Contact-Coupled Impact of Slender Rods: Analysis and Experimental Validation

Abstract

To validate models of contact mechanics in low speed structural impact, slender rods were impacted in a drop tower, and measurements of the contact and vibration were compared to analytical and finite element (FE) models. The contact area was recorded using a novel thin-film transfer technique, and the contact duration was measured using electrical continuity. Strain gages recorded the vibratory strain in one rod, and a laser Doppler vibrometer measured speed. The experiment was modeled analytically on a one-dimensional spatial domain using a quasi-static Hertzian contact law and a system of delay differential equations. The three-dimensional FE model used hexahedral elements, a penalty contact algorithm, and explicit time integration. A small submodel taken from the initial global FE model economically refined the analysis in the small contact region. Measured contact areas were within 6% of both models’ predictions, peak speeds within 2%, cyclic strains within 12 με (RMS value), and contact durations within 2 μs. The global FE model and the measurements revealed small disturbances, not predicted by the analytical model, believed to be caused by interactions of the non-planar stress wavefront with the rod’s ends. The accuracy of the predictions for this simple test, as well as the versatility of the diagnostic tools, validates the theoretical and computational models, corroborates instrument calibration, and establishes confidence that the same methods may be used in experimental and computational study of contact mechanics during impact of more complicated structures. Recommendations are made for applying the methods to a particular biomechanical problem: the edge-loading of a loose prosthetic hip joint which can lead to premature wear and prosthesis failure.

Application of the finite element submodeling technique in a single point contact and wear problem

“…20 This process becomes particularly heavy when wear is simulated over a long period of time and/or in case of complex three-dimensional (3D) geometries. Despite a discrete number of papers have discussed the use of submodeling to efficiently solve the contact mechanics, 5,[21][22][23][24][25][26] only a few studies are focused on the application of this technique to wear analyses.…”