An explainable physics-constrained deep neural network to predict the mechanical response of high-strength concrete across strain rates

Accurate prediction of the rate-dependent mechanical response of high-strength concrete (HSC) remains challenging, particularly under dynamic loading conditions where experimental data are limited and material behavior exhibits strong nonlinearity. This study proposes a physics-constrained deep neural network for predicting the compressive stress–strain response of HSC across strain rates ranging from 10⁻⁵ s⁻¹ to 110 s⁻¹. A multi-fidelity dataset combining experimental measurements and validated finite element simulations is constructed for three concrete grades (C60, C80, and C110). The model integrates domain-informed constraints, including zero-stress enforcement at initial strain and regime-dependent monotonicity conditions implemented through automatic differentiation. A phase-stratified SHAP analysis is employed to evaluate feature contributions across deformation regimes. The framework achieves high predictive accuracy (R² > 0.99), with peak stress errors below 2%, while accurately capturing dynamic increase factors and post-peak softening behavior. The interpretability results align with known deformation mechanisms of concrete, demonstrating that physics-guided learning with multi-fidelity data provides a reliable and interpretable approach for modelling quasi-brittle materials under rate-dependent loading.