  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.
