Mathematics and mechanics of liquid crystal elastomers

Abstract

Due to their complex material responses in the presence of external stimuli, liquid crystal elastomers have many potential applications in science, manufacturing, and medical research. The modelling of these materials requires a multiphysics approach, linking traditional continuum mechanics with liquid crystal theory. 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. Constitutive parameters of real manufactured materials have also an inherent variation that needs to be taken into account. In this talk, I will present an overview 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 characterisation of these fascinating materials.