Modeling hierarchical nanoporous metals, characterized by complex ligament networks across multiple length scales [1], is computationally demanding. Multiaxial stresses occur in higher hierarchy ligaments, which add to the complexity of the problem and require an understanding of multiaxial material behavior. For finite element (FE) modeling, we propose separating the hierarchical nanoporous structure into upper and lower levels, enabling an efficient analysis of structure-property relationships. To reduce computational cost, we aim to use surrogate models and FE-beam models for predicting the mechanical behavior of the lower level of hierarchy.\\[1ex]
Our study focuses on idealized diamond FE-beam models representing the lower hierarchy, with yield surfaces exhibiting anisotropy. These surfaces are effectively described by data-driven techniques such as artificial neural networks and support vector classification (SVC) [2]. These methods are extended to predict yield surfaces after preloads [3]. Integrating the trained SVC into an Abaqus UMAT yielded promising results for small deformations under a non-associated flow rule. However, challenges arose regarding convergence in the plastic regime and predicting complex load histories. Thus, we redirected our focus to recurrent neural networks (RNN) for predicting the stress response directly from strain paths, incorporating load history. While this approach is not entirely new [4], its application to hierarchical modeling of nanoporous metals introduces novelty. Our findings show that these RNNs successfully predict the response for load paths within the higher-level ligaments, assuming incompressible material behavior. The extension of this approach to account for the compressible behavior of the lower level of hierarchy holds promising potential.