In this study we investigate an axisymmetric Hertzian contact problem of a rigid sphere pressing into an elastic half-space under cyclic loading. A numerical solution is sought to obtain a steady state, which demands a large amount of computer memory and computing speed. To achieve a tractable problem, the current numerical model uses a "static reduction" technique, which employs only a contact stiffness matrix rather than the entire stiffness of the problem and is more accurate than the approach used by most finite element codes. Investigation of the tendency of contact behavior in the transient and steady states confirms that a steady state exists, showing converged energy dissipation. The dependence of dissipation on load amplitude shows a power law of load amplitude less than 3, which may explain some deviations in the experimental findings.
Bibliographical noteFunding Information:
This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology ( Grant no. 2012R1A1A2042106 ). The authors are grateful for the valuable suggestions of Professor J. R. Barber of the University of Michigan, Ann Arbor.
All Science Journal Classification (ASJC) codes
- Modelling and Simulation
- Materials Science(all)
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Applied Mathematics