Analysis Of A Rubber Wedge Contacting With A Rigid Notch And The Finite Element Computation

In this paper, by using the strain energy function given by the document [9], one kind of typical contact problem of large deformation between a rubber wedge and a rigid notch is studied. By analyzing the strain near the rubber wedge with complicate manipulation, the analytical solutions are obtained. The results show that there is neither expending sector nor shrinking sector in the contact problem between the rubber wedge and rigid notch. When the rubber wedge is compressed into the rigid notch, the points on the same radius before deformation distribute evenly. The deformation of the wedge tip in the direction of radius possesses singularity and the singular exponentδdepends on the ratioβ/αand the material constant n . And the deformation of the wedge tip in the direction of angle doesn't possess singularity. The deformation of the angle of the wedge tip is different from a constant angle, and this constant angle is equal to the ratioβ/αof the wedge angle to the notch. And the components stresses are independent of the angleθafter deformation.This paper also carry on the contrast with the asymptotic analysis solution of the strain energy function proposed from document [9] and the asymptotic analysis solution of the strain energy function proposed from document [32]. The distributions of deformation and stress of the rubber wedge tip are basic consistent that they are obtained from the two strain energy function. The difference between the components stress of the direction of radius and the components stress of the direction of angle obtained from document [9] is smaller than the one obtained from document [32]. But the components stress of the direction of radius is bigger than the components stress of the direction of angle. By using the non-linear finite element analysis software MSC.Marc, the contact of the rubber wedge and the rigid notch is simulated. Making use of development platform provided by MSC.Marc, a user subroutine named uelastomer is programmed and the strain energy function obtained from document [9] and [32] is programmed into MSC.Marc. It obtains the numerical results about the contact problem of the rubber wedge and the rigid notch. And it also carries on the contrast with the numerical results and the theoretic solution. By the curves of stress and strain obtained by finite element analysis which show that the points on the same radius before deformation distribute evenly, the deformation of the wedge tip in the direction of radius possesses singularity, the deformation of the wedge tip in the direction of angle doesn't possess singularity. Their figures fit well. These also testify that the user subroutine is valid and applicable.