Diaz-Calleja R, Riande E
ITE, Polytechnic University of Valencia, Valencia, Spain.
Eur Phys J E Soft Matter. 2012 Jan;35(1):2. doi: 10.1140/epje/i2012-12002-5. Epub 2012 Jan 18.
The biaxial stretching of sheets of liquid crystalline neo-Hookean elastomer has been studied in the isotropic case. The results suggest two types of laminate structures in the process of quasiconvexification of the free energy, a fact that implies the appearance of several shear terms in the deformation gradient matrix. More that one decomposition of the deformation gradient is possible, which is consistent with a bifurcation in the undeformed configuration (λ = 1) . This situation is similar to the well-known Rivlin's problem of the triaxial symmetric traction of a neo-Hookean cube. The problem can easily be generalized for an anisotropic material by introducing a semisoft term in the free-energy expression. In this case, the horizontal plateau corresponding to the minimal energy, characteristic of the soft elasticity, disappears, and only an equilibrium condition is obtained.
在各向同性情况下，对液晶新胡克弹性体片材的双轴拉伸进行了研究。结果表明，在自由能准凸化过程中存在两种类型的层状结构，这一事实意味着在变形梯度矩阵中出现了几个剪切项。变形梯度可能有不止一种分解方式，这与未变形构型（λ = 1）中的分岔现象一致。这种情况类似于著名的新胡克立方体三轴对称牵引的里夫林问题。通过在自由能表达式中引入一个半软项，可以很容易地将该问题推广到各向异性材料。在这种情况下，对应于最小能量的水平平台消失了，该平台是软弹性的特征，并且仅得到一个平衡条件。
