Designing spongy-bone-like cellular materials: Matched topology and anisotropy

Abstract

Bone is a natural material with properties such as high specific stiffness and strength. These exceptional mechanical properties are attributed to the meso-scale structure and elastic anisotropy of spongy bone. Replicating the topological traits and mechanical properties of spongy bone presents a novel opportunity to develop high-performance cellular materials. To achieve this, we propose an innovative framework for designing biomimetic cellular materials that match the trabecular structure and elastic anisotropy of spongy bone. This framework introduces a forward-flow design process that utilizes gradient-based feature tuning on a low-dimensional feature vector, transforming the complex inverse design problem into an efficient iterative process. A key innovation in our approach is the use of a pre-trained generative model, SliceGAN, to reconstruct 3D unit cells from 2D micro-CT images. This significantly reduces the cost and time associated with traditional layer-by-layer CT scans typically required for 3D training data. Numerical homogenization is then used to determine the effective elastic stiffness matrix, and a Fourier neural operator is trained to predict these matrices efficiently, greatly enhancing the computational efficiency of the design process. Using this framework, we successfully designed unit cells with topological traits and elastic anisotropy that closely approximate those of natural spongy bone. This opens new avenues for developing spongy-bone-mimetic cellular materials with exceptional mechanical properties. Moreover, the framework's versatility allows it to be extended to the design of other bio-inspired cellular materials.