Topology optimization of contact-aided thermo-mechanical regulators

TL;DR

This work addresses the challenge of designing thermo-mechanical regulators whose heat transfer is nonlinearly tunable through deformation and contact. It introduces a fully coupled non-linear thermo-mechanical finite element framework augmented with a third medium contact model and couples it with topology optimization using a PDE filter, Heaviside projection, SIMP interpolation, adjoint sensitivity, and MMA updates. The main contributions include the demonstration of contact-aided thermal regulators (switches, diodes, triodes), analysis of thermal contact resistance via the ersatz material parameter $\delta_o^\kappa$, and validation against analytical solutions and body-fitted mesh results in 2D plane strain. The approach enables robust, gradient-based design of non-linear heat-transfer devices that leverage self-contact for potential applications in electronics cooling, climate control, and space systems.

Abstract

Topology optimization is used to systematically design contact-aided thermo-mechanical regulators, i.e. components whose effective thermal conductivity is tunable by mechanical deformation and contact. The thermo-mechanical interactions are modeled using a fully coupled non-linear thermo-mechanical finite element framework. To obtain the intricate heat transfer response, the components leverage self-contact, which is modeled using a third medium contact method. The effective heat transfer properties of the regulators are tuned by solving a topology optimization problem using a traditional gradient based algorithm. Several designs of thermo-mechanical regulators in the form of switches, diodes and triodes are presented.

Figures (20)

• Figure 1: A schematic of a thermal switch leveraging contact.
• Figure 2: The rod with dimensions $(L,H)$ = ($6$ cm $\times$$1$ cm).
• Figure 3: The analytical and numerical average normal reaction fluxes versus the applied displacement for varying $\delta_o^\kappa$.
• Figure 4: The analytical and numerical temperature distributions over the $L_c\approx 0.04$ m rod for varying thermal contact resistances, i.e. varying $\delta_o^\kappa$.
• Figure 5: The thermal contact conductance, $1/R_{th}$, versus the applied pressure for varying $\delta_o^\kappa$.