# Field-level prediction of mid-plane stress tensor fields in concrete target penetration: a cross-velocity graph neural operator surrogate

arXiv: https://arxiv.org/abs/2609.10032 · HTML: https://mlsanity.com/paper/2609.10032/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 37 references that are in the map.
- First posted on arXiv 9 Sep 2026.

## Builds on (most cited first, 3 of 3)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)

## Abstract (arXiv)

Although the impact resistance of concrete has been studied extensively, a framework linking mesoscale heterogeneity to full-field stress-tensor prediction has been lacking. Data were generated with a full-scale aggregate-resolved LS-DYNA model (projectile diameter 45 mm, mass 2.13 kg, target diameter 500 mm x thickness 200 mm, mesh 10 mm), verified against published penetration experiments (Frew 2006, Hanchak 1992, Forrestal 1996) by configuration similarity. The dataset contains six-component stress-tensor fields on the X-Z mid-plane for 400 cases (4 impact velocities x 100 aggregate seeds). Three contributions are reported. First, case-by-case verification of the terminal penetration state delimited the rest-state validity of penetration depth and anchored reliable observables to rigid-body motion and field-level stress evolution. Second, a field-level graph neural operator surrogate learned the time-varying stress-field evolution and evaluated cross-velocity leave-one-out extrapolation. Third, the full-scale, aggregate-resolved, cross-velocity, per-seed database was established as a reproducible resource. Cases at 100, 135 and 200 m/s still moved at window end (negative velocity, i.e. rebound), and only one 165 m/s case arrested. Penetration depth is therefore not reported as a rest-state scalar except for the single arrested case (69.33 mm); nose-node depth differences were confirmed as numerical artifacts of displacement integration after erosion. The single-step relative L2 error was 0.6977, reported honestly; autoregressive rollout from frame 11 to 39 took about 144 ms, a speedup of about 3.6x10^3 to 4.3x10^3 relative to single-core LS-DYNA, reported as application value. Validation is bounded by configuration similarity and field-level self-consistency; the framework is a simulation-trained decision-support method within the studied parameter space.