A Micromechanical Machine Learning Framework for Hyperelastic Particle-Reinforced Composites

This paper presents a novel physics-informed neural network (PINN) framework for the micromechanical modeling of hyperelastic particle-reinforced composites. The approach integrates the tangent second-order (TSO) homogenization estimate with an artificial neural network (ANN) to predict the effective nonlinear hyperelastic behavior. The TSO method provides an efficient, physics-based prior estimate of the composite’s strain energy density, while the ANN learns the complex discrepancy between this estimate and the real value, obtained from high-fidelity direct numerical simulation (DNS) in this work. This hybrid strategy reduces the learning dimensionality, enhancing predictive accuracy with limited training data. The framework is trained on DNS data generated for neo-Hookean composites under various loading states, particle volume fractions, and particle-to-matrix stiffness contrasts. Comprehensive validations demonstrate that the PINN accurately captures the stress-strain responses for different microstructural parameters and material constants. Furthermore, the model exhibits remarkable generalization capability, successfully predicting the mechanical behavior of composites governed by the more nonlinear Mooney–Rivlin constitutive law, despite being trained exclusively on neo-Hookean-based data. The results confirm that the proposed PINN framework is a robust, accurate, and efficient tool for learning and predicting the complex hyperelastic behavior of particle-reinforced composites.