A POD-TANN approach for the multiscale modeling of materials and macroelement derivation in geomechanics

This paper introduces a novel approach that combines Proper Orthogonal Decomposition (POD) with Thermodynamics-based Artificial Neural Networks (TANN) to capture the macroscopic behavior of complex inelastic systems and derive macroelements in geomechanics. The methodology leverages POD to extract macroscopic Internal State Variables from microscopic state information, thereby enriching the macroscopic state description used to train an energy potential network within the TANN framework. The thermodynamic consistency provided by TANN, combined with the hierarchical nature of POD, allows to reproduce complex, non-linear inelastic material behaviors as well as macroscopic geomechanical systems responses. The approach is validated through applications of increasing complexity, demonstrating its capability to reproduce high-fidelity simulation data. The applications proposed include the homogenization of continuous inelastic representative unit cells and the derivation of a macroelement for a geotechnical system involving a monopile in a clay layer subjected to horizontal loading. Eventually, the projection operators directly obtained via POD, are exploit to easily reconstruct the microscopic fields. The results indicate that the POD-TANN approach not only offers accuracy in reproducing the studied constitutive responses, but also reduces computational costs, making it a practical tool for the multiscale modeling of heterogeneous inelastic geomechanical systems.