Likely striping in stochastic nematic elastomers

2021

Nonlinearity

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When a liquid crystal elastomer layer is bonded to an elastic layer, it creates a bilayer with interesting properties that can be activated by applying traction at the boundaries or by optothermal stimulation. Here, we examine wrinkling responses in three-dimensional nonlinear systems containing a monodomain liquid crystal elastomer layer and a homogeneous isotropic incompressible hyperelastic layer, such that one layer is thin compared to the other. The wrinkling is caused by a combination of mechanical forces and external stimuli. To illustrate the general theory, which is valid for a range of bilayer systems and deformations, we assume that the nematic director is uniformly aligned parallel to the interface between the two layers, and that biaxial forces act either parallel or perpendicular to the director. We then perform a linear stability analysis and determine the critical wave number and stretch ratio for the onset of wrinkling. In addition, we demonstrate that a plate model for the thin layer is also applicable when this is much stiffer than the substrate.Recommended by Dr Oliver O'Reilly.

Section: Wrinkling Under Biaxial Stretchmentioning

confidence: 99%

Liquid crystal elastomers wrinkling

2021

Nonlinearity

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“…The resulting elastic stresses then can be used to analyze the final deformation, where the particular geometry also plays a role (Figure 1). 61,62 To describe an incompressible nematic material, we combine isotropic hyperelastic and neoclassical strain-energy density functions as follows: 63 where, on the right-hand side, the first term is the energy of the "parent" elastic matrix, and the second term is the neoclassical-type function. Specifically, n is a unit vector for the localized direction of uniaxial nematic alignment in the present configuration; F = GA is the deformation gradient tensor with respect to the reference isotropic state (see Figure 1 and also Figure 1 of Reference 38), with G = a 1/3 n ⊗ n + a −1/6 (I − n ⊗ n) as the "spontaneous" (or "natural") deformation tensor and A the (local) elastic deformation tensor; G 0 = a 1/3 n 0 ⊗ n 0 + a −1/6 (I − n 0 ⊗ n 0 ) is the spontaneous deformation tensor with n 0 the director orientation at cross-linking, which may be spatially varying; and a > 0 is a temperature-dependent shape parameter, which we assume to be spatially independent (i.e., no differential swelling).…”

Section: General Set-upmentioning

confidence: 99%

“…89 However, our results can be easily extended to other choices of strain-energy density functions. 63 We analyzed shear striping under biaxial stretch, and assumed that the nematic director can only rotate in the biaxial plane. To achieve this, we set n 0 = [0,0,1] T and n = [0,sinθ,cosθ] T , where θ ∈ [0,π/2], in a Cartesian system of reference, and examined small shear perturbations of biaxial extensions, with gradient tensor 63 where a > 1 is the nematic shape parameter, λ > 0 is the stretch ratio, and ε > 0 is the small perturbation.…”

Section: Soft Elasticity and Stress Plateausmentioning

confidence: 99%

Instabilities in liquid crystal elastomers

2021

MRS Bulletin

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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.

“…Denoting by n 0 the reference orientation of the local director corresponding to the cross-linking state, n and n 0 may differ both by a rotation and a change in r. Many macroscopic deformations of nematic elastomers induce a director reorientation whereby the director aligns in the direction of the largest principal stretch associated with the deformation. The strain energy given by (2.1) satisfies the following conditions, which are inherited from isotropic finite elasticity [51]: Material objectivity. This states that constitutive equations must be invariant under changes of frame of reference.…”

Section: An Ideal Liquid Crystal Elastomermentioning

confidence: 99%

“…represents the neoclassical strain-energy function defined by (2.1), with the NH strain-energy density of the elastic network given by (3.3), {λ 2 i } i=1,2,3 and {e i } i=1,2,3 denote, respectively, the principal eigenvalues and principal eigenvectors of the deformation tensors FF T and F T F (see also [51,52]), and…”

Section: (B) the Pseudo-anelastic Energy Function For Liquid Crystal mentioning

confidence: 99%

A pseudo-anelastic model for stress softening in liquid crystal elastomers

2020

Proc. R. Soc. A.

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Liquid crystal elastomers exhibit stress softening with residual strain under cyclic loads. Here, we model this phenomenon by generalizing the classical pseudo-elastic formulation of the Mullins effect in rubber. Specifically, we modify the neoclassical strain-energy density of liquid crystal elastomers, depending on the deformation and the nematic director, by incorporating two continuous variables that account for stress softening and the associated set strain. As the material behaviour is governed by different forms of the strain-energy density on loading and unloading, the model is referred to as pseudo-anelastic. We then analyse qualitatively the mechanical responses of the material under cyclic uniaxial tension, which is easier to reproduce in practice, and further specialize the model in order to calibrate its parameters to recent experimental data at different temperatures. The excellent agreement between the numerical and experimental results confirms the suitability of our approach. Since the pseudo-energy function is controlled by the strain-energy density for the primary deformation, it is valid also for materials under multiaxial loads. Our study is relevant to mechanical damping applications and serves as a motivation for further experimental tests.