A projection-based reduced-order model for parametric quasi-static nonlinear mechanics using an open-source industrial code

TL;DR

This paper introduces a projection-based reduced-order modeling approach for parametric nonlinear mechanics problems, integrated into an industrial finite element code, to significantly reduce computational costs in simulations involving various parameters.

Contribution

It develops an adaptive POD-Greedy algorithm with hyper-reduction and an efficient stress reconstruction error indicator, tailored for industrial nonlinear mechanics applications.

Findings

Successfully applied to a 3D elastoplastic system.

Achieved significant reduction in computational time.

Validated accuracy and efficiency of the reduced model.

Abstract

We propose a projection-based model order reduction procedure for a general class of parametric quasi-static problems in nonlinear mechanics with internal variables. The methodology is integrated in the industrial finite element code code aster. Model order reduction aims to lower the computational cost of engineering studies that involve the simulation to a costly high-fidelity differential model for many different parameters, which correspond, for example to material properties or initial and boundary conditions. We develop an adaptive algorithm based on a POD-Greedy strategy, and we develop an hyper-reduction strategy based on an element-wise empirical quadrature in order to speed up the assembly costs of the reduced-order model by building an appropriate reduced mesh. We introduce a cost-efficient error indicator which relies on the reconstruction of the stress field by a Gappy-POD strategy. We present numerical results for a three-dimensional elastoplastic system in order to illustrate and validate the methodology.