Unified data-driven constitutive modeling of mechanical metamaterials across truss, shell, and plate topologies

The macroscopic large deformation response of mechanical metamaterials is governed by the stress distribution within their evolving mesostructures in addition to the elasto-plastic behavior of their constituent solid phase. As a consequence, their homogenized stress-strain response exhibits features of combined isotropic, kinematic and distortional hardening. To investigate the mechanical behavior of lattice materials, we build finite element models of the representative unit cell (RUC) of truss, shell and plate lattices of cubic symmetry. Training data sets are generated comprised of random walk type of strain paths in 6D (input sequences) and the corresponding macroscopic stress histories (output sequences). A comprehensive hyperparameter study exploring the effects of network architecture, training data set size and strain path characteristics, revealed that a compact minimal state cell (MSC) model with only 5,000 parameters achieves excellent generalization after training on merely 6,000 sequences. Using the same fixed architecture, the model is successfully trained and validated for FCC-truss lattices, BCC-shell lattices and FCC/SC-plate lattices. For reference, the anisotropic Deshpande-Fleck plasticity model is calibrated to the same data. The comparison illustrates the remarkably high predictive accuracy of the data-driven framework, demonstrating its potential as general surrogate modeling strategy for complex lattice metamaterials. The MSC model’s applicability to large-scale analysis is also demonstrated through hemispherical punch indentation, where MSC simulations with a few thousand solid elements reproduce the response of a detailed shell model with millions of elements.