A problem for a nanosized penny-shaped fracture in an infinite homogeneous isotropic elastic medium is considered. The fracture is opened by applying an axisymmetric normal traction to its surface. The surface energy in the Steigmann–Ogden form is acting on the boundary of the fracture. The problem is solved by using the Boussinesq potentials represented by the Hankel transforms of certain unknown functions. With the help of these functions, the problem can be reduced to a system of two singular integro-differential equations. The numerical solution to this system can be obtained by expanding the unknown functions into the Fourier–Bessel series. Then the approximations of the unknown functions can be obtained by solving a system of linear algebraic equations. Accuracy of the numerical procedure is studied. Various numerical examples for different values of the surface energy parameters are considered. Parametric studies of the dependence of the solutions on the mechanical and the geometric parameters of the system are undertaken. It is shown that the surface parameters have a significant influence on the behaviour of the material system. In particular, the presence of surface energy leads to the size-dependency of the solutions and smoother behaviour of the solutions near the tip of the crack.

考虑了无限均质各向同性弹性介质中纳米尺寸的便士形断裂的问题。通过在其表面施加轴对称法向张力来打开骨折。Steigmann–Ogden形式的表面能作用于裂缝的边界。通过使用某些未知函数的Hankel变换表示的Boussinesq势可解决该问题。借助这些功能，可以将问题简化为两个奇异的积分微分方程组。通过将未知函数扩展为傅立叶-贝塞尔级数，可以获得该系统的数值解。然后，可以通过求解线性代数方程组来获得未知函数的近似值。研究了数值程序的准确性。考虑了用于表面能参数的不同值的各种数值示例。对解决方案对系统的机械和几何参数的依赖性进行了参数研究。结果表明，表面参数对材料系统的行为有重要影响。特别地，表面能的存在导致溶液的尺寸依赖性以及靠近裂纹尖端的溶液的较平滑行为。