Thermomechanical cloaking via compatibility-driven topology optimization

This study presents a novel topology optimization framework for thermomechanical cloaking by introducing the compatibility of cloak interface (CCI). The essence is to make the actual boundary conditions along the exterior of the cloak consistent with the target boundary conditions, including the Dirichlet and Neumann conditions (i.e., temperature and thermal loads for thermal cloaking, displacement and nodal forces for mechanical cloaking). Compared to conventional design strategies, the proposed method offers a unified design framework for the rational design of multifunctional cloaking without being restricted by the invariance requirement of transformation-based approaches. At the same time, this method only requires analysis of the cloak region during the optimization process, thereby reducing the computational cost. Furthermore, the explicit topology optimization based on Moving Morphable Voids (MMV) produces cloaks with geometric information, enabling its practical application. Several numerical examples demonstrate the method’s effectiveness, robustness, and adaptability for thermal and multifunctional cloaking in lattice and continuum structures with various shaped openings, as well as multiple load cases. The current design strategy is extendable to other multiphysics cloaking applications, offering new insights into advanced functional material design.