Inverse design of mechanical metamaterials that harness instabilities

Metamaterials derive their properties from their structure rather than their chemical composition. Their microstructure is specifically designed to create new functionalities not found in nature. Harnessing instabilities is a prominent practice of turning continuous deformations into a discrete response, allowing for sequential transformations, multistability and hysteretic behavior. Despite the complex behavior that these mechanical metamaterials show, their architecture is often surprisingly simple. An iconic example of auxetic material is an elastomeric material patterned with circular pores. While several studies focused on the effects of pore shape and pore distribution, the mechanical properties can only be tuned within limits set by a few geometrical parameters. Our aim is to reverse this paradigm. We introduce a stochastic topology optimization strategy, to inversely design mechanical metamaterials with targeted buckling behavior. Our study, while first focusing on optimizing structure with assigned buckling force, extends at designing structures with predefined post-buckling behavior. This opens up exciting opportunities for the design of soft robots where functionalities can be encoded in the material itself. We complement our results with experimental verification.