Contact Interaction of a Rigid Stamp and a Porous Elastic Cylinder of Finite Dimensions

This article investigates an axisymmetric contact problem involving the interaction between a rigid cylindrical stamp and a poroelastic cylinder of finite dimensions, based on the Cowin–Nunziato theory of media with voids. The stamp is assumed to have a flat base and to be in frictionless contact with the cylinder. The cylinder, in turn, rests on a rigid base without friction, with no normal displacements or tangential stresses on its lateral surface. Under an applied vertical force, the stamp undergoes displacement, compressing the poroelastic cylinder. The mathematical formulation of this problem involves expressing the unknown displacements within the cylinder and the variation in pore volume fraction as a series of Bessel functions. This representation reduces the problem to an integral equation of the first kind, describing the distribution of contact stresses beneath the stamp. The kernel of the integral equation is explicitly provided in its transformed form. The collocation method is employed to solve the integral equation, enabling the determination of contact stresses and the relationship between the indenter’s displacement and the applied force. A comparative model parameter analysis is performed to examine the effects of different material porosity parameters and model geometrical characteristics on the results.