Indentation of a Functionally Graded Plate by a Rigid Spherical Indenter

Indentation of a functionally graded (FG) plate with finite dimensions by a rigid spherical punch is considered. The plate is simply supported and the contact of the plate and the punch is assumed to be frictionless. A literature review of the problem shows that most researchers consider the Hertzian contact model, but this model is not accurate especially for plates made of nonhomogeneous and anisotropic materials. Here, the contact rule will be derived by solving the equations of equilibrium in terms of displacement field. Two higher order deformation theories will be considered for the displacement field of the plate. One of these theories neglects the changes in plate thickness while the other one considers the changes in plate thickness. The stressstrain relation is assumed to be linear. The gradient of mechanical properties variation is considered through the thickness of the plate and is modeled by a polynomial function and the Poisson’s ratio is kept constant. In order to validate the analytical results, a simulation of the problem will be done by Abaqus software. The results obtained by the two deformation theories are compared to each other and with those of the software simulation. The effect of gradient changes and plate dimensions on the contact rule will be investigated. The analytical results obtained from each of the two considered deformation theories are in good agreement with each other and with those of acquired from Abaqus, for small plate thicknesses, showing that considering the changes in plate thickness is not necessary for this condition. As the plate thickness increases, the analytical results obtained from the two deformation theories deviate from each other, but the results from the theory which considers the changes in plate thickness are in proper agreement which those acquired from Abaqus simulation.

کلیدواژه ها:

Functionally Graded Plate ، Higher Order Deformation Theory ، Contact Mechanics ، Finite Element Analysis