The complete nonlinear resultant 2D model of shell thermodiffusion is developed. All 2D balance laws and the entropy imbalance are formulated by direct through-the-thickness integration of respective 3D laws of continuum thermodiffusion. This leads to a more rich thermodynamic structure of our 2D model with several additional 2D fields not present in the 3D parent model. Constitutive equations of elastic thermodiffusive shells are discussed in more detail. They are formulated from restrictions imposed by the resultant 2D entropy imbalance according to Coleman–Noll procedure extended by a set of 2D constitutive equations based on heuristic assumptions.

中文翻译：

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壳热扩散的非线性合成理论

建立了壳热扩散的完整非线性合成二维模型。所有2D平衡定律和熵失衡是通过连续热扩散的各个3D定律的直接整个厚度积分来制定的。这导致我们的2D模型具有更丰富的热力学结构，而3D父模型中不存在几个其他2D场。弹性热扩散壳的本构方程被更详细地讨论。它们是根据由Coleman-Noll程序根据结果2D熵不平衡所施加的限制而公式化的，该过程由基于启发式假设的一组2D本构方程扩展而成。