Thickness effect on the contact behavior of a composite laminate indented by a rigid sphere

Abstract

A modified Hertz contact law is proposed for the contact problem of a laminated plate indented by a rigid sphere, which involves the effects of the thickness, in-plane dimensions and boundary conditions of the plate. The model shows that the deflection difference between the center and the edge of the contact area is a key factor dominating the effects of these variables on the force–indentation response. The modified contact law is assumed to follow the same mathematical formulation as the Hertz law. However, the contact stiffness is no longer constant but varies as a function of the contact force due to the thickness effect. The predictions of the force–indentation response show improved agreement over early work by Yang and Sun. Over the present analysis range, the thickness effect may be negligible if the plate thickness is greater than 2 mm. On the other hand, the thickness has a more significant effect on the force–indentation response if the plate thickness is less than 2 mm. Moreover, the in-plane dimensions and the boundary conditions of the plate show little influence on the force–indentation response within the present scope of analysis.