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The distinction between “reinforcement” and “cloaking” has been overlooked in optimization-based design of devices intended to conceal a defect in an elastic medium. In the former, a so-called “cloak” is severely biased toward one or a few specific elastic disturbances, whereas in the latter, an “unbiased cloak” is effective under any elastic disturbance. We propose a two-stage approach for optimization-based design of elastostatic cloaks that targets true, unbiased cloaks. First, we perform load-case optimization to find a finite set of worst-case design loads. Then we perform topology optimization of the cloak microstructure under these worst-case loads using a judicious choice of the objective function, formulated in terms of energy mismatch. Although a small subset of the infinite load cases that the cloak must handle, these highly nonintuitive, worst-case loads lead to designs that approach perfect and unbiased elastostatic cloaking. In demonstration, we consider elastic media composed of spinodal architected materials, which provides an ideal testbed for exploring elastostatic cloaks in media with varying anisotropy and porosity, without sacrificing manufacturability. To numerically verify the universal nature of our cloaks, we compare the elastic response of the medium containing the cloaked defect to that of the undisturbed medium under many random load cases not considered during design. By using digital light processing additive manufacturing to realize the elastic media containing cloaked defects and analyzing their response experimentally using compression testing with digital image correlation, this study provides a physical demonstration of elastostatic cloaking of a three-dimensional defect in a three-dimensional medium.
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This content will become publicly available on June 1, 2026
Simultaneous Thermal–Electrical Cloak and Camouflage Via Level-Set-Based Topology Optimization
Abstract Cloaks are devices designed to conceal objects from detection. With the advancement of metamaterials, there is an increasing interest in developing multifunctional cloaks to cater to various application scenarios. This article proposes a level-set-based shape and topology optimization scheme to design simultaneous thermal and electrical cloaking devices. Unlike classical methods such as coordinate transformation and scattering cancelation, which are vulnerable to high material anisotropy, the proposed method employs only naturally occurring bulk materials, greatly facilitating physical realization. The bifunctional cloak is achieved by reproducing the reference temperature and electrical potential fields within the evaluation domain through the optimal layout of two thermally and electrically conductive materials. Using a similar formulation, we extend the proposed method to design a thermal–electrical camouflage device that can conceal a sensor while allowing it to remain functional. This study presents a method to simultaneously achieve sensing and camouflaging in multiphysical fields using topology optimization. Previous research has generally addressed these functionalities separately; in contrast, we integrate them into a unified framework. To demonstrate the method’s potential, we provide examples of bifunctional cloaks and camouflage devices. The dependency of the optimization results on the initial designs is also briefly investigated. Despite exhibiting a notable reliance on the initial guesses, as with any gradient-based method, the objective functions based on the least-square error are sufficiently small, demonstrating the effectiveness of the cloak. This study holds promise for inspiring further exploration of metadevices with multiple functionalities.
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- Award ID(s):
- 2213852
- PAR ID:
- 10634654
- Publisher / Repository:
- ASME Journal of Mechanical Design
- Date Published:
- Journal Name:
- Journal of Mechanical Design
- Volume:
- 147
- Issue:
- 6
- ISSN:
- 1050-0472
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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