  In the present work, neural networks are applied to formulate parametrised
hyperelastic constitutive models. The models fulfill all common mechanical
conditions of hyperelasticity by construction. In particular, partially
input-convex neural network (pICNN) architectures are applied based on
feed-forward neural networks. Receiving two different sets of input arguments,
pICNNs are convex in one of them, while for the other, they represent arbitrary
relationships which are not necessarily convex. In this way, the model can
fulfill convexity conditions stemming from mechanical considerations without
being too restrictive on the functional relationship in additional parameters,
which may not necessarily be convex. Two different models are introduced, where
one can represent arbitrary functional relationships in the additional
parameters, while the other is monotonic in the additional parameters. As a
first proof of concept, the model is calibrated to data generated with two
differently parametrised analytical potentials, whereby three different pICNN
architectures are investigated. In all cases, the proposed model shows
excellent performance.
