Anisotropy and failure in trabecular structures: a deep learning approach

Accurate prediction of bone fragility requires understanding how the anisotropic and disordered trabecular architecture governs nonlinear mechanical behavior. However, hierarchical organization, intrinsic disorder, and material heterogeneity hinder both direct numerical modeling and the development of robust deep learning surrogates. To address these challenges, we initiate the development of a general deep learning framework for predicting the mechanical response of anisotropic, disordered architectures using simplified yet representative Voronoi-based structures that emulate trabecular networks. A dataset of 10 000 two-dimensional beam-based Voronoi tessellations with tunable anisotropy and cell density was generated and analyzed through nonlinear finite element simulations under uniaxial compression with periodic boundary conditions. Nonlinear structural responses were quantified via effective stiffness and strength, examining trends with respect to geometric descriptors. Three Multi-Layer Perceptron models were trained using different input representations, from global descriptors to explicit nodal coordinates. The model trained on global parameters achieved the best predictive accuracy (R2 = 0.77 for stiffness, R2 = 0.88 for strength), indicating that coarse geometrical descriptors are sufficient to capture first-order mechanical trends, while coordinate-based inputs highlight the limitations of MLP architectures for variable-size structural data. These results demonstrate that simple models can predict key effective properties from global geometry, establishing a foundation for data-driven modeling of trabecular analogs. Future work will integrate graph-based architectures, enhanced datasets, and 3D nonlinear simulations to develop a unified predictive framework for bone-inspired and architected materials.