Finite electro-elasticity with physics-augmented neural networks

In the present work, a machine learning based constitutive model for electro-mechanically coupled material behavior at finite deformations is proposed. Using different sets of invariants as inputs, an internal energy density formulated convex neural network. this way, fulfills polyconvexity condition which ensures stability, well thermodynamic consistency, objectivity, symmetry, and growth conditions. Depending on considered invariants, physics-augmented can either be applied compressible or nearly incompressible behavior, arbitrary symmetry classes. The applicability versatility approach demonstrated by calibrating it transversely isotropic data generated with analytical potential, effective modeling analytically homogenized, rank-one laminate composite numerically homogenized cubic metamaterial. These examinations show excellent generalization properties that networks offer also multi-physical such nonlinear electro-elasticity.