  In the present work, two machine learning based constitutive models for
finite deformations are proposed. Using input convex neural networks, the
models are hyperelastic, anisotropic and fulfill the polyconvexity condition,
which implies ellipticity and thus ensures material stability. The first
constitutive model is based on a set of polyconvex, anisotropic and objective
invariants. The second approach is formulated in terms of the deformation
gradient, its cofactor and determinant, uses group symmetrization to fulfill
the material symmetry condition, and data augmentation to fulfill objectivity
approximately. The extension of the dataset for the data augmentation approach
is based on mechanical considerations and does not require additional
experimental or simulation data. The models are calibrated with highly
challenging simulation data of cubic lattice metamaterials, including finite
deformations and lattice instabilities. A moderate amount of calibration data
is used, based on deformations which are commonly applied in experimental
investigations. While the invariant-based model shows drawbacks for several
deformation modes, the model based on the deformation gradient alone is able to
reproduce and predict the effective material behavior very well and exhibits
excellent generalization capabilities. In addition, the models are calibrated
with transversely isotropic data, generated with an analytical polyconvex
potential. For this case, both models show excellent results, demonstrating the
straightforward applicability of the polyconvex neural network constitutive
models to other symmetry groups.
