A compatible boundary condition-based topology optimization paradigm for static mechanical cloak design

We propose a novel compatible boundary condition-based topology optimization formulation for realizing static mechanical cloaking of linear elastic structures. The key idea is to make the actual boundary conditions along the exterior of the cloaking region consistent with the reference boundary conditions, including the displacement and the nodal force, by designing the cloak structure solely. This compatible boundary condition-based optimization paradigm is not only applicable to various shaped voids (e.g., circle, ellipse, star, Mickey, square, “DUT” logo) and diverse loading conditions (e.g., pressure-sliding, biaxial-stretching, linear-stretching, random-stretching, stretching-sliding) but also demonstrates insensitivity to element quantities and slight variations of external load, ensuring consistent and robust elastostatic cloaking performance. Additionally, adopting the Moving Morphable Voids (MMV) method guarantees the optimized structures have the merits of explicit geometric boundaries and easy fabrication. Numerical examples and experimental validation demonstrate the effectiveness of the proposed approach. The present approach can be easily extended for cloak design in three dimensions and multiphysics.