A data-driven reduced-order surrogate model for entire elastoplastic simulations applied to representative volume elements

Projection-based model-order reduction approaches are accurate and fast for simulations with periodic boundary conditions: the use of only a limited number of global basis functions generally provides an excellent accuracy. In contrast to (hyper)elasticity, (hyper)elastoplasticity yields non-elliptical partial differential equations. Consequently, many global basis functions are needed to achieve a reasonable accuracy. The fact that many basis functions are required for hyperelasto- plasticity is not only problematic because a relatively large number of degrees of freedom remains, it also entails the need for many integration points in the online simulations (the stress update must be iteratively computed in each iteration). This contribution investigates two approaches to keep the number of global basis functions of finitely plastically deforming representative volume element simulations small - ultimately in order to keep the number of reduced quadrature
points of the hyperreduction small. This is performed by combining the global basis functions with local interpolation functions. For both extensions, we investigate two ways to identify the global basis functions. Although the results are clearly improved, a truly consistent trend is lacking for the time being. On the other hand, several avenues can be taken to improve the frameworks.