Learning hyperelastic anisotropy from data via a tensor basis neural network

Anisotropy in the mechanical response of materials with microstructure is common and yet difficult to assess model. To construct accurate models given only stress-strain data, we employ classical representation theory, novel neural network layers, L1 regularization. The proposed tensor-basis can discover both type orientation anisotropy provide an model stress response. method demonstrated data from hyperelastic off-axis transverse isotropy orthotropy, as well less well-defined symmetries induced by fibers or spherical inclusions. Both plain feed-forward networks input-convex formulations are developed tested. Using latter, a polyconvex potential be established, which, satisfying growth condition guarantee existence boundary value problem solutions.