Unveiling the Mechanism Behind the Asymmetric Bending Compliance of Thin-Walled U-Shaped Strips: A Study Inspired by Plant Leaves

• Published in: Acta mechanica solida Sinica Vol. 36; no. 1; pp. 156 - 165
• Main Authors: Wei, Anran, Guo, Zhenbin, Guo, Fenglin
• Format: Journal Article
• Language: English
• Published: Singapore Springer Nature Singapore 01.02.2023
• Subjects: Classical Mechanics; Engineering; Surfaces and Interfaces; Theoretical and Applied Mechanics; Thin Films; Bending; Thin-walled beam; Thin plate; Bioinspired study; Buckling
• ISSN: 0894-9166; 1860-2134
• DOI: 10.1007/s10338-022-00361-0

Inspired by the shape of some plant leaves, we find that the thin-walled U-shaped strips exhibit different compliances under bending with opposite orientations. The asymmetric bending compliance is attributed to the buckling of sidewalls of strips caused by the bending-induced compression. Integrating the Euler–Bernoulli beam theory with the Kirchhoff–Love thin plate theory, a theoretical model is derived for the in-depth understanding of the sidewall buckling. For pure bending, the critical moment applied to the strip for the sidewall buckling is found to be insensitive to the height, width and length of strip, which is the result of the compromise between the opposite geometric effects on the buckling behavior of sidewalls and the characteristics of cross sections. Then the critical moment can be approximated as a linear function of flexural rigidity D = E t 3 / 12 1 - ν 2 , where t is the wall thickness of strip, E is Young’s modulus, and v is Poisson’s ratio. These predictions by our model agree well with the results obtained by finite element analysis. We also investigate the buckling behavior of sidewalls for bending under transverse loads, considering the loading conditions of concentrated force and distributed force. Our study unveils the mechanism behind the asymmetric bending compliance of thin-walled U-shaped strips. These results would offer convenient guidance for the promising engineering applications related to this structure, such as the design of soft robots with enhanced locomotion performance.