Methods of Numerical Solution of Problems of Thermo-Plasticity Taking into Account the Stress Mode

This study presents advanced numerical methods for analyzing the elastic–plastic stress–strain behavior of compound bodies subjected to thermo-force loading. The constitutive equations utilized in the analysis incorporate considerations for the temperature-dependent properties of isotropic materials, stress mode variations, and deformation history. Specifically, these equations capture two nonlinear dependencies involving the invariants of the stress–strain state and the stress mode angle. To enhance algorithmic clarity, the relationships between stress and strain tensor components are reformulated into a generalized form of Hooke’s law, augmented with additional terms. The paper outlines a procedure for successive approximations to facilitate numerical computations. The findings of the numerical simulations are presented to provide valuable insights into the complex behavior of these compound bodies under diverse loading conditions.