We derive a Föppl-von Kármán-type constitutive model for solid liquid crystalline plates where the nematic director may or may not rotate freely relative to the elastic network. To obtain the reduced two-dimensional model, we rely on the deformation decomposition of a nematic solid into an elastic deformation and a natural shape change. The full solution to the resulting equilibrium equations consists of both the deformation displacement and stress fields. The model equations are applicable to a wide range of thin nematic bodies subject to optothermal stimuli and mechanical loads. For illustration, we consider certain reversible natural shape changes in simple systems which are stress free, and their counterparts, where the natural deformations are blocked and internal stresses appear. More general problems can be addressed within the same framework.

我们推导了固态液晶板的Föppl-vonKármán型本构模型，其中向列指向矢可能相对于弹性网络自由旋转，也可能不自由旋转。为了获得简化的二维模型，我们依靠向列固体的变形分解为弹性变形和自然形状变化。所得平衡方程的完整解包括变形位移和应力场。模型方程适用于受光热刺激和机械载荷作用的各种薄向列体。为了说明起见，我们考虑了在无应力的简单系统中的某些可逆的自然形状变化，以及与之对应的自然变形受阻且内部应力出现的对应形状。