A numerical method for solving rough contact problems based on the multi-level multi-summation and conjugate gradient techniques

Polonsky, I. A.; Keer, Leon M.

doi:10.1016/s0043-1648(99)00113-1

Cited by 514 publications

(288 citation statements)

References 44 publications

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“…The next, more complicated problem arising in the field of elastic contact mechanic is the opposite task: Solve the indentation problem of a rigid indenter pressed in an elastic half-space with an a priori unknown contact area. Then conjugate gradient algorithms are used, like the modified form by Polonsky and Keer [21]. The procedures named above are supposed to be known and are used in the following calculations.…”

Section: The Boundary Element Methodsmentioning

confidence: 99%

The Boundary Element Method for Viscoelastic Material Applied to the Oblique Impact of Spheres

Kusche

2016

FU Mech Eng

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Abstract. The Boundary Element Method (BEM) for elastic materials is extended to deal with viscoelastic media. This is obtained by making use of a similar form of the fundamental solution for both the materials. Some considerations are attributed to the difference of the normal and the tangential contact problem. Both normal and tangential problems are furthermore assumed to be decoupled. Then the oblique impact of hard spheres with an incompressible viscoelastic half-space (linear standard-model) is studied. By assuming stick conditions during impact, one obtains the dependence of the two coefficients of restitution as functions of two input parameters. This result is expressed in an elegant and compact form of the fitting function.

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Section: The Boundary Element Methodsmentioning

confidence: 99%

The Boundary Element Method for Viscoelastic Material Applied to the Oblique Impact of Spheres

Kusche

2016

FU Mech Eng

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“…The set of in formulas (4)- (8) and formula (9) are solved using a single-loop iterative scheme based on the conjugate gradient method combined with a DC-FFT (Discrete-Convolution Fast Fourier Transform) technique to calculate the displacement u z [30,32,33]. This method was applied to render the contact area and the contact pressure at the 100th, 80,000th and 430,000th and 500,000th cycle.…”

Section: Lubrication Regimementioning

confidence: 99%

On the Growth Rate of Tribomaterial in Bovine Serum Lubricated Sliding Contacts

et al. 2016

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Considering total hip arthroplasty, so-called tribolayers (aka tribomaterial), consist of carbonaceous material from the periprosthetic joint fluid or bovine serum mixed with nanometer size metal and oxide wear particles. Currently, its growth sequence and rate are unknown. Thus, smooth surfaces of low-Carbon (LC-) vs. high-Carbon (HC-)CoCrMo (Cobalt-Chromium-Molybdenum) alloys have been worn in a conforming contact under bovine serum lubrication by means of a pin-on-ball wear tester. These tests were interrupted at certain numbers of cycles in order to weigh the specimens, characterize the topography, and investigate the wear appearances. In addition, after cleaning in ethanol and anionic detergent, before-and-after comparison rendered the weight of the tribomaterial. This revealed that, during run-in, the specimens gained weight by generating tribomaterial. Afterwards the loss of material surpassed the generation of new tribomaterial and a steady weight-loss was measured. Topography measurements were used as input data for contact mechanics calculations. Apparently the incipient, locally high contact stresses accelerated tribochemical reactions. After run-in, the contact situation changes and leads to a much smaller generation rate. This paper provides information about the growth sequence and rate of such tribomaterial formation. It further highlights the significance of highly localized contact stress as an important factor for tribomaterial generation.

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“…Based on the works developed in (Johnson, 1985;Polonsky & Keer, 1999), the model for the contact in the normal direction consists in the following equations and inequalities: …”

Section: The Contact Model In the Normal Directionmentioning

confidence: 99%