Konrad Friedrichs | Searcharxiv

arXiv2026

Reliable training of neural hyperelastic models via full-field data

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.

cond-mat.mtrl-sci↗

arXiv2026

Precise, efficient and flexible modeling of crystallizing elastomers based on physics-augmented neural networks

We propose a precise and efficient physics-augmented neural network (PANN) to model strain-induced crystallization in rubbery polymers. We demonstrate that the model can be flexibly employed for both unfilled and filled natural rubber (NR). The approach is based on a two potential framework, similar to the concept of generalized standard materials (GSMs). To describe the material behavior, neural network-based free energy and dissipation potentials are employed. The evolution of crystallinity is derived from the two potentials. To ensure boundedness of the crystallinity, a novel constrained GSM-type evolution problem is proposed. To this end, two additional Lagrange multipliers together with the corresponding Karush-Kuhn-Tucker conditions are introduced. As a result, it is guaranteed that crystallinity can be interpreted as a variable of concentration type. The neural network-based potentials ensure all physically desirable properties by construction. Most importantly, objectivity, material symmetry and thermodynamic consistency are automatically fulfilled. In addition, an alternative derivation of the governing model equations in time-discrete form is presented based on an incremental variational framework, which also serves as the basis for a finite element implementation. We demonstrate the predictive capability of the PANN using three different experimental data sets from literature, considering both stress and crystallinity evolution at material point level as well as the corresponding field distributions in a notched specimen. Moreover, we show that model parameterization is also possible when experimental crystallinity data is not available, still enabling suitable stress predictions.

cond-mat.mtrl-sci↗