Since the atomistic mechanism against monolayer graphene deformations has not been well comprehended, modeling graphene’s mechanical properties is still an open question. The torsional stiffness associated with Gaussian curvature, in particular, is extremely difficult to understand and estimate via either experiments or simulations. In this paper, using the bond-orbital model (BOM) based on the tight-binding (TB) method, we find out that graphene can be model as the Föppl-von Karman plate with four independent mechanical parameters, and present the clear connections between the mechanical parameters and the chemical bonds for the first time. Our TB theory reveals that the Gaussian modulus only relies on the torsion of the adjacent \(\pi\)-orbitals, and elucidates that the independence between out-of-plane and in-plane mechanical parameters comes from the geometrical irrelevance between the bond-formation energy of \(\sigma\)-bonds and that of \(\pi\)-bonds. Besides, the constraints on two out-of-plane mechanical parameters are given through the thermodynamic stability requirement: the Gaussian modulus \(k_{G} < 0\) and the bending modulus \(k_{B} > - k_{G} /2\). The mechanical parameters obtained by our TB theory are well agreed with experiments and Quantum calculations.

由于针对单层石墨烯变形的原子机理尚未得到很好的理解，因此对石墨烯的机械性能进行建模仍然是一个悬而未决的问题。尤其是，与高斯曲率相关的扭转刚度非常难以通过实验或模拟来理解和估计。本文使用基于紧密结合（TB）方法的键轨道模型（BOM），我们发现石墨烯可以建模为具有四个独立机械参数的Föppl-vonKarman板，并给出清晰的连接机械参数和化学键之间的关系首次出现。我们的TB理论表明，高斯模量仅取决于相邻\（\ pi \）的扭转轨道，并阐明面外和面内机械参数之间的独立性来自\（\ sigma \）-键的键形成能与\（\ pi \）的键形成能之间的几何无关性-债券。此外，通过热力学稳定性要求给出了两个平面外机械参数的约束条件：高斯模量\（k_ {G} <0 \）和弯曲模量\（k_ {B}>-k_ {G} / 2 \）。通过我们的结核病理论获得的机械参数与实验和量子计算完全吻合。