Hyper Reduction of finite strain elasto-plastic models

The aim of this work is to propose a new method to compute the reduced state variables related to a known POD basis. The classical Galerkin formulation of the reduced governing equation related to a POD basis is not efficient for medium size elasto-plastic problems (about 20000 Degrees of freedom). In such problems the computational cost related to the local integration of the nonlinear constitutive equations is very important. It can constitute 80% of the total computational cost. The classical POD basis applied to primal variables (the displacements) does not affect the efficiency of the integration of the constitutive equations. To overcome this drawback we propose a Petrov-Galerkin formulation related to a Reduced Integration Domain (RID). This RID is created by selecting few elements of the mesh to perform the local integration of the constitutive equations. This is a generic approach coined Hyper Reduction, which have been successfully applied to simplify nonlinear thermal transient models. The novelty of this work is the extension of the Hyper Reduction method to the problems involving internal variables. A 3D finite strain elasto-plastic model is considered to illustrate the capabilities of the Hyper reduction method.