NeuberNet: a neural operator solving elastic-plastic partial differential equations at V-notches from low-fidelity elastic simulations.

Stress concentrations at geometric irregularities such as reentrant corners make it challenging to efficiently simulate localized plastic deformation in engineering materials. Fully nonlinear models capture these effects accurately but are computationally costly, whereas simplified elastic analyses neglect important nonlinearities. Here, we present NeuberNet, a Multi-Task Nonlinear Manifold Decoder that learns mappings between far-field displacement boundary conditions from low-fidelity elastic simulations and the corresponding high-resolution stress and strain fields derived from elastic-plastic axisymmetric solid mechanics, under assumptions of small-scale plasticity and bilinear isotropic hardening. NeuberNet serves as a data-driven implementation of the substructuring principle, designed to model complex geometries by activating plastic behavior only near stress raisers where nonlinearities arise. We provide guidelines for mesh resolution in low-fidelity simulations, demonstrate NeuberNet's ability to identify violations of the small-scale plasticity assumption, and assess its robustness to nonlinear hardening laws. We also show that NeuberNet generalizes to 3D problems with axisymmetric geometries and non-symmetric boundary conditions. Overall, NeuberNet provides a reliable and computationally efficient framework for small-scale plasticity analysis.