Establish mesh-scale convergence

Establish systematically the convergence of the 10 mm hexahedral mesh for aggregate-resolved concrete penetration, including its effects on field resolution, depth extraction, and local stress amplitudes.

Background

The concrete target and projectile are discretized with 10 mm hexahedral elements. This resolution is adopted as a compromise between computational cost and aggregate resolution, but aggregates near the mesh scale are represented by only a small number of elements.

Because the surrogate is trained on fields generated with this discretization, unresolved mesh dependence may affect the local stress tensor, erosion behavior, and penetration observables. The paper explicitly notes that mesh convergence has not been systematically examined, so the reliability of these quantities under mesh refinement remains unresolved.

References

A finer mesh would improve the field resolution, but the number of elements grows with the third power and the computational cost increases markedly, so that the 10 mm mesh represents a compromise between computational cost and aggregate resolution, and aggregates larger than the mesh scale (about 10 to 25 mm) are resolved by 1 to 3 elements relative to the mesh scale. The convergence of this mesh scale has not been studied systematically, and is declared honestly as a mesh resolution constraint.

— Field-level prediction of mid-plane stress tensor fields in concrete target penetration: a cross-velocity graph neural operator surrogate  (2609.10032 - Du et al., 9 Sep 2026) in Section 2.3, Numerical solution settings