Recent research extended the non-adhesive contact problems between an incompressible layer and a rigid indenter to adhesive cases in the limit of the Johnson–Kendall–Roberts (JKR) model, where it simply changes the boundary condition. The governing equation of this problem is in the form of Poisson’s equation, and there are two boundary conditions, one of which serves to determine the extent of the contact area. This makes it possible to develop a numerical solution of an adhesive thin incompressible layer indentation problem. For a numerical implementation, we have devised a finite element formulation with a moving mesh technique satisfying the slope boundary condition, which determines the actual extent of the contact area. We shall apply the proposed numerical method to an adhesive contact problem by a spherical rigid indenter to demonstrate the validity of the method. Furthermore, we will compare the characteristics of the JKR indentation solutions between a half-space and a thin incompressible layer.

最近的研究在Johnson-Kendall-Roberts（JKR）模型的极限范围内将不可压缩层与刚性压头之间的非粘性接触问题扩展到了粘性情况，在该模型中，边界条件只是改变了。此问题的控制方程采用泊松方程的形式，并且存在两个边界条件，其中一个边界条件用于确定接触区域的范围。这使得可以开发粘性薄的不可压缩层压痕问题的数值解决方案。对于数值实现，我们已经设计了一种使用满足斜率边界条件的移动网格技术的有限元公式，该公式确定了接触面积的实际范围。我们将通过球形刚性压头将提出的数值方法应用于胶粘剂接触问题，以证明该方法的有效性。此外，我们将比较半空间和不可压缩的薄层之间的JKR压痕解决方案的特征。