Liquid crystal elastomers (LCEs) are a class of materials which exhibit an anisotropic behavior in their nematic state due to the main orientation of their rod-like molecules called mesogens. The reorientation of mesogens leads to the well-known actuation properties of LCEs, i.e. exceptionally large deformations as a consequence of particular external stimuli, such as temperature increase. Another key feature of nematic LCEs is the capability to undergo deformation by constant stresses while being stretched in a direction perpendicular to the orientation of mesogens. During this plateau stage, the mesogens rotate towards the stretching direction. Such characteristic is defined as semisoft elastic response of nematic LCEs. We aim at modeling the semisoft behavior in a dynamic finite element method based on a variational-based mixed finite element formulation. The reorientation process of the rigid mesogens relative to the continuum rotation is introduced by micropolar drilling degrees of freedom. Responsible for the above-mentioned characteristics is an appropriate free energy function. Starting from an isothermal free energy function based on the small strain theory, we aim to widen it into the framework of large strains by identifying tensor invariants. In this work, we analyze the isothermal influence of the tensor invariants on the mechanical response of the finite element formulation and show that its space-time discretization preserves mechanical balance laws in the discrete setting.

液晶弹性体（LCE）是一类在向列态下表现出各向异性行为的材料，这是由于其被称为介晶的棒状分子的主要取向所致。介晶的重新取向导致了众所周知的LCE的驱动特性，即由于特定的外部刺激（例如温度升高）而导致异常大的变形。向列液晶电子的另一个关键特征是能够在恒定应力的作用下发生变形，同时在垂直于介晶取向的方向上拉伸。在此平台阶段，介晶朝拉伸方向旋转。这种特性被定义为向列LCE的半软弹性响应。我们的目标是基于基于变分的混合有限元公式，在动态有限元方法中对半软行为进行建模。刚性介晶相对于连续介质旋转的重新取向过程是通过微极钻井自由度引入的。负责上述特性的是适当的自由能函数。从基于小应变理论的等温自由能函数开始，我们的目标是通过识别张量不变量将其扩展到大应变的框架。在这项工作中，我们分析了张量不变量对有限元公式的机械响应的等温影响，并表明其时空离散在离散设置中保留了机械平衡定律。