Polytope Sector Based Synthesis and Analysis of Microstructural Architectures With Tunable Thermal Conductivity and Expansion

Abstract

The aim of this paper is to (1) introduce an approach, called polytope sectorbased synthesis (PSS), for synthesizing 2D or 3D microstructural architectures that exhibit a desired bulkproperty directionality (e.g., isotropic, cubic, orthotropic, etc.), and (2) provide general analytical methods that can be used to rapidly optimize the geometric parameters of these architectures such that they achieve a desired combination of bulk thermal conductivity and thermal expansion properties. Although the methods introduced can be applied to general beambased microstructural architectures, we demonstrate their utility in the context of an architecture that can be tuned to achieve a large range of extreme thermal expansion coefficients—positive, zero, and negative. The materialpropertycombination region that can be achieved by this architecture is determined within an Ashbymaterialproperty plot of thermal expansion versus thermal conductivity using the analytical methods introduced. These methods are verified using finiteelement analysis (FEA) and both 2D and 3D versions of the design have been fabricated using projection microstereolithography.