Efficient Thermo-Viscoplastic Analysis Using a Multi-Level hp-Finite Cell Method with Non-Negative Moment Fitting
For researchers in computational mechanics, this method improves the efficiency of simulating complex thermo-mechanical problems with history-dependent material behavior.
The paper extends the multi-level hp Finite Cell Method to efficiently simulate thermo-viscoplastic problems with temperature-dependent materials, using a non-negative moment fitting quadrature scheme that reduces integration points while maintaining accuracy, achieving substantial computational savings.
An extension of the multi-level hp Finite Cell Method is proposed for the simulation of thermoviscoplastic problems with temperature-dependent material behavior. The approach combines hierarchical adaptive refinement with a non-negative moment fitting (NNMF) quadrature scheme for efficient and robust integration of non-linear, history-dependent constitutive models on cut cells. The NNMF formulation yields sparse, positive quadrature rules that significantly reduce the number of integration points while maintaining stability and accuracy. An error-indicator-driven hp-refinement strategy enables localized resolution of strain and thermal gradients during the non-linear solution process. The framework is implemented within a partitioned thermo-mechanical scheme and evaluated on benchmark and application-oriented examples. The results demonstrate improved accuracy and substantial computational savings compared to standard integration approaches.