论文标题
Nematic弹性体双层的伽马连接结果：放松和致动
Gamma-convergence results for nematic elastomer bilayers: relaxation and actuation
论文作者
论文摘要
我们计算由软性弹性液体晶体组成的薄双层结构的有效能量，这些晶体在各种几何状态和功能构型中。我们的重点是弹性基础中的秩序相互作用，该弹性基础由附着在列中底物的各向同性层组成。我们计算γ-限制，因为层厚度在两个主要缩放机制中消失，表现出自发性应力松弛和形状的变形，在这两种情况下都允许平面外移。这扩展了[*]的平面应变模型，显示了完全耦合的宏观现有现有基础的渐近出现。随后，我们专注于致动和计算活性板上的nematic粉底上与施加电场相互作用的渐近构型。从分析的角度来看，电场的存在及其相关的静电工作将总能量变成了非凸和非强制功能。我们表明，平衡解决方案是系统的最低点点，最大最大的序列传递到极限，并且极限系统可以在应用的电场下施加机械工作。 [*]：P。Cesana和A. A.LeónBaldelli。 “列马弹性材料基础的变分建模”。在：应用科学中的数学模型和方法14（2018）
We compute effective energies of thin bilayer structures composed by soft nematic elastic-liquid crystals in various geometrical regimes and functional configurations. Our focus is on order-strain interaction in elastic foundations composed of an isotropic layer attached to a nematic substrate. We compute Gamma-limits as the layers thickness vanishes in two main scaling regimes exhibiting spontaneous stress relaxation and shape-morphing, allowing in both cases out-of-plane displacements. This extends the plane strain modelling of [*], showing the asymptotic emergence of fully coupled macroscopic active-nematic foundations. Subsequently, we focus on actuation and compute asymptotic configurations of an active plate on nematic foundation interacting with an applied electric field. From the analytical standpoint, the presence of an electric field and its associated electrostatic work turns the total energy into a non-convex and non-coercive functional. We show that equilibrium solutions are min-max points of the system, that min-maximising sequences pass to the limit and, that the limit system can exert mechanical work under applied electric fields. [*]: P. Cesana and A. A. León Baldelli. "Variational modelling of nematic elastomer foundations". In: Mathematical Models and Methods in Applied Sciences 14 (2018)
