Data-driven finite element method with RVE generated foam data

This paper presents a model-free data-driven strategy for linear and non-linear finite element computations of open-cell foam. Employing sets of material data, the data-driven problem is formulated as the minimization of a distance function subjected to the physical constraints from the kinematics and the balance laws of the mechanical problem. The material data sets of the foam are deduced here from representative microscopic material volumes. These volume elements capture the stochastic characteristics of the open-cell microstructure and the properties of the polyurethane material. Their computation provides the required stress-strain data used in the macroscopic finite element computations without postulating a specific constitutive model. The paper shows how to efficiently derive suitable material data sets for the different (non-)linear and (an-)isotropic material behavior cases. Exemplarily, we compare data-driven finite element computations with linearized and finite deformations and show that a linear kinematic is sufficiently accurate to capture the material's non-linearity up to 50% of straining. The numerical example of a rubber sealing illustrates possible areas of application, the expenditure, and the proposed strategy's versatility.