The lack of experimental investigations on graphene fostered researchers to focus on its mechanical modeling. Being graphene a one-atom-thick sheet, many authors developed continuum membrane models to analyze its mechanical behavior. However, an entirely nonlinear approach in finite elasticity has not been presented so far. In this work, the equilibrium problem of anisotropic hyperelastic graphene membranes is addressed. Strain and stress measures are expressed under the hypothesis of homogeneous deformations and the boundary-value problem is formulated for a graphene membrane subjected to biaxial loads. The stability of the equilibrium configurations is assessed through an energy criterion. Explicit relations between stretches and stresses of the membrane are derived for the cases of uniaxial and equibiaxial loads. Unexpectedly, bifurcation and multiple equilibrium solutions are found when graphene is subjected to equibiaxial loads. A linearization of the finite theory is presented and the expressions of Young’s modulus and Poisson’s ratio of graphene are derived. The formulation proposed in this work may be the basis for accurate investigations of the mechanics of graphene subjected to large deformations.

石墨烯实验研究的缺乏促使研究人员专注于其机械建模。由于石墨烯是一个原子厚的薄片，许多作者开发了连续膜模型来分析其力学行为。然而，到目前为止还没有提出有限弹性中完全非线性的方法。在这项工作中，解决了各向异性超弹性石墨烯膜的平衡问题。应变和应力测量是在均匀变形的假设下表示的，并且边界值问题是为承受双轴载荷的石墨烯膜制定的。平衡配置的稳定性通过能量标准进行评估。对于单轴和等双轴载荷的情况，可以导出膜的拉伸和应力之间的明确关系。不料，当石墨烯受到等双轴载荷时，会发现分叉和多重平衡解。提出了有限理论的线性化，并导出了石墨烯的杨氏模量和泊松比的表达式。这项工作中提出的公式可能是准确研究石墨烯经受大变形的力学的基础。