The three-dimensional problem of contact between a spherical indenter and a multi-layered structure bonded to an elastic half-space is investigated. The layers and half-space are assumed to be composed of transversely isotropic materials. By the use of Hankel transforms, the mixed boundary value problem is reduced to an integral equation, which is solved numerically to determine the contact stresses and contact region. The interior displacement and stress fields in both the layer and half-space can be calculated from the inverse Hankel transform used with the solved contact stresses prescribed over the contact region. The stress components, which may be related to the contact failure of coatings, are discussed for various coating thicknesses.

a b s t r a c tThis paper presents a two-dimensional contact stress analysis to investigate the effects of multiple inclusions on the contact pressure and subsurface stresses in an elastic half-plane. The boundary element method is used to analyze the contact problem where a set of integral equations is derived on the contact region and the matrix-inclusion interfaces. As the contact region is unknown a priori, an iterative procedure is implemented to determine the actual contact region and the contact pressure, and the tractions and displacements on the matrix-inclusion interfaces are obtained by solving the integral equations numerically. Numerical results show that the inclusions near contact surface could cause significant alterations in the contact pressure distribution. The stiff inclusions could toughen the surrounding material and reduce the internal stresses while the soft inclusions could increase the subsurface stresses.

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The three-dimensional problem of a multilayered composite containing an arbitrarily oriented crack is considered in this paper. The crack problem is analyzed by the equivalent body force method, which reduces the problem to a set of singular integral equations. To compute the kernels of the integral equations, the stiffness matrix for the layered medium is formulated in the Hankel transformed domain. The transformed components of the Green’s functions and derivatives are determined by solving the stiffness matrix equations, and the kernels are evaluated by performing the inverse Hankel transform. The crack-opening displacements and the three modes of the stress intensity factor at the crack front are obtained by numerically solving the integral equations. Examples are given for a penny-shaped crack in a bimaterial and a three-material system, and for a semicircular crack in a single layer adhered to an elastic half-space.

Free surface displacements, stress intensity factors, and energy release rates are calculated for planar slip zones in an elastic half‐space subjected to a prescribed shear stress drop. Although the method can treat arbitrarily shaped planar zones and distributed stress drops, for simplicity, results are presented only for circular and elliptic zones and uniform stress drops. Calculations of the stress intensity factors and energy release rates for various geometries indicate that solutions for the half‐space differ by less than 10% from those in the full space if the distance from the slip zone center to the free surface is greater than the downdip width of the slip zone. In addition, the influence of the free surface is greater for decreasing dip angle. For slip zones that are near the free surface and, especially, those that break the surface there is a coupling between slip and normal relative displacement. That is, for a prescribed shear stress drop and zero normal stress change, slip induces relative normal displacement. As example applications, these solutions are used to reexamine the coseismic geodetic data from three earthquakes: 1966 Parkfield, 1983 Borah Peak, and 1987 Whittier Narrows. The geometries, moments, and stress drops are similar to those inferred in previous studies using dislocation methods. However, the stress drop inferred here may be more reliable because stress drop is one of the parameters adjusted to fit the observed surface deformations. In addition, the method makes it possible to estimate the critical energy release rate at the termination of rupture. Values for the Parkfield, Borah Peak, and Whittier Narrows earthquakes are 1.5.×106 J/m2, 1.2×106 J/m2, and 2×108 J/m2, respectively.