We develop graph-based surrogate models to predict strain localization and collapse load in 2D elastic-perfectly plastic porous solids. Plastic deformation is represented using a Delaunay graph, where nodes correspond to void centers, edges represent potential shear bands, and edge values encode the local integral of the plastic work rate (PWR). Two edge-regression graph neural network (GNN) models are built. The first is a purely data-driven model (DDM) that maps local geometric features – edge length and orientation – to PWR. The second is a hybrid model (HM) that augments the GNN with a mechanistic prior from a limit load analysis model (LLAM) and learns a correction to its upper-bound bias. The models are trained on a dataset of 1200 representative volume elements with 20% porosity. The DDM can reliably reconstruct shear band patterns, but its accuracy deteriorates when applied to porosity values different from that seen in training. The HM, like the LLAM, does not fully capture the spatial pattern, but it removes the LLAM systematic bias and achieves uniformly low errors in total work rate for porosities ranging from 10% to 30%. Moreover, the HM requires less training data than the DDM and is more robust across random seeds. These results show that coupling a GNN with a physics-based prior yields a fast and data-efficient surrogate that preserves accuracy in macroscopic quantities while retaining meaningful spatial information, thereby offering a practical route to predict the collapse of porous solids while accounting for the exact locations of a very large number of voids.

Simulating the mechanical response of advanced materials can be done more accurately using concurrent multiscale models than with single-scale simulations. However, the computational costs stand in the way of the practical application of this approach. The costs originate from microscale Finite Element (FE) models that must be solved at every macroscopic integration point. A plethora of surrogate modeling strategies attempt to alleviate this cost by learning to predict macroscopic stresses from macroscopic strains, completely replacing the microscale models. In this work, we introduce an alternative surrogate modeling strategy that allows for keeping the multiscale nature of the problem, allowing it to be used interchangeably with an FE solver for any time step. Our surrogate provides all microscopic quantities, which are then homogenized to obtain macroscopic quantities of interest. We achieve this for an elasto-plastic material by predicting full-field microscopic strains using a graph neural network (GNN) while retaining the microscopic constitutive material model to obtain the stresses. This hybrid data-physics graph-based approach avoids the high dimensionality originating from predicting full-field responses while allowing non-locality to arise. In addition, this approach introduces beneficial inductive bias to the model by encoding microscopic geometrical features. By training the GNN on a variety of meshes, it learns to generalize to unseen meshes, allowing a single model to be used for a range of microstructures. The embedded microscopic constitutive model in the GNN implicitly tracks history-dependent variables and leads to improved accuracy. While the microscopic stresses are fully dependent on the microscopic strains, we found it crucial to include both microscopic strains and stresses in the loss function. We demonstrate for several challenging scenarios that the surrogate can predict complex macroscopic stress–strain paths. As the computation time of our method scales favorably with the number of elements in the microstructure compared to the FE method, our method can significantly accelerate FE² simulations.