A multi-field decomposed model order reduction approach for thermo-mechanically coupled gradient-extended damage simulations

TL;DR

This paper introduces a novel multi-field decomposed model order reduction method for complex thermo-mechanical damage simulations, significantly reducing computational costs while maintaining accuracy.

Contribution

It proposes a new multi-field MOR technique based on snapshot decomposition and separate projections for each physical field, enhancing stability and precision in nonlinear, multi-physical problems.

Findings

Reduces computational expenses in damage simulations

Maintains high accuracy compared to traditional methods

Demonstrates effectiveness through numerical benchmarks

Abstract

Numerical simulations are crucial for comprehending how engineering structures behave under extreme conditions, particularly when dealing with thermo-mechanically coupled issues compounded by damage-induced material softening. However, such simulations often entail substantial computational expenses. To mitigate this, the focus has shifted towards employing model order reduction (MOR) techniques, which hold promise for accelerating computations. Yet, applying MOR to highly nonlinear, multi-physical problems influenced by material softening remains a relatively new area of research, with numerous unanswered questions. Addressing this gap, this study proposes and investigates a novel multi-field decomposed MOR technique, rooted in a snapshot-based Proper Orthogonal Decomposition-Galerkin (POD-G) projection approach. Utilizing a recently developed thermo-mechanically coupled gradient-extended damage-plasticity model as a case study, this work demonstrates that splitting snapshot vectors into distinct physical fields (displacements, damage, temperature) and projecting them onto separate lower-dimensional subspaces can yield more precise and stable outcomes compared to conventional methods. Through a series of numerical benchmark tests, our multi-field decomposed MOR technique demonstrates its capacity to significantly reduce computational expenses in simulations involving severe damage, while maintaining a high level of accuracy.