  We propose a new approach for unsupervised learning of hyperelastic
constitutive laws with physics-consistent deep neural networks. In contrast to
supervised learning, which assumes the availability of stress-strain pairs, the
approach only uses realistically measurable full-field displacement and global
reaction force data, thus it lies within the scope of our recent framework for
Efficient Unsupervised Constitutive Law Identification and Discovery (EUCLID)
and we denote it as NN-EUCLID. The absence of stress labels is compensated for
by leveraging a physics-motivated loss function based on the conservation of
linear momentum to guide the learning process. The constitutive model is based
on input-convex neural networks, which are capable of learning a function that
is convex with respect to its inputs. By employing a specially designed neural
network architecture, multiple physical and thermodynamic constraints for
hyperelastic constitutive laws, such as material frame indifference,
(poly-)convexity, and stress-free reference configuration are automatically
satisfied. We demonstrate the ability of the approach to accurately learn
several hidden isotropic and anisotropic hyperelastic constitutive laws -
including e.g., Mooney-Rivlin, Arruda-Boyce, Ogden, and Holzapfel models -
without using stress data. For anisotropic hyperelasticity, the unknown
anisotropic fiber directions are automatically discovered jointly with the
constitutive model. The neural network-based constitutive models show good
generalization capability beyond the strain states observed during training and
are readily deployable in a general finite element framework for simulating
complex mechanical boundary value problems with good accuracy.
