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Large deflection of a bilayer soft strip due to incompatibility of isotropic volumic expansion

各向同性体积膨胀导致的双层条结构大挠度弯曲

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Abstract

Since the traditional bending theory of bilayers was mainly for linear elastic materials with the assumption of infinitesimal deformation, here we study the bending of a bilayer soft strip with large deformation. The strip under investigation is comprised of an active layer and a passive layer, where only the active layer is assumed to be subjected to an isotropic volumic expansion. A bending theory for the large deformation of the strip is then developed. The subsequent analysis indicates that our theoretical predictions agree well with the finite element simulation, which, however, can significantly diverge from those predicted by the traditional theory under certain circumstances. With our theory, it is also shown that there exists an optimal modulus ratio or thickness ratio for a bilayer strip to achieve a maximal curvature. We suggest that our theory may greatly facilitate the design of soft bilayer strips that can be potentially employed in varied fields.

摘要

传统双层材料的弯曲理论主要针对小变形、线弹性材料. 这里我们研究了双层条的大变形弯曲, 建立了一个描述双层条大变形弯曲的理论. 理论中假设双层条由一个主动层和一个被动层组成, 只有主动层会产生各向同性体积膨胀. 分析表明我们的理论预测与有限元模拟符合较好, 而在某些情况下会与传统理论预测有明显的差异. 我们理论分析还表明, 存在能使双层条得到最大曲率的最佳模量比及厚度比. 我们的理论可促进软质双层条带材的设计, 可广泛用于多个领域.

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Acknowledgements

This work was supported by Zhejiang Provincial Natural Science Foundation of China (Grant No. LZ23A020004), and the National Natural Science Foundation of China (Grant No. 11872334).

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Authors and Affiliations

  1. Department of Engineering Mechanics, Zhejiang University, Hangzhou, 310058, China

    Puyu Cao  (曹圃瑜) & Bin Chen  (陈彬)

  2. School of Aeronautics and Astronautics, Zhejiang University, Hangzhou, 310058, China

    Yan Xu  (徐彦)

Authors
  1. Puyu Cao  (曹圃瑜)
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  2. Yan Xu  (徐彦)
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  3. Bin Chen  (陈彬)
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Contributions

Puyu Cao contributed to the methodology, software, investigation, and writing. Yan Xu contributed to the investigation and writing. Bin Chen contributed to the conceptualization, methodology, investigation, and writing.

Corresponding authors

Correspondence to Yan Xu  (徐彦) or Bin Chen  (陈彬).

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Cao, P., Xu, Y. & Chen, B. Large deflection of a bilayer soft strip due to incompatibility of isotropic volumic expansion. Acta Mech. Sin. 39, 422374 (2023). https://doi.org/10.1007/s10409-022-22374-x

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