Physics‐Informed Recurrent Neural Networks for Predicting Elasto‐Plastic Behavior in Hierarchical Finite Element Modeling

ABSTRACT Nanoporous gold, with its hierarchical structure comprising interconnected networks on multiple length scales, poses significant computational challenges for traditional modeling methods. To solve this challenge, this study introduces a physics‐informed recurrent neural network (RNN) to model the homogenized material response of a diamond beam‐based representative volume element representing the lower level of hierarchy (LL), which was integrated as a material subroutine within an upper level (UL) finite element simulation. The RNN predicts the tangent stiffness matrix as a primary output from given strain trajectories. Secondary outputs such as stress, plastic strain, and plastic energy increments are derived through embedded physical relationships, ensuring physical consistency across the outputs. The RNN architecture enforces positive energy dissipation inherently through positive eigenvalues of the tangent stiffness matrix and further through penalization of negative energy increments, promoting thermodynamically consistent predictions. A two‐level hierarchical approach is employed, where the 2D UL model is subjected to uniaxial strain, while multiaxial strain conditions naturally arise locally within the structure. The inclusion of the LL significantly modifies the strain trajectories observed at the UL, while stress trajectories, although maintaining their general trend, experience considerable changes in magnitude. This approach demonstrates the capability to efficiently simulate hierarchical materials, capturing the influence of LL porosity on the UL material behavior while maintaining physical consistency. Additionally, the model allows for straightforward integration into finite element frameworks like Abaqus, offering a computationally efficient method for studying complex hierarchical materials.