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

Abstract

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.

Instabilities in liquid crystal elastomers

“…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).…”

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.…”

Rapid Surface Charge Mapping Based on a Liquid Crystal Microchip

“…These molecules in a liquid crystal can still flow and change position, similar to a liquid. Also, liquid crystals are highly sensitive to external influences such as temperature, electric fields, and mechanical stress [36,37]. By manipulating these factors, it is possible to control the orientation and alignment of the liquid crystal molecules, leading to changes in their optical properties, such as light transmission, polarization, and refractive index [38].…”