Multiscale data-driven modeling of the thermomechanical behavior of granular media with thermal expansion effects

A multiscale data-driven (MSDD) methodology is proposed for simulating the thermomechanical behavior of granular materials subjected to thermal expansion. The macroscale is handled using a continuous model based on the Finite Volume Method (FVM), while the microscale response is captured at Representative Volume Elements (RVEs) with the Discrete Element Method (DEM). To significantly reduce the computational cost of the analyses, the microscale DEM computations are not performed online, $i.e.$, simultaneously with the macroscale FVM ones, as generally done in standard multiscale approaches. Instead, they are performed in advance to create a comprehensive database of RVE solutions under different initial conditions and thermal strains. This dataset is then used to train an Artificial Neural Network (ANN), which serves as a surrogate model for the macroscale solver. The MSDD approach is validated against pure DEM solutions of problems with distinct thermal conditions. Remarkably, we demonstrate that with only three input parameters, namely porosity, fabric, and thermal strain, the surrogate model can predict the microstructure evolution, as well as the updated conductivity and Cauchy stress tensors of the granular assembly. This allows for a generally accurate simulation of transient thermomechanical analyses at a drastically lower computational cost than the pure DEM approach.