A fast numerical method based on the Cauchy singular integral equations is presented to determine the contact pressure and extents for the contact of two-dimensional similar isotropic bodies when the contact area consists of two separate regions. The partial-slip problem is then solved to determine shear tractions using an equivalence principle. The extents of the contact are not all independent but related to a compatibility equation constraining the displacements of an elastic body in contact with an equivalent rigid body. A similar equation is found for the extents of the stick zones in partial-slip problems. The effects of load history are incorporated into the shear solution. The method is applicable to a wide range of profiles and it provides significant gains in computational efficiency over the finite element method (FEM) for both the pressure and partial-slip problems. The numerical results obtained are compared with that from the FEM for a biquadratic indenter with a single concavity and showed good agreement. Lastly, the transition behavior from double to single contacts in biquadratic profiles is investigated.
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