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This paper presents a model-free data-driven strategy for linear andnon-linear finite element computations of open-cell foam. Employing sets ofmaterial data, the data-driven problem is formulated as the minimization of adistance function subjected to the physical constraints from the kinematics andthe balance laws of the mechanical problem.  The material data sets of the foam are deduced here from representativemicroscopic material volumes. These volume elements capture the stochasticcharacteristics of the open-cell microstructure and the properties of thepolyurethane material. Their computation provides the required stress-straindata used in the macroscopic finite element computations without postulating aspecific constitutive model. The paper shows how to efficiently derive suitablematerial data sets for the different (non-)linear and (an-)isotropic materialbehavior cases.  Exemplarily, we compare data-driven finite element computations withlinearized and finite deformations and show that a linear kinematic issufficiently accurate to capture the material's non-linearity up to 50% ofstraining. The numerical example of a rubber sealing illustrates possible areasof application, the expenditure, and the proposed strategy's versatility.

Data-driven finite element method with RVE generated foam data