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

Twisting instabilities in elastic ribbons with inhomogeneous pre-stress: a macroscopic analog of thermodynamic phase transition

We study elastic ribbons subject to large, tensile pre-stress confined to a central region within the cross-section. These ribbons can buckle spontaneously to form helical shapes, featuring regions of alternating chirality (phases) that are separated by so-called perversions (phase boundaries). This instability cannot be described by classical rod theory, which incorporates pre-stress through effective natural curvature and twist; these are both zero due to the mirror symmetry of the pre-stress. Using dimension reduction, we derive a one-dimensional (1D) 'rod-like' model from a plate theory, which accounts for inhomogeneous pre-stress as well as finite rotations. The 1D model successfully captures the qualitative features of torsional buckling under a prescribed end-to-end displacement and rotation, including the co-existence of buckled phases possessing opposite twist, and is in good quantitative agreement with the results of numerical (finite-element) simulations and model experiments on elastomeric samples. Our model system provides a macroscopic analog of phase separation and pressure-volume-temperature state diagrams, as described by the classical thermodynamic theory of phase transitions.Comment: 29 pages; 11 figure

Helical Structures Mimicking Chiral Seedpod Opening and Tendril Coiling

Helical structures are ubiquitous in natural and engineered systems across multiple length scales. Examples include DNA molecules, plants’ tendrils, sea snails’ shells, and spiral nanoribbons. Although this symmetry-breaking shape has shown excellent performance in elastic springs or propulsion generation in a low-Reynolds-number environment, a general principle to produce a helical structure with programmable geometry regardless of length scales is still in demand. In recent years, inspired by the chiral opening of Bauhinia variegata’s seedpod and the coiling of plant’s tendril, researchers have made significant breakthroughs in synthesizing state-of-the-art 3D helical structures through creating intrinsic curvatures in 2D rod-like or ribbon-like precursors. The intrinsic curvature results from the differential response to a variety of external stimuli of functional materials, such as hydrogels, liquid crystal elastomers, and shape memory polymers. In this review, we give a brief overview of the shape transformation mechanisms of these two plant’s structures and then review recent progress in the fabrication of biomimetic helical structures that are categorized by the stimuli-responsive materials involved. By providing this survey on important recent advances along with our perspectives, we hope to solicit new inspirations and insights on the development and fabrication of helical structures, as well as the future development of interdisciplinary research at the interface of physics, engineering, and biology