Heterogeneous Mechanical Metamaterials with Extreme Bulk-To-Shear Modulus Ratio: An Evolutionary Design Approach

Most non-stochastic architected materials proposed to date have been based on periodic structures with a homogeneous topology and uniform materiality. Topologically and materially heterogeneous mechanical metamaterials promise novel capabilities, expanding the design space through growth in degrees of freedom. However, this leads to increased design complexity, as the space of possible solutions becomes a high-dimensional domain. We present a computational design automation framework for novel heterogeneous mechanical meta-material designs with a CMA-ES black-box evolutionary algorithm at its core, and demonstrate its application through a case study on new 2D pentamode meta-materials. Pentamodes are defined by extreme values of the bulk-to-shear modulus ratio (B/G) and are of particular interest due to both their unusual properties, being very stiff under compression yet easy to deform in shear, and potential as building blocks for the realization of any physically possible and desired elastic property. For the pentamode case study, this approach resulted in irregular composite structures with large B/G ratios, many structures having values between 1–3 × 10⁴, a range well above previously reported experimental values of 10³. The new meta-material systems it generated do not present the point-like connections of the classic pentamode diamond-type lattice, which is a key practical limitation for application. This work shows that population-based metaheuristic computational methods can reliably generate novel mechanical metamaterial designs capable of achieving more extreme performance than more traditional metamaterial design approaches.