A clustering-enhanced potential-based reduced order homogenization framework for nonlinear heterogeneous materials

Abstract

This paper proposes a data-driven approach to improve the efficiency of computational homogenization for nonlinear hyperelastic materials with different microstructures in a small strain context. By combining clustering analysis and Proper Orthogonal Decomposition (POD) with efficient sampling, a reduced order model is established to accurately predict elastoplasticity under monotonic loadings. The microscopic RVE is spatially divided into multiple clusters using the k-means clustering algorithm during the offline phase. As suggested in Kunc and Fritzen (2019a), the reduced order model is constructed using reduced bases of deformation gradient fluctuations on the microscale. In contrast to the conventional displacement-based approach, deformation gradient fluctuations are employed to generate the POD snapshots. To improve the prediction accuracy and reduce the cost of offline computation, the energy minimum point set generation method proposed by Kunc and Fritzen (2019b) is employed. Numerical results show a acceleration factor in the order of 10-100 compared to a purely POD-based model can be archived, which significantly improves the applicability for structural analysis, while maintaining a sufficient accuracy level.