Physics-Informed Graph Neural Networks to Reconstruct Local Fields Considering Finite Strain Hyperelasticity

TL;DR

This paper introduces P-DivGNN, a physics-informed graph neural network that reconstructs local stress fields in hyperelastic materials, enabling faster predictions for large-scale micro-structural simulations.

Contribution

The paper presents a novel physics-informed GNN framework that accurately predicts local stress distributions considering finite strain hyperelasticity, incorporating physical constraints and periodic boundary conditions.

Findings

Achieves accurate local stress field reconstruction in hyperelastic materials.

Provides significant computational speed-ups over traditional finite element methods.

Effectively handles varying geometries and nonlinear responses.

Abstract

We propose a physics-informed machine learning framework called P-DivGNN to reconstruct local stress fields at the micro-scale, in the context of multi-scale simulation given a periodic micro-structure mesh and mean, macro-scale, stress values. This method is based in representing a periodic micro-structure as a graph, combined with a message passing graph neural network. We are able to retrieve local stress field distributions, providing average stress values produced by a mean field reduced order model (ROM) or Finite Element (FE) simulation at the macro-scale. The prediction of local stress fields are of utmost importance considering fracture analysis or the definition of local fatigue criteria. Our model incorporates physical constraints during training to constraint local stress field equilibrium state and employs a periodic graph representation to enforce periodic boundary conditions. The benefits of the proposed physics-informed GNN are evaluated considering linear and non linear hyperelastic responses applied to varying geometries. In the non-linear hyperelastic case, the proposed method achieves significant computational speed-ups compared to FE simulation, making it particularly attractive for large-scale applications.