Likely striping in stochastic nematic elastomers

Abstract

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 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’.