Full-field damage reconstruction from discrete-element particle states: A multi-modal neural operator and benchmark for rock direct shear

Abstract

Discrete-element method (DEM) simulation of rock direct shear resolves grain-scale cracking, but records it only as a list of broken bonds: a sparse binary point set that describes the three-dimensional crack field only implicitly. This work proposes a multi-modal neural operator that reconstructs, in one forward pass, the full crack field and the macroscopic response of a direct-shear specimen from a coarse-grained snapshot of its particle state at that instant. Bond-breakage events are recast into a continuous damage density field by Gaussian-kernel accumulation; density, initial-position and displacement fields enter a Transformer encoder as independent modalities, fused by cross-modal attention and decoded by two heads into three macroscopic scalars and a 6 4 3 damage field. Against a binary target trained with an imbalance-aware loss, that recasting buys learnability and costs positional fidelity, the two cancelling at native readout density. On a released benchmark of 1275 PFC3D cases and 26,872 frames, scored against eight baselines on a held-out split, it is statistically indistinguishable from the strongest on shear displacement, while convolutional baselines keep an edge on voxel-level crack overlap—the families are complementary rather than substitutable. These figures are stated against the DEM reference, itself anchored to laboratory direct shear over σ n = 10 –60 MPa (calibration experiments at R 2 = 0.941 , an independent shale dataset at R 2 = 0.953 ); the benchmark’s 1 and 5 MPa levels fall below it and mark the applicability boundary. The reconstructions stay physically consistent: cumulative input work explains crack accumulation at a pooled R 2 = 0.907 , against 0.845 for the DEM ground truth. Beyond rock direct shear, it is a route to full-field damage reconstruction from discrete simulations.

The authors' abstract, as published at the source. Computational Particle Mechanics, 2026 · DOI ↗