Reliable training of neural hyperelastic models via full-field data

Abstract

We present a systematic investigation of the robustness and limitations of equilibrium gap-based calibrations for hyperelastic physics-augmented neural networks (PANNs), where we consider the special case of isotropic and polyconvex PANNs. In full-field parameterizations, it is commonly assumed that the displacement field is captured with sufficient spatial resolution for an accurate evaluation of the deformation field, and that the specimen is thin enough for plane stress to hold to a good approximation. Since these assumptions are never ideally satisfied in real experiments, we investigate, using synthetically generated data, how severely an under-resolved surface measurement and a non-negligible specimen thickness can affect the model parameterization. Furthermore, we perform calibration on real experimental data for a set of inhomogeneous specimen geometries. We show that the coverage of the admissible deformation states during calibration governs the ability of a model to generalize to unseen geometries and load cases; this ability can be improved further by appropriate combinations of specimens. Accurately depicting the material behavior underlying this rich data, however, requires a sufficiently flexible constitutive model, for which PANNs are well suited. Yet a rich coverage of deformation states alone is not sufficient: unless the calibration data comprise biaxial-tension-like states, models that include the second deformation invariant extrapolate unphysically towards equi-biaxial tension, whereas restricting the PANN to the first invariant remains reliable.