Design of Nonperiodic Microarchitectured Materials That Achieve Graded Thermal Expansions

The aim of this paper is to introduce an approach for optimally organizing a variety of nonrepeating compliant-mechanism-like unit cells within a large deformable lattice such that the bulk behavior of the lattice exhibits a desired graded change in thermal expansion while achieving a desired uniform stiffness over its geometry. Such lattices with nonrepeating unit cells, called nonperiodic microarchitectured materials, could be sandwiched between two materials with different thermal expansion coefficients to accommodate their different expansions and/or contractions induced by changing ambient temperatures. This capability would reduce system-level failures within robots, mechanisms, electronic modules, or other layered coatings or structures made of different materials with mismatched thermal expansion coefficients. The closed-form analytical equations are provided, which are necessary to rapidly calculate the bulk thermal expansion coefficient and Young's modulus of general multimaterial lattices that consist first of repeating unit cells of the same design (i.e., periodic microarchitectured materials). Then, these equations are utilized in an iterative way to generate different rows of repeating unit cells of the same design that are layered together to achieve nonperiodic microarchitectured material lattices such that their top and bottom rows achieve the same desired thermal expansion coefficients as the two materials between which the lattice is sandwiched. A matlab tool is used to generate images of the undeformed and deformed lattices to verify their behavior and an example is provided as a case study. The theory provided is also verified and validated using finite-element analysis (FEA) and experimentation.