Asymptotic analysis and finite element calculation of a rubber notch contacting with a rigid wedge

In this paper, the strain energy function given by Knowles-Sternberg in 1973 is used, and the contact problem of a rubber notch with a rigid wedge is analayzed. The basic equations of the deformation field near the notch corner are derived and solved. An analytical solution is obtained for the expanding sector while the numerical sotution is given for two shrinking sectors. A special interesting case is that a half rubber-like plane contacts with a rigid wedge, for which the completely analytical solutions are obtained for both expanding sector and shrinking sectors. The analysis of this paper is also valid for the contact problem of a rubber wedge with a rigid wedge. To verify the analytical results, a finite element program of nonlinear elasticity is made with which the same problem is calculated, and the results are consistent with the analytical results very well.