NeuberNet: a neural operator solving elastic-plastic PDEs at V-notches from low-fidelity elastic simulations

We present NeuberNet, a nonlinear manifold decoder that learns a family of operator mappings on the domain of reentrant corners between far-field displacement boundary conditions obtained with low-fidelity elastic simulations and the high-resolution stress and strain fields that stem from the elastic-plastic axisymmetric solid mechanics equations, under the only assumptions of small-scale plasticity and bilinear isotropic hardening. We envision NeuberNet as a data-driven application of the substructuring principle in solid mechanics, engineered to simulate complex geometries by employing plastic material behavior only in the vicinity of stress raisers where nonlinearities are most likely to occur. We provide practical guidelines for mesh resolution in the initial low-fidelity elastic simulations; we show how NeuberNet can detect violations of the small-scale plasticity assumption, signaling the need for full-scale nonlinear models when required; finally, we show that NeuberNet can perform zero-shot inference on 3D problems with axisymmetric geometries and non-symmetric boundary conditions.