BIAXIAL LOADING OF NEO-CLASSICAL LIQUID CRYSTAL ELASTOMERS:CONSTITUTIVE RELATIONS AND SOFT BEHAVIOR  

作　　者：Hao Huang Zhi Zeng Yongzhong Huo 

机构地区：[1]Department of Mechanics and Engineering Science,Fudan University,Shanghai 200433,China [2]Woodruff School of Mechanical Engineering,Georgia Institute and Technology,Atlanta,GA 30332,USA

出　　处：《Acta Mechanica Solida Sinica》2012年第5期493-509,共17页固体力学学报（英文版）

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

摘　　要：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.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.

关 键 词：soft materials constitutive relation NONLINEAR biaxial loading larger deformation inverse methods liquid crystal elastomer 

分 类 号：O753.2[理学—晶体学] TG306[金属学及工艺—金属压力加工]