Homogenization and corrector results for a stochastic coupled thermoelastic model

The aim of this research is to explore new homogenization results for a stochastic linear coupled thermoelastic model. We focus on a stochastic equation of motion coupled with a stochastic heat equation, representing the linear thermoelastic behavior of composite anisotropic materials with a periodic heterogeneous structure. These materials are subjected to random external forces and heat sources. By employing the periodic unfolding method and leveraging probabilistic compactness results from Prokhorov and Skorokhod, we obtain homogenization, convergence of the associated stochastic energies, and corrector results.