Elastic-plastic analysis of a rolling disk by finite elements

An elastic-plastic finite element method is employed to determine the stress distribution in a circular disk rolling on a rigid track and subjected to hub loads. This model can be assumed to represent a railroad wheel. Of particular interest are the stresses that exceed the initial yield limit near the point of contact. The material constitutive laws considered herein represent elastic-perfectly plastic and strain hardening materials that obey Mises' yield condition. It is shown that unloading of the previously yielded elements due to rotation can be easily handled by the direct stiffness tangent modulus approach. Total and plastic strains, and the plastic work in the disk model are given for the entire rolling history of the disk. It is also demonstrated that the disk will shake down to a purely elastic steady state for load values beyond the initial yield if the material of the disk exhibits even a small amount of strain hardening.