Design of multi-material isotropic auxetic microlattices with zero thermal expansion

Abstract

Auxetic metamaterials are a type of mechanical metamaterials possessing negative Poisson’s ratios and displaying counter-intuitive deformation behavior, which are useful for a range of potential applications. However, two limitations restrain their further development and practical application. First, most current designs are not isotropic, although isotropic materials offer wide-ranging applications due to their identical properties in different directions. Second, most engineering design problems require multifunctionalities of structures, such as both the auxetic behavior during deformation and thermal stability over various temperatures ranges. To overcome the above two shortcomings, this paper will develop a systematic method for designing novel three-dimensional auxetic microlattices. A density-based topology optimization method will be used to distribute two phases of solid materials within a given cubical design domain, and the optimization is formulated under the assumption that all intermediate designs during the optimization will have at least elastic cubic symmetry. The optimized microlattices will exhibit desired properties, including elastic isotropy, negative Poisson’s ratio, and zero thermal expansion. A newly designed multi-material auxetic microlattice will be numerically demonstrated through finite element analysis to validate its elastic isotropy, auxetic property, and zero thermal expansion for withstanding temperature changes.