A novel approach for accurate development of the incremental plastic multiplier and consistent tangent operator in thermo-elasto-plastic modeling of materials

In the present research, new and accurate equations were developed for the incremental plastic multiplier (IPM) and the consistent tangent operator (CTO) to solve numerical problems in thermo-elasto-plastic (TEP) processes using the finite element method (FEM). To ensure accuracy, all material hardening coefficients were treated as temperature-dependent, and no terms and their derivatives in the analytical-mathematical solution were ignored. Two UMAT (User MATerial) subroutines with temperature-independent and temperature-dependent parameters were programmed for the EP and TEP behavior, respectively. Finite element models were created using both the Abaqus (R) built-in material models and the newly developed UMAT subroutines, designated as the reference and new models, respectively. In the reference model, flow stress was implemented using tabulated plastic strain and temperature data available in Abaqus (R), while in the new model, the flow stress (yield function) was derived and numerically calculated based on the developed formulation. The new equations were successfully validated by comparing the results from the new model with those from the reference model. The developed IPM and CTO can be used for accurate predictions of strains, stresses, and temperatures in TEP problems, making them well-suited for industrial applications.