An adaptive domain-based POD/ECM hyper-reduced modeling framework without offline training

Abstract

This work presents a reduced-order modeling framework that precludes the need for offline training and adaptively adjusts its lower-order solution space as the analysis progresses. The analysis starts with a fully-solved step and elements are clustered based on their strain response. Elements with the highest strains are solved with a local/global approach in which degrees of freedom from elements undergoing the highest amount of nonlinearity are fully-solved and the rest is approximated by a Proper Orthogonal Decomposition (POD) reduced model with full integration. Elements belonging to the remaining clusters are subjected to a hyper-reduction step using the Empirical Cubature Method (ECM). Online error estimators are used to trigger a retraining process once the reduced solution space becomes inadequate. The performance of the framework is assessed through a series of numerical examples featuring a material model with pressure-dependent plasticity.