Neural networks meet hyperelasticity: A guide to enforcing physics

In the present work, a hyperelastic constitutive model based on neural networks is proposed which fulfills all common conditions by construction, and in particular, applicable to compressible material behavior. Using different sets of invariants as inputs, potential formulated convex network, thus fulfilling symmetry stress tensor, objectivity, symmetry, polyconvexity, thermodynamic consistency. addition, physically sensible behavior ensured using analytical growth terms, well normalization terms ensure undeformed state be free with zero energy. polyconvex, invariant-based are for both isotropic transversely By these an exact way, physics-augmented combines sound mechanical basis extraordinary flexibility that offer. Thus, it harmonizes theory hyperelasticity developed last decades up-to-date techniques machine learning. Furthermore, non-negativity network-based potentials numerically examined sampling space admissible deformations states, which, best authors' knowledge, only possibility considered nonlinear models. For network model, required reduced considerations. proof Neo-Hooke presented. The applicability demonstrated calibrating data generated potentials, followed application finite element simulations. adaption noisy shown its [...]