Instabilities in liquid crystal elastomers

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.