A variational physics-informed graph neural network for heterogeneous solid mechanics
Stress localization in heterogeneous solids is governed by the bimaterial interface, where the displacement field remains $C^0$-continuous, while in-plane stresses jump due to the stiffness mismatch. Coordinate-based physics-informed neural networks (PINNs) represent this jump via a prescribed regularization width or a weighted interface penalty, making their accuracy sensitive to how phase-contrast changes are handled. This work presents a variational, label-free physics-informed graph neural network (PI-GNN) in which the heterogeneity is carried by the discretization rather than by the trial field. The solver operates on a conforming adaptive mesh graph, assigns constitutive behavior pe...
| Authors | Aashay Rajan Yadav, Amiya Prakash Das, Ratna Kumar Annabattula |
|---|---|
| Primary category | math.NA |
| Published | 10 September 2026 |
| Last updated at source | 10 September 2026 |
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