Topology Optimization of Thermal Circuits using Thermo-mechanical Metamaterials (TMMs)

  • Torres, Alberto (DEVCOM Army Research Laboratory)
  • Gaynor, Andrew (DEVCOM Army Research Laboratory)
  • Wetzel, Eric (DEVCOM Army Research Laboratory)

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Thermal management systems are of the utmost importance in many industrial, commercial, and military applications. Engineering solutions addressing thermal management include static materials and structures, such as insulators, heat sinks, and thermal spreaders; or more complex devices and systems such as fans, liquid circulators, flow heat exchangers, and thermoelectrics. Relative to these complex systems, static solutions can be advantageous due to low cost, compact size, and limited power or control burdens. However, they cannot actively adapt to changing thermal conditions or requirements. In response, the U.S. Army has developed a lattice-based, additively manufactured thermo-mechanical metamaterial (TMMs) and has demonstrated its dynamic thermal capabilities. These TMM systems are composed of thermally conductive elements arranged on a deformable lattice; the location, direction, and magnitude of applied strain is used to control thermal contact paths between elements. These compact TMM systems require low power but actively switch from conductive to insulative and provide active thermal steering between heat sources and sinks. In our present work, a topology optimization framework is developed for rapid design of “thermal circuit” layouts that leverage TMMs. An idealized Tetrakis Square mesh composed of truss elements models thermal pathways throughout the underlying lattice. These thermal circuits are actuated under distinct strain conditions, meaning various “states” are handled by the same topology, each with their own objective functions. This multi-state operation is enforced throughout the optimization by separating physical material placement and actuated state selection into separate design fields, with inspiration drawn from recent works addressing selective projection in additive manufacturing. The Augmented Lagrangian is leveraged to ensure individual TMM cell constraints are adhered to across multiple states. Presented examples demonstrate Army-relevant objective functions, with designs producing adaptive thermal circuits that act as a unified thermal management system capable of actively switching between multiple thermal solutions.