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Biaxial Loading of Neo-Classical Liquid Crystal Elastomers: Constitutive Relations and Soft Behavior

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Abstract

The thermo-order-mechanical behaviors of liquid crystal elastomers (LCEs) under biaxial loading are studied in this paper. Inverse method for nonlinear elastic problems is utilized by imposing biaxial stretching to thin rectangular samples. Neo-classical elastic energy is used together with the Landau-de Gennes nematic free energy. Under plane stress assumptions, the constitutive equations are derived. Due to the possible reorientations of the liquid crystal molecules induced by the imposed biaxial loading, the in-plane nonlinear stress-strain relations can have different expressions depending on which loading axis will have the largest effective principal strain. And the free energy is a multi-well non-convex potential function. As shown by some typical loading paths, the LCE samples will exhibit an anisotropic nonlinear elastic behavior, as long as the loading has not induced a reorientation of the liquid crystal molecules. When this did occur, jumps of stresses could take place for dead loadings due to the losing of stability.

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Authors and Affiliations

  1. Department of Mechanics and Engineering Science, Fudan University, Shanghai, 200433, China

    Hao Huang & Yongzhong Huo

  2. Woodruff School of Mechanical Engineering, Georgia Institute and Technology, Atlanta, GA, 30332, USA

    Zhi Zeng

Authors
  1. Hao Huang
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  2. Zhi Zeng
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  3. Yongzhong Huo
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Correspondence to Yongzhong Huo.

Additional information

Project supported by National Natural Science Foundation of China (Nos. 11072062 and 11172068) and the Research Fund for the Doctoral Program of Higher Education of China (No. 20110071110013).

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Huang, H., Zeng, Z. & Huo, Y. Biaxial Loading of Neo-Classical Liquid Crystal Elastomers: Constitutive Relations and Soft Behavior. Acta Mech. Solida Sin. 25, 493–509 (2012). https://doi.org/10.1016/S0894-9166(12)60044-5

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  • DOI: https://doi.org/10.1016/S0894-9166(12)60044-5

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