Abstract

Large deflections relevant for suspended circular graphene sheets with simply supported boundaries are computed by a theory for 2D membranes subjected to several types of vertical axisymmetric forces, based on the principle of virtual power (PVP). Corresponding stress–strain relations are provided in the form of a nonlinear hyperelastic material model for graphene. When approximating the deflections through Fourier series, the PVP yields a nonlinear algebraic system of equations, which is solved by the iterative Newton–Raphson procedure. The new computational efficient method is validated through comparison of the numerical results it provides, with predictions obtained from experimental nanoindentaion measurements.

摘要

基于虚拟功率 (PVP) 原理，通过受多种类型垂直轴对称力的二维膜理论计算了与具有简单支撑边界的悬浮圆形石墨烯片相关的大挠度。相应的应力-应变关系以石墨烯的非线性超弹性材料模型的形式提供。当通过傅里叶级数近似挠度时，PVP 产生一个非线性代数方程组，通过迭代 Newton-Raphson 程序求解。通过比较它提供的数值结果与从实验纳米压痕测量获得的预测，验证了新的计算有效方法。