Instabilities in liquid crystal elastomers

Abstract

Stability is an important and fruitful avenue of research for liquid crystal elastomers. At constant temperature, upon stretching, the homogeneous state of a nematic body becomes unstable, and alternating shear stripes develop at very low stress. Moreover, these materials can experience classical mechanical effects, such as necking, void nucleation and cavitation, and inflation instability, which are inherited from their polymeric network. We investigate the following two problems: First, how do instabilities in nematic bodies change from those found in purely elastic solids? Second, how are these phenomena modified if the material constants fluctuate? To answer these questions, we present a systematic study of instabilities occurring in nematic liquid crystal elastomers, and examine the contribution of the nematic component and of fluctuating model parameters that follow probability laws. This combined analysis may lead to more realistic estimations of subsequent mechanical damage in nematic solid materials. Because of their complex material responses in the presence of external stimuli, liquid crystal elastomers have many potential applications in science, manufacturing, and medical research. The modeling of these materials requires a multiphysics approach, linking traditional continuum mechanics with liquid crystal theory, and has led to the discovery of intriguing mechanical effects. An important problem for both applications and our fundamental understanding of nematic elastomers is their instability under large strains, as this can be harnessed for actuation, sensing, or patterning. The goal is then to identify parameter values at which a bifurcation emerges, and how these values change with external stimuli, such as temperature or loads. However, constitutive parameters of real manufactured materials have an inherent variation that should also be taken into account, thus the need to quantify uncertainties in physical responses, which can be done by combining the classical field theories with stochastic methods that enable the propagation of uncertainties from input data to output quantities of interest. The present study demonstrates how to characterize instabilities found in nematic liquid crystal elastomers with probabilistic material parameters at the macroscopic scale, and paves the way for a systematic theoretical and experimental study of these fascinating materials.

A Rod Theory for Liquid Crystalline Elastomers

“…To describe an ideal nematic LCE, we assume the following strain-energy density function [20,[40][41][42][43][44],…”

“…Here, we adopt the neoclassical strain-energy function, and assume the isotropic phase at high temperature as the reference configuration [8,[11][12][13][14], instead of the cross-linking nematic phase [2,5,56,[62][63][64]74]. We exploit theoretically the multiplicative decomposition of the deformation gradient from the reference configuration to the current configuration into an elastic distortion followed by a natural shape change [20,[41][42][43][44]. This multiplicative decomposition is similar to those found in the constitutive theories of thermoelasticity, elastoplasticity, and morphoelasticity [19,37] (see [18,53] as well), but it is also different in the sense that the stress-free geometric change is superposed on the elastic deformation, which is directly applied to the reference state.…”

Nematic liquid crystalline elastomers are aeolotropic materials

“…The strain-energy density describing an ideal monodomain nematic liquid crystalline (NLC) solid takes the general form [64][65][66][67]73]…”

“…In §2, we recall the neoclassical model for ideal nematic elastomers, with the isotropic phase at high temperature as the reference configuration [29,[58][59][60][61], instead of the nematic phase at cross-linking [14][15][16]32,33,62,63]. Phenomenologically, this choice is motivated by the multiplicative decomposition of the effective deformation into an elastic distortion, followed by a natural stress-free shape change [64][65][66][67]. This multiplicative decomposition is similar to those found in the constitutive theories of thermoelasticity, elastoplasticity and growth [68,69] (see also [70,71]), but it is also different in the sense that the elastic deformation is directly applied to the reference state.…”

A mathematical model for the auxetic response of liquid crystal elastomers

“…The so-called soft elasticity phenomenon where alternating shear stripes occur at very low stress has been studied extensively. Its theoretical explanation is that, for these materials, the energy is minimized by a state exhibiting a microstructure of many homogeneously deformed parts [8,14–22].…”