A physics-coupled graph neural operator for mid-plane six-component stress tensor field prediction in concrete penetration

Abstract

The penetration-resistant design of concrete structures requires the spatiotemporal evolution of the stress field within the target, whereas in design only the strength grade, the geometry and the projectile parameters are known, and the aggregate arrangement is not. Empirical formulae and scalar-output surrogates serve design screening, and mesoscale finite element models resolve the aggregate-scale response, but one solution cannot cover random aggregate samples at scale, and no framework links mesoscale heterogeneity to field-level prediction. A physics-coupled graph neural operator (PC-GNO) is proposed, which learns in function space the evolution of the mid-plane six-component stress tensor field. The training data are generated by full-scale, aggregate-resolved finite element models and comprise 359 cases at the impact velocities of 100, 135 and 165 m/s, corresponding to compressive strengths of 14, 23 and 48 MPa; the data source is verified by laboratory measurements. The coupling strength of message passing is constructed from the impedance contrast across the material interface, and the update is constrained by spectral normalization. Under the single-step primary setting, the mean accuracy of the three levels is 80.16% (91.45%, 77.80% and 71.22%), i.e. 27.81, 42.46 and 34.16 percentage points above the preceding-frame field of the same window; with 20 664 parameters it exceeds the 87.9% of the best Fourier neural operator configuration (about 812 times as many parameters) and the 71.0% of the closed-form linear regression. The output is the complete six-component tensor field rather than a fixed engineering quantity, so that strength criteria and energy indicators follow from one set of weights. For field-level response prediction in concrete penetration, this result provides a data-driven route, with conditions of applicability defined by the training and the evaluation.