A Message Passing Neural Network Surrogate Model for Bond-Associated Peridynamic Material Correspondence Formulation
This work addresses computational efficiency for engineering applications using peridynamics, but it is incremental as it applies an existing neural network method to a specific domain problem.
The paper tackles the high computational cost of the bond-associated peridynamic material correspondence formulation by proposing a message-passing neural network surrogate model, which reduces computation time via GPU acceleration while maintaining physical objectivity.
Peridynamics is a non-local continuum mechanics theory that offers unique advantages for modeling problems involving discontinuities and complex deformations. Within the peridynamic framework, various formulations exist, among which the material correspondence formulation stands out for its ability to directly incorporate traditional continuum material models, making it highly applicable to a range of engineering challenges. A notable advancement in this area is the bond-associated correspondence model, which not only resolves issues of material instability but also achieves high computational accuracy. However, the bond-associated model typically requires higher computational costs than FEA, which can limit its practical application. To address this computational challenge, we propose a novel surrogate model based on a message-passing neural network (MPNN) specifically designed for the bond-associated peridynamic material correspondence formulation. Leveraging the similarities between graph structure and the neighborhood connectivity inherent to peridynamics, we construct an MPNN that can transfers domain knowledge from peridynamics into a computational graph and shorten the computation time via GPU acceleration. Unlike conventional graph neural networks that focus on node features, our model emphasizes edge-based features, capturing the essential material point interactions in the formulation. A key advantage of this neural network approach is its flexibility: it does not require fixed neighborhood connectivity, making it adaptable across diverse configurations and scalable for complex systems. Furthermore, the model inherently possesses translational and rotational invariance, enabling it to maintain physical objectivity: a critical requirement for accurate mechanical modeling.