A thermomechanical, polar continuum formulation under finite strains is proposed for anisotropic materials using a multiplicative decomposition of the deformation gradient. First, the kinematics and conservation laws for three-dimensional, polar, and nonpolar continua are obtained. Next, these kinematics and conservation laws are connected to their corresponding counterparts for surface continua, based on Kirchhoff–Love assumptions. Then the shell material models are extracted from three-dimensional material models for finite-temperature problems using established connections. The weak forms are obtained for both three-dimensional nonpolar continua and Kirchhoff–Love shells. These formulations are expressed in tensorial form so that they can be used in both curvilinear and Cartesian coordinates. They can be used to model anisotropic crystals and soft biological materials.

中文翻译：

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各向异性体积和表面连续体的非线性热机械公式

使用变形梯度的乘法分解为各向异性材料提出了有限应变下的热机械极性连续体公式。首先，获得了三维、极地和非极地连续体的运动学和守恒定律。接下来，基于 Kirchhoff-Love 假设，这些运动学和守恒定律与其对应的表面连续体对应物相关联。然后使用已建立的连接从有限温度问题的三维材料模型中提取壳材料模型。对于三维非极性连续体和基尔霍夫-洛夫壳都获得了弱形式。这些公式以张量形式表示，因此它们可用于曲线坐标和笛卡尔坐标。