Data-driven finite element method with RVE generated foam data

The data-driven finite element method proposed by Kirchdoerfer and Ortiz [1] allows to elude the material modeling step. Instead, a previously obtained data set is used directly in the algorithm to describe the material behavior under deformation. Usually, this data set is expected to be gained experimentally. The following empirical treatment is skipped in the data-driven framework and the data is implemented in the algorithm directly. The data-driven problem is rewritten as a minimization problem of a distance function subject to the conservation laws. This paper presents a computational approach to deduce a data set prior to the finite element computation. Representative volume element computations are conducted to deduce a macroscopic material behavior of a polyurethane foam structure. The typical linear load regime of the foam allows us to generate a large material database which can be used as an input for the data-driven finite element computation. Furthermore, we also work out how to proceed in the case of (non-)linear and (an-)isotropic material behavior in order to obtain suitable material data sets. The numerical example which is conducted with the foam data is a typical rubber sealing profile. In the data-driven computation itself, we use a numerical method proposed in [2] to decrease the computing and storage demands.