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

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.

Automated summary

In this paper, a projection-based model order reduction procedure is proposed for parametric quasi-static problems in nonlinear mechanics. The procedure aims to reduce the computational cost and accelerate the assembly cost of the reduced-order model. A cost-efficient error indicator is also introduced to validate the method's effectiveness.