Dimension reduction via $$\Gamma $$ Γ -convergence for soft active materials

Abstract

Abstract. We present a rigorous derivation of dimensionally reduced theories for thin sheets of nematic elastomers, in the finite bending regime. Focusing on the case of twist nematic texture, we obtain 2D and 1D models for wide and narrow ribbons exhibiting spontaneous flexure and torsion. We also discuss some variants to the case of twist nematic texture, which lead to 2D models with different target curvature tensors. In particular, we analyse cases where the nematic texture leads to zero or positive Gaussian target curvature, and the case of bilayers.

A micromechanical-based model of stimulus responsive liquid crystal elastomers

“…In the following, we compare our statistical mechanics approach to a rigorous theoretical model that is suitable for describing the bending of nematic plates [25]. According to this approach, a region of the LCE that has nematic order defined by the director (i.e.…”

“…the unit vector representing the local order of the nematic mesogens) deforms spontaneously when an isotropic-to-nematic transition occurs. This deformation is quantified by the following right Cauchy-Green deformation tensor [25]: (26) where is a material-dependent parameter that varies with temperature and it is fitted from the experimental data. It can also be a function of the plate thickness ; however, in this study we assume to be constant for each specimen.…”

“…Here, we assess the mechanical response of LCE-based elements to thermal stimuli through a quantitative, physics-based micromechanical model. Results from simulations are compared to experimental data from [14] and to theoretical results from [25]. The paper is organized as follows: Section 2 is devoted to illustrating a statistical description of the microstructure of elastomers.…”

Spontaneous morphing of equibiaxially pre-stretched elastic bilayers: The role of sample geometry

“…Some of the interesting spontaneous morphing behaviour of Liquid Crystal Elastomers can be reproduced in pre-stretched bilayers, made of simple (i.e., not-active) elastic materials. It is shown in (Agostiniani and DeSimone, 2017a;Bartels et al, 2017;DeSimone, 2017) that, by "engineering" the prestretch in each of the two layers of a bilayer one can reproduce different structural models, such as bistable shells and shells with very low stiffness with the respect to twisting, as discussed in (Guest and Pellegrino, 2006) and (Guest et al, 2011), respectively. Moreover, by shaping the mid-plane of the bilayer in the form of a long, narrow rectangle, and varying the angle between the long axis of the rectangle and the uniaxial prestretch direction in one of the layers, one can produce tunable helical ribbons as in (Chen et al, 2011).…”

Special issue on ‘active behavior in soft matter and mechanobiology’

“…Curatolo, Gabriele, and Teresi present a constitutive theory for active solids that couples swelling and growth [11]. Using Gamma-convergence, Agostiniani and DeSimone derive plate and rod models for soft active materials such as nematic elastomers [12]. Nardinocchi and Puntel apply the theory of geometric composites to bilayered gel beams to reveal unexpected hardening effects [13].…”