Unbiased mechanical cloaks

• 成果类型: Article
• 署名作者: Senhora, Fernando Vasconcelos; Sanders, Emily D.; Paulino, Glaucio H.
• 署名单位: University System of Georgia; Georgia Institute of Technology; University System of Georgia; Georgia Institute of Technology; Princeton University; Princeton University
• 刊物名称: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• ISSN/ISSBN: 0027-9202
• DOI: 10.1073/pnas.2415056122
• 发表日期: 2025-05-13
• 关键词: topology; optimization; DESIGN

摘要

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.