论文标题
随机列弹性体中的可能条纹
Likely striping in stochastic nematic elastomers
论文作者
论文摘要
对于单构域的nematic弹性体，我们构建了合并纯粹的弹性和新古典型应变 - 能量密度。受到随机弹性的最新发展的启发，我们将这些模型扩展到了随机弹性纽扣形式，其中模型参数是由连续级别的空间独立概率密度函数定义的。为了研究这些系统的行为并证明了概率参数的效果，我们重点介绍了在拉伸的列弹性体中明确给出溶液的经典剪切条问题。我们发现，与新古典的情况不同，在新古典的情况下，不均匀变形发生在与弹性模量无关的通用间隔内发生，对于弹性纽约模型，关键间隔取决于材料参数。对于随机扩展，此间隔的界限是概率的，并且同质和不均匀的状态在两者都具有给定概率的意义上竞争。我们将此间隔内的不均匀模式称为“可能的条纹”。
For monodomain nematic elastomers, we construct generalised elastic-nematic constitutive models combining purely elastic and neoclassical-type strain-energy densities. Inspired by recent developments in stochastic elasticity, we extend these models to stochastic-elastic-nematic forms where the model parameters are defined by spatially-independent probability density functions at a continuum level. To investigate the behaviour of these systems and demonstrate the effects of the probabilistic parameters, we focus on the classical problem of shear striping in a stretched nematic elastomer for which the solution is given explicitly. We find that, unlike in the neoclassical case where the inhomogeneous deformation occurs within a universal interval that is independent of the elastic modulus, for the elastic-nematic models, the critical interval depends on the material parameters. For the stochastic extension, the bounds of this interval are probabilistic, and the homogeneous and inhomogeneous states compete in the sense that both have a a given probability to occur. We refer to the inhomogeneous pattern within this interval as "likely striping".
