Soft elastic response of stretched sheets of nematic elastomers: a numerical study
Soft elastic response of stretched sheets of nematic elastomers: a numerical study
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DOI：
10.1016/s0022-5096(01)00120-x
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发表时间：
2002-07-01
影响因子：
5.3
通讯作者：
Dolzmann, G
中科院分区：
文献类型：
--
作者：
Conti, S;DeSimone, A;Dolzmann, G
在向列弹性体薄片上的拉伸实验揭示了试样的软变形模式和部分微观结构的形成。这两种现象都是存在从随机的、各向同性的相位到排列的、向列相的对称性破缺相变的表现。由Bladon等人提出的微观能量。Rev. E 47 (1993) R 3838)对这种转变进行了建模，提供了与对称性相关的零能量状态的连续体，这些状态可以以不同的方式组合以实现各种零能量宏观变形。我们用宏观有效能量来代替微观能量，也就是所谓的准象面化。这个过程产生了系统物理的粗粒度描述，在能量学中正确地解释了状态变量的（能量最优的）精细振荡，但在运动学中平均。准象阵化能量的知识使我们能够有效地计算有限元素，并模拟在向列弹性体片上的数值拉伸实验。我们的数值实验表明，在一个关键的、几何相关的拉伸下，没有反作用力产生，在更大的拉伸下，一个力通过部分薄片传递，尽管细相混合物从大多数样品中消失。我们从计算的变形梯度中重建了微观结构的可能组成，从而解决了向列指向器的局部取向。(C) 2002 Elsevier Science Ltd.版权所有。
Stretching experiments on sheets of nematic elastomers have revealed soft deformation modes and formation of microstructure in parts of the sample. Both phenomena are manifestations of the existence of a symmetry-breaking phase transformation from a random, isotropic phase to an aligned, nematic phase. The microscopic energy proposed by Bladon et al. (Phys. Rev. E 47 (1993) R 3838) to model this transition delivers a continuum of symmetry-related zero-energy states, which can be combined in different ways to achieve a variety of zero-energy macroscopic deformations. We replace the microscopic energy with a macroscopic effective energy, the so-called quasiconvexification. This procedure yields a coarse-grained description of the physics of the system, with (energetically optimal) fine-scale oscillations of the state variables correctly accounted for in the energetics, but averaged out in the kinematics. Knowledge of the quasiconvexified energy enables us to compute efficiently with finite elements, and to simulate numerically stretching experiments on sheets of nematic elastomers. Our numerical experiments show that up to a critical, geometry-de pendent stretch, no reaction force arises, At larger stretches, a force is transmitted through parts of the sheet and, although fine phase mixtures disappear from most of the sample. microstructures survive in some pockets, We reconstruct from the computed deformation gradients a possible composition of the microstructure, thereby resolving the local orientation of the nematic director. (C) 2002 Elsevier Science Ltd. All rights reserved.