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 (ISVs) 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 for accurate modeling of complex, non-linear material behavior and reliable macroscopic geomechanical systems responses. The effectiveness of this approach is validated through applications of increasing complexity, demonstrating its capability to handle various material behaviors and microstructural topologies. These applications include the homogenization of continuous inelastic representative unit cells (RUCs) and the derivation of a macroelement for a geotechnical system involving a monopile in a clay layer subjected to horizontal loading. The results indicate that the proposed POD-TANN methodology not only achieves high accuracy in reproducing stress-strain responses, but also significantly reduces computational costs, making it a practical tool for the multiscale modeling of heterogeneous inelastic systems, and the efficient derivation of macroelements for complex geomechanical problems.