A model of in-plane graphene deformation is developed by considering a linear chain of atoms with regard to the independent moment interaction and noncentral force interaction between atoms. A discrete and continuous beam models of the linear chain of atoms are constructed. Assuming that each graphene atom interacts only with its nearest neighbors, the atomic system is replaced by a beam system using the obtained continuous beam model of the linear atomic chain. A discrete-continuous and continuous models of graphene are derived. The first one is a special molecular dynamics model, and the second is a plane stress model of the moment theory of elasticity with independent displacement and rotation fields. The elastic constants of the second model are determined through the atomic structure parameters of graphene. It is shown that the problems of in-plane graphene deformation can be solved using both the discrete-continuous model (beam system model) and the continuous model as the plane stress model of the moment theory of elasticity with independent displacement and rotation fields with known elastic constants.

中文翻译：

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面内变形下石墨烯的离散连续和连续矩模型

通过考虑原子之间的独立力矩相互作用和非中心力相互作用的线性原子链，开发了面内石墨烯变形模型。构建了线性原子链的离散和连续梁模型。假设每个石墨烯原子仅与其最近的邻居相互作用，原子系统被使用线性原子链的连续束模型的束系统代替。衍生出石墨烯的离散-连续和连续模型。第一个是特殊的分子动力学模型，第二个是具有独立位移和旋转场的弹性矩理论的平面应力模型。第二个模型的弹性常数是通过石墨烯的原子结构参数确定的。