Modeling two-dimensional chiral materials is a challenging problem in continuum mechanics because three-dimensional theories reduced to isotropic two-dimensional problems become nonchiral. Various approaches have been suggested to overcome this problem. We propose a new approach to this problem by formulating an intrinsically two-dimensional model which does not require references to a higher dimensional one. We are able to model planar chiral materials starting from a geometrically nonlinear Cosserat-type elasticity theory. Our results are in agreement with previously derived equations of motion but can contain additional terms due to our nonlinear approach. Plane wave solutions are briefly discussed within this model.

中文翻译：

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平面中的几何非线性 Cosserat 弹性：手性的应用

二维手征材料建模是连续介质力学中的一个具有挑战性的问题，因为简化为各向同性二维问题的三维理论变得非手性。已经提出了各种方法来克服这个问题。我们提出了一种解决这个问题的新方法，它制定了一个不需要参考更高维模型的内在二维模型。我们能够从几何非线性 Cosserat 型弹性理论开始对平面手征材料进行建模。我们的结果与先前导出的运动方程一致，但由于我们的非线性方法可能包含附加项。在这个模型中简要讨论了平面波解决方案。