Porous and particulate materials with internal microstructure exhibit complex constitutive mechanical responses, but informing constitutive laws based on microstructural information remains a significant challenge. We demonstrate a surrogate modeling approach to this problem, using both Gaussian processes and neural network regression techniques in combination with representative volume element (RVE) simulations that include microstructural detail. These techniques are demonstrated primarily in the context of the mechanical response of hyperelastic foams, with preliminary results for rheology of frictional granular materials. Arbitrary three-dimensional kinematic states are explored in RVE simulations, and regression in the resulting strain-stress space produces a robust data-driven constitutive model. We use principal decompositions of the conjugate tensorial variables (strain or strain rate, and stress) to guarantee objectivity, and discuss results for both a purely data-driven approach and a hybrid of a data-driven and empirical model, where the data is used to augment rather than replace traditional models. In particular, the latter approach provides a practical solution to extrapolation in data-driven models.
Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA-0003525.