Anisotropy tailoring in geometrically isotropic multi-material lattices - Sondipon Adhikari (Extreme Mechanics Letters, 2020)
This article proposes the concept of anisotropy tailoring in multi-material lattices based on a mechanics-based bottom-up framework. It is widely known that isotropy in a mono-material lattice can be obtained when the microstructure has an isotropic geometry. For example, regular hexagonal lattices with a unit cell comprised of six equal members and equal internal angle of each, show isotropy in the elastic properties. Such limited microstructural configuration space for having isotropy severely restricts the scope of many multi-functional applications such as space filling in 3D printing. We first demonstrate that there are multiple structural geometries in mono-material lattices that could lead to isotropy. It is shown that the configuration space for isotropy can be expanded by multiple folds when more than one intrinsic material is introduced in the unit cell of a lattice. We explicitly demonstrate different degrees of anisotropy in regular geometrically isotropic lattices by introducing the multi-material architecture. The contours of achieving minimum anisotropy, maximum anisotropy and a fixed value of anisotropy are presented in the design space consisting of geometric and multi-material parameters. Proposition of such multi-material microstructures could essentially expand the multi-functional design scope significantly, offering a higher degree of flexibility to the designer in terms of choosing (or identifying) the most suitable microstructural geometry. An explicit theoretical characterization of the contours of anisotropy along with physical insights underpinning the configuration space of multi-material and geometric parameters will accelerate the process of its potential exploitation in various engineered multi-functional materials and structural systems across different length-scales with the demand of any specific degree of anisotropy but limitation in the micro-structural geometry.