Efficient Numerical Modeling of Hertzian Line Contact for Material With Inhomogeneities

The present work proposes an efficient and general-purpose numerical approach for handling two-dimensional inhomogeneities in an elastic half plane. The inhomogeneities can be of any shape, at any location, with arbitrary material properties (which can also be non-homogeneous). To perform the numerical analysis, we first derive an explicit closed-form solution for a rectangular inclusion with uniform eigenstrain components, where the inclusion is aligned with the surface of the half plane. In view of the equivalent inclusion method, an inhomogeneity problem can be converted to a corresponding inclusion problem. In order to determine the distribution of the equivalent eigenstrain, the computational domain is meshed into rectangular elements whose resultant contributions can be efficiently computed using an efficient algorithm based on fast Fourier transform (FFT). In principle, there is no specific limitation on the type of the external load, although our major concern is the contact analysis. Parametric studies are performed and typical results highlighting the deviation of the current solution from the classical Hertzian line contact theory are presented.