Exploiting length-dependent effects for the design of single-material systems with enhanced thermal transport properties

Abstract

Topology optimization approaches for thermal transport problems generally rely on the presence of high contrast in thermal conductivity between constituent materials. Even though this might result in topological configurations that are optimal according to some desired thermal metric, the resulting systems might be impractical from a mechanical standpoint: high contrast in thermal conductivity generally translates into disparate ranges of thermal expansion, which in turn may lead to mechanical failure. In this paper, we focus on the combination of multi-scale modeling and topology optimization techniques for the design of polycrystalline single-material systems with enhanced thermal transport properties. Spatial variation of the length-dependent thermal conductivity is achieved by grading the characteristic grain size of the microstructure. We adopt a multi-scale approach to compute the attainable range of thermal conductivity due to grain-size effect, given maximum and minimum grain sizes and an operating temperature range. Then, we utilize an adaptive topology optimization technique to obtain an optimal grain size distribution, while accounting for manufacturing constraints. Through a series of specific examples, we demonstrate the extent to which thermal transport properties can be optimized without resorting to the adoption of multi-material systems.

Foundations of Intelligent Additive Manufacturing

“…It is usually a minimization problem which is solved during the design step of the object with various methods approximating a solution like gradient descent or genetic algorithms. In contrast to traditional approaches to topology optimization, recent work [18] combines topology optimization techniques with advanced microstructural models [19] to optimize the microstructural distribution within a component rather than its macroscopic topology. This multi-scale optimization approach is particularly well suited to 3D printing applications, as this manufacturing process inherently produces microstructures that affect the local material properties of the component, e.g., through the introduction of voids or preferred directions, and hence its performance.…”

“…By modifying the closed-loop control of a 3D printer, we can aim to create specific microstructures to obtain the wanted values for local parameters in the topology optimization. This approach is developed in [18] where a microstructural optimization is performed, enabling the computation of multiscale optimization by tailoring microstructure to obtain desired macroscopic properties. Topology optimization can notably be used to achieve a desired stiffness by minimizing the final weight, for example with Michell structures [20].…”

“…[21] studies the topology optimization of structures subject to design-dependent Fig. 3: Example of multi-scale topology optimization in which the microstructure of the component is optimized pointwise for optimal thermal transport [18]. loads while [22] studies tradeoff curves for topology optimization under design constraints.…”