Discrete Empirical Interpolation Method for nonlinear softening problems involving damage and plasticity

TL;DR

This paper introduces a reduced order modeling approach using POD-based DEIM combined with an arc-length method to efficiently simulate complex damage and plasticity behaviors in nonlinear softening problems, significantly reducing computational effort.

Contribution

It presents a novel integration of DEIM and arc-length methods for reduced order modeling of damage-plasticity models with softening, validated through complex numerical examples.

Findings

High accuracy reduced models achieved

Significant speedup in simulations

Effective handling of damage and plasticity behaviors

Abstract

Accurate simulations are essential for engineering applications, and intricate continuum mechanical material models are constructed to achieve this goal. However, the increasing complexity of the material models and geometrical properties lead to a significant increase in computational effort. Model order reduction aims to implement efficient methods for accelerating the simulation process while preserving a high degree of accuracy. Numerous studies have already demonstrated the benefits of this method for linear elastic material modeling. However, in the present work, we investigate a two-surface gradient-extended damage-plasticity model. We conducted complex simulations with this model, demonstrating both damage behavior and softening. The POD-based discrete empirical interpolation method (DEIM) is introduced and implemented. To accomplish simulations with DEIM and softening behaviour, we propose the implementation of a reduced form of the arc-length method. Existing research on calculating models with both damage and softening behavior using the DEIM and arc-length method is limited. To validate the methods, two numerical examples are thoroughly investigated in this study: a plate with a hole and an asymmetrically notched specimen. The results show that the proposed methods can create a reduced order model with high accuracy and a significant speedup of the simulation. For both examples, the analysis is conducted in three steps: first, plasticity without damage is examined, followed by damage without plasticity, and finally, the combination of plasticity and damage is investigated.