A unified multi-perspective quadratic manifold for mitigating the Kolmogorov barrier in multiphysics damage

TL;DR

This paper introduces a novel multi-perspective quadratic manifold-based reduced-order model that effectively captures complex nonlinear damage evolution in multiphysics problems, overcoming the limitations of traditional linear ROMs caused by the Kolmogorov barrier.

Contribution

It proposes a unified multi-perspective quadratic manifold framework with a multi-field and multi-state decomposition strategy for improved modeling of damage in multiphysics simulations.

Findings

Mitigates the Kolmogorov barrier in linear ROMs

Ensures smooth and monotonic error reduction with increasing modes

Demonstrates robustness and efficiency in multiphysics damage problems

Abstract

In multiphysics damage problems, material degradation is often modeled using local or global damage variables, whose evolution introduces strong nonlinearities and significant computational costs. Linear projection-based reduced-order models (ROMs) are widely used to accelerate these simulations but often fail to capture complex nonlinear damage evolution effectively. This limitation arises from the slow decay of the Kolmogorov n-width, which leads to a phenomenon known as the Kolmogorov barrier in linear approximation. To overcome this challenge, this study proposes a novel unified multi-perspective (multi-field and multi-state) quadratic manifold-based ROM framework for thermo-mechanically coupled damage-plasticity problems. A key feature lies in a multi-field and multi-state decomposition strategy that is grounded in the material's physical response to guide the selection of mode numbers for each coupled field. Moreover, the framework decouples both material states and physical fields, providing clearer insights into the contributions and interactions of each field within the overall multiphysics simulation. Benchmark tests demonstrate that the proposed approach mitigates the Kolmogorov barrier of linear projection-based ROMs by ensuring a smooth and monotonic decrease in error as the number of modes increases. The proposed multi-perspective quadratic manifold framework offers a robust and flexible approach for efficiently reducing complex damage-involved multiphysics problems and shows strong potential for industrial applications.