Efficient hyper reduced-order model (HROM) for parametric studies of the 3D thermo-elasto-plastic calculation

• The improved hyper-reduced order model is developed.
• The 3D thermo-elasto-plastic problem is resolved with three reduced bases.
• The Grassmann manifold interpolation is employed for generating new POD bases.
• The parametric studies are performed on varying thermal load and yield stress.
• A gain of CPU 25 is obtained for the parametric studies with errors smaller than 10%.

This paper focuses on a 3D thermo-elasto-plastic localized thermal source simulation and its parametric analysis with high CPU efficiency in the reduced-order model (ROM) framework. The hyper reduced-order model (HROM) is introduced and improved with two choices. Firstly, three reduced bases are constructed: one for the displacement increments, one for the plastic strain increments and one for the stress state. Equilibrium equation in plasticity relies on the knowledge of plastic strain rate, hence the plastic strain has to be included into the variable to be reduced, and the incremental form is adopted in the paper. It is shown that the introduction of an extra stress basis greatly improves the quality and the efficiency of the ROM. Secondly, the reduced state variables of plastic strain increments are determined in a reduced integration domain. Concerning the parametric analysis, the interpolation of the reduced bases is based on the Grassmann manifold, which permits to generate the new proper orthogonal decomposition bases for the modified parameters. In order to increase the convergence rate, the plastic strain interpolated from snapshots (the reference cases with full FEM calculations) is considered as the initial value of each time step for the modified problem of parametric studies. As a result, the plastic calculation is always done on the confined domain and only a few iterations are then required to reach static and plastic admissibility for each time step. The parametric studies on varying thermal load and yield stress show high versatility and efficiency of the HROM coupled with Grassmann manifold interpolation. A gain of CPU time of 25 is obtained for both cases with a level of accuracy smaller than 10%.