A General Three-Dimensional Numerical Technique for Determining the Contact Area of an Arbitrary Punch on an Elastic Half-Space

The paper presents a numerical method for determining the contact area in three-dimensional elastostatic normal contact without friction. The method makes use of the theorem developed by Barber, the contact area is that over which the total indentation force achieves its maximum value. By approximating the punch by linear interpolation, the analytical expression for the indentation force is derived by virtue of the reciprocal theorem. The physical meaning of the parameter which determines the contact boundary is discussed, and its feasible range corresponding to the contact area is found. Then, the numerical algorithm for determining the parameter is developed and applied to solve several normal contact problems. The results show that the proposed numerical method possesses a good property on accuracy and convergency.