Smooth indentation of a multilayer laminate by a cylindrical indentor

The smooth contact between a rigid cylindrical indentor and a composite laminate with arbitrary ply-orientation is investigated. An exact Green‘s function for the surface displacement of an anisotropic beam under cylindrical bending is derived from Jonesʹs displacement formulation. By matching the displacements of the top surface of the anisotropic laminate and those of the rigid indentor within the contact region, we can find the contact stress distribution, the magnitude of contact force and the indentation. This exact Greenʹs function approach is also valid for the indentation analysis between an orthotropic laminate and a cylindrical indentor. To simplify the contact analysis, the multilayered laminate is homogeneized as an orthotropic medium using the 3-D effective moduli theory, and thus forms an orthotropic solution. Numerical results for laminates with arbitrary ply-orientation subjected to cylindrical indentation are evaluated to verify the applicability of the proposed exact Green‘s function method. Simplified orthotropic solutions applying the 3-D effective moduli theory are also compared with the exact Green‘s function solution with obvious agreement.