Physics-Informed Gaussian Process Regression Framework for Modeling the Dynamic Behavior of Concrete under High Pressure and High Strain Rates

Understanding the dynamic behavior of concrete under high pressure and high strain rates is critical for designing resilient materials in civil and defense applications. Traditional phenomenological constitutive models, which rely on empirical laws, often conflate the effects of various mechanisms—such as intrinsic material properties and structural inertia—thereby limiting their generalizability and predictive capability in extreme scenarios. Moreover, the high cost of experimental setups for these conditions results in sparse datasets, underscoring the need for constitutive models that can quantify uncertainty alongside their predictions.
To address these challenges, this study introduces a novel, physics-informed, thermodynamically constrained Gaussian Process Regression (GPR) framework. By incorporating the physics of crack growth dynamics and adhering to thermodynamic principles, this framework eliminates the reliance on phenomenological descriptions governing rate effects and provides a mechanistic understanding of concrete behavior under high pressure and high strain rates. The GPR model delivers robust predictions of material behavior while simultaneously quantifying uncertainties inherent in sparse data regimes. Trained with simulation and experimental data from triaxial compression tests and confined Split-Hopkinson bar tests, the GPR model is subsequently validated using gas-gun impact experiments.
The proposed framework offers a comprehensive understanding of the interplay between strain rate, pressure, and material microstructure, advancing the predictive capabilities of constitutive models for concrete under extreme loading conditions. These findings demonstrate the transformative potential of physics-informed machine learning in the development of constitutive laws for brittle solids.