Single-shot forward and inverse hierarchical architected materials design for nonlinear mechanical properties using an Attention-Diffusion model

Inspired by natural materials, hierarchical architected materials can achieve enhanced properties including achieving tailored mechanical responses. However, the design space for such materials is often exceedingly large, and both predicting mechanical properties of complex hierarchically organized materials and designing such materials for specific target properties can be extremely difficult. In this paper we report a deep learning approach using an attention-based diffusion model, capable of providing both, forward predictions of nonlinear mechanical properties as a function of the hierarchical material structure as well as solving inverse design problems in order to discover hierarchical microstructure candidates for a specified nonlinear mechanical response. We exemplify the method for a system of compressively loaded four-hierarchy level materials derived from a family of honeycomb structures, where patterns of distributed buckling events are unitary deformation events that control small-and large-scale deformation behavior. Our model offers exquisite single-shot end -to-end performance in both forward and inverse directions across the entire range of deformation regime, and is capable of rapidly discovering multiple solutions that satisfy a design objective in accordance with the known physical behavior elucidated by, and validated with, coarse-grained simulations. The model provides an effective way towards biologically inspired materials design for high-throughput discovery in order to achieve diverse nonlinear constitutive relationships.