A contact problem for a poroelastic halfspace containing an embedded inextensible membrane

The paper examines the axisymmetric problem of the indentation of a poroelastic halfspace that is reinforced with an inextensible permeable/impermeable membrane located at a finite depth by a rigid indenter. The constitutive behavior of the poroelastic halfspace is described by the three-dimensional theory of poroelasticity proposed by M.A. Biot. The contact conditions between the indenter and the poroelastic halfspace are varied to accommodate both adhesive/frictionless contact and impermeable/permeable conditions. The formulation of the mixed boundary value problems uses the stress function approaches applicable to semi-infinite domains. Successive applications of Laplace and Hankel integral transforms are used to reduce the mixed boundary value problems to sets of coupled Fredholm integral equations of the second kind. These integral equations are solved using numerical approaches, applicable both for the solution of the systems of coupled equations and for Laplace transform inversion, to examine the time-dependent displacement of the rigid indenter. The analytical-numerical estimates for the time-dependent displacements of the rigid indenter are compared with results obtained using a finite element approach.