INCIPIENT SEPARATION BETWEEN A FRICTIONLESS FLAT PUNCH AND AN ANISOTROPIC MULTILAYERED HALF-PLANE

A solution to the frictionless contact of rigid flat indenters on arbitrarily layered, anisotropic half planes is obtained using Fourier transforms and the local-global stiffness matrix technique. The local-global stiffness matrix method involves reformulating the problem in terms of interfacial displacements as the basic unknowns, and has been shown to be an efficient method for solving mixed boundary-value problems of laminated media. The contact problem of a rigid punch gives rise to a mixed boundary condition of known displacement gradient and unknown pressure distribution in the contact area. This mixed boundary condition is reduced to a singular integral equation involving the unknown pressure using the asymptotic properties of the global stiffness matrix. A solution for the contact pressure distribution is then obtained from the singular integral equation using a technique provided by Erdogan. which involves the use of orthogonal Chebychev polynomials. The results are employed to determine the boundaries between full and two-region, and full and three-region, contact solution zones in separation parameter spaces that illustrate the effect of geometric and material parameters on the incipient separation between a flat punch and the top layer of a half plane laminated with isotropic, transversely isotropic and monoclinic plies.