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

Area of Science:

• Computational mechanics
• Materials science
• Machine learning

Background:

• Simulating localized plastic deformation in engineering materials with stress concentrations is computationally intensive.
• Fully nonlinear models are accurate but costly; elastic analyses are efficient but neglect nonlinearities.

Purpose of the Study:

• To introduce NeuberNet, a Multi-Task Nonlinear Manifold Decoder, for efficient small-scale plasticity analysis.
• To develop a data-driven method that maps low-fidelity elastic simulations to high-resolution elastic-plastic stress and strain fields.

Main Methods:

• NeuberNet learns mappings between far-field displacement boundary conditions and stress/strain fields.
• Utilizes elastic-plastic axisymmetric solid mechanics under small-scale plasticity and bilinear isotropic hardening assumptions.
• Implements a data-driven substructuring principle to activate plasticity near stress raisers.

Main Results:

• NeuberNet provides computationally efficient and reliable small-scale plasticity analysis.
• Demonstrates generalization to 3D problems with axisymmetric geometries and non-symmetric boundary conditions.
• Offers guidelines for mesh resolution and identifies violations of the small-scale plasticity assumption.

Conclusions:

• NeuberNet offers a robust and computationally efficient framework for analyzing small-scale plasticity.
• The method effectively models complex geometries by focusing nonlinear analysis on critical regions.
• NeuberNet enhances the accuracy of simulations where traditional methods face computational or accuracy trade-offs.