law of thermodynamics. As a result, a dependence of the stress tensor rate on the free energy function and the yield function is obtained.