Clustering Based Model Order Reduction For Hyper Elastoplastic Material Models

A Reduced Order Model (ROM) is developed that can accurately predict the elastoplastic simulations for practical applications. Non-linear solid mechanics problems are computationally expensive because of (i) large numbers of Degrees Of Freedom (DOFs), (ii) large numbers of quadrature points that must be visited at each iteration to construct the force column and stiffness matrix, and (iii) effectively no quadratic convergence occurs because the state (i.e. elastic or elastoplastic) of each quadrature point must be iteratively estimated. Reduced order modelling based on proper orthogonal decomposition (POD) is employed to reduce the DOFs (and at a later stage, yet not reported in this presentation, hyperreduction will be developed which requires less quadrature points to construct the force column and stiffness matrix, so that less iterations are needed). At the offline stage of the POD method, elastic and plastic characteristics of the snapshot solutions are not well captured by POD basis vectors, because the POD basis vectors are spatially smooth. This results in a lack of accuracy at the online stage. The work focuses on improving the precision of POD method by utilising machine learning techniques. The idea of the proposed ROM is to separate the snapshots into multiple groups based on the deformation pattern. Unsupervised learning methods are utilized to group the snapshots into multiple clusters. The ROM is generated by obtaining the POD basis vectors from snapshots of individual clusters. So that plasticity induced
localisation is better represented in the POD basis vectors. Different unsupervised learning strategies are investigated, and the computational efficiency of the developed ROM is demonstrated with numerical examples considering hyper elastoplastic material model.