Morphogenetic mechanical metamaterials: Emerging tensor properties from self-organized structures.

Understanding how living organisms spontaneously develop complex functional structures motivates new strategies in engineering design. Here, we introduce a decentralized generative model based on morphogenesis to autonomously grow mechanical structures with controlled tensorial properties. By adapting Turing's reaction-diffusion concept through anisotropic diffusion, our approach enables the local emergence of microstructures exhibiting tailored stiffness and anisotropy, achieving target orthotropic tensors without adjoint or topology optimization loops. The synthesis of these structures relies on a database linking morphogenetic parameters to effective elastic tensors obtained through homogenization techniques. We experimentally demonstrate this concept through a mechanical cloaking example, validating our method's capability to independently control local anisotropy and rigidity, and effectively conceal structural defects from mechanical fields. This approach circumvents the iterative global solves required by topology optimization, while preserving local control over anisotropy and stiffness across large design domains.