Adaptivity for clustering-based reduced-order modeling of localized history-dependent phenomena

This article introduces adaptivity in Clustering-based Reduced Order Models (ACROMs). The strategy is demonstrated for a particular CROM called Self-Consistent Clustering Analysis (SCA), extending it into the Adaptive Self-Consistent Clustering Analysis (ASCA) method. This is shown to improve predictions of Representative Volume Elements (RVEs) of materials exhibiting history-dependent localization phenomena such as plasticity, damage and fracture. The overall approach is composed of three main building blocks: target clusters selection criterion, adaptive cluster analysis, and computation of cluster interaction tensors. In addition, an adaptive clustering solution rewinding procedure and a dynamic adaptivity split factor strategy are suggested to further enhance the adaptive process. The ASCA method is shown to perform better than its static counterpart when capturing the multi-scale elasto-plastic behavior of a particle–matrix composite and predicting the associated fracture and toughness. The proposed adaptivity strategy can be followed in other CROMs to extend them into ACROMs, opening new avenues to explore adaptivity in this context.