NN-EUCLID: Deep-learning hyperelasticity without stress data

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