FINN: fabric-informed neural network for data-driven discovery of constitutive relations for granular materials

Conventional machine learning approaches predominantly focus on macroscopic stress–strain correlations, neglecting crucial microstructural descriptors of granular systems. This study proposes a fabric-informed neural network (FINN) that innovatively incorporates fabric evolution as a physical constraint and synergistically combines it with scientific discovery techniques to identify governing equations without prior physical assumptions. An oscillatory simple shear flow of granular materials with different shear amplitudes is simulated separately using the discrete-element method to create the dataset for model training and equation discovery. Systematic validations are conducted to examine the generalisation ability of the discovered evolution law across diverse particle properties and boundary conditions, including variations in shear protocols, confining pressures and model dimensions. Remarkably, the equation discovered from the training sets successfully predicts the evolution of the fabric in complex oscillatory shear loading scenarios. Furthermore, the fabric evolution law is extended by establishing a quantitative relationship between rolling friction coefficients and equation parameters, enabling accurate prediction of fabric anisotropy for previously unseen particle angularities. The study also extends to two-phase composite materials, demonstrating that the discovered laws accurately represent the reduced anisotropy and distinct kinetics induced by varying fractions of soft particles. This framework provides a general solution for discovering the evolution law governing granular microstructures, advancing the continuum constitutive modelling of granular materials.