Efficient Thermo-Viscoplastic Analysis Using a Multi-Level hp-Finite Cell Method with Non-Negative Moment Fitting

TL;DR

This paper introduces an advanced multi-level hp-Finite Cell Method with non-negative moment fitting for efficient, accurate thermoviscoplastic simulations involving complex temperature-dependent behaviors.

Contribution

It extends the multi-level hp-Finite Cell Method with a novel NNMF quadrature scheme and adaptive refinement for improved efficiency in non-linear thermoviscoplastic analysis.

Findings

Reduced number of integration points with maintained accuracy.

Enhanced computational efficiency over standard methods.

Effective localized resolution of thermal and strain gradients.

Abstract

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.