Multigrid numerical simulation of contact mechanics of elastic materials with 3D heterogeneous subsurface topology

Boffy, Hugo; Venner, Cornelis H.

doi:10.1016/j.triboint.2015.06.015

Cited by 18 publications

(17 citation statements)

References 41 publications

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“…The unknown displacements and contact pressure of top boundary can be solved with Eqs. (2)-(4) [14].…”

Section: Top Boundary Equationsmentioning

confidence: 99%

“…The equations are discretized on a uniform grid using a finite difference approach, see Appendix A. The discrete equations are solved using multigrid techniques [9,14]. An iterative process is designed using a Gauss-Seidel (consecutive) relaxation scheme for the displacement equations with special treatment for the boundary equations to ensure a good error smoothing which is essential for a multigrid solver.…”

Section: Numerical Techniquementioning

confidence: 99%

“…It is proved the developed multigrid algorithm possess high accuracy and efficiency. Later, it was extended to 3D contact mechanics with heterogeneous material [14]. In this paper, the multigrid method is demonstrated to be very well suited to solve the computationally even more demanding problem of contact mechanics and subsurface stress field for bearing material with heterogeneous properties on the very local scale of grains including anisotropy.…”

Section: Introductionmentioning

confidence: 99%

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Multigrid solution of 2D and 3D stress fields in contact mechanics of anisotropic inhomogeneous materials

Zhang

Boffy

Venner

2020

Tribology International

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Increasing demands on performance of machines lead to severer operating conditions of rolling bearings, i.e. higher loads, less lubricant, thinner lubricant films. Under these conditions, the effects of inhomogeneity and anisotropy on the fatigue life become more important. Accurate prediction of such effects requires detailed surface pressure and subsurface stress calculations. For practically relevant 3D cases with realistic grain sizes, this can only be done with very efficient numerical solution methods. In this paper, multigrid techniques are demonstrated to yield the required performance. The influence of inclusions, crystal orientation and roughness on the Von Mises stress distribution is investigated. The algorithm is suited for subsurface material analysis and optimization as well as for computational diagnostics using image analysis. (B. Zhang).Tribology International xxx (xxxx) xxx-xxx 0301-679X/

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“…The unknown displacements and contact pressure of top boundary can be solved with Eqs. (2)-(4) [14].…”

Section: Top Boundary Equationsmentioning

confidence: 99%

Section: Numerical Techniquementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Multigrid solution of 2D and 3D stress fields in contact mechanics of anisotropic inhomogeneous materials

Zhang

Boffy

Venner

2020

Tribology International

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“…In a previous paper, Boffy and Venner 30 developed a multigrid solution method for contact problems between three-dimensional elastic heterogeneous materials. The contact problem has been incorporated as boundary condition in the multigrid solution of the displacement equations for the volume (Lamé elasticity equations).…”

Section: Full Numerical Lubrication Model With Smooth Surfacesmentioning

confidence: 99%

“…The primary unknowns (displacements and pressure) in a regular grid arrangement are smoothed and updated simultaneously as detailed in literature. 30 Note that this process can be coupled with line iteration scheme, in the EHL problem along the direction of the flow. This combination allows one to reduce the number of multigrid cycles and may help to deal with very high loading conditions; however, its cost in terms of CPU time is substantial and this method has not been implemented for this study.…”

Section: Full Numerical Lubrication Model With Smooth Surfacesmentioning

confidence: 99%

Effects of material heterogeneity on surface fatigue for rough lubricated rolling–sliding contacts

Morales-Espejel

Boffy

Venner

2016

Proceedings of the Institution of Mechanical Engineers, Part J:

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In view of increasingly severe operating conditions and the use of composite (strongly) heterogeneous materials, detailed modelling and optimisation methods are needed to predict the effects of subsurface material topology, either by design or resulting from inclusions and material anisotropy, on rolling-sliding contact fatigue life. In this paper, a method is proposed showing that such predictions can at present be obtained for realistic configurations on small-scale computers by integrating efficient numerical solution of the 3D displacement and stress field in the (heterogeneous) material with fast rough surface-lubricated contact models. Contact pressures, subsurface stresses and surface fatigue effects are shown for cases of bonded individual or multiple (clusters) of statistically distributed inhomogeneities close to the surface in realistic actual rolling–sliding rough contact geometries. The model contributes to the development of optimised failure criteria for composite/heterogeneous materials close to the surface.

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Local grid refinement in multigrid method for point contact problems of polycrystalline anisotropic material under dry and lubricated conditions

Zhang

Vlogman

Andric³

et al. 2022

Friction

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Predicting rolling bearing fatigue life requires knowledge of the three-dimensional (3D) stress fields in the roller and raceway near the lubricated contact. Owing to the increasingly severe operating conditions, the effect of localized features such as surface roughness, subsurface inclusions, and even the crystallographic structure of the material becomes important. Achieving such detail requires (locally) extremely dense gridding in simulations, which in 3D is a major challenge. Multigrid techniques have been demonstrated to be capable of solving such problems. In this study, multigrid techniques are shown to further increase the efficiency of the solution by exploiting local grid refinement while maintaining the simplicity of a uniform discretization. This is achieved by employing increasingly finer grids only locally, where the highest resolution is required. Results are presented for dry contact and elastohydrodynamically lubricated contact cases, circular as well as elliptic, with varying crystallographic structure, and with surface roughness. The results show that the developed algorithm is very well suited for detailed analysis, with also excellent prospects for computational diagnostics involving actual material crystallographic structure from electron backscatter diffraction measurements.

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Multigrid numerical simulation of contact mechanics of elastic materials with 3D heterogeneous subsurface topology

Cited by 18 publications

References 41 publications

Multigrid solution of 2D and 3D stress fields in contact mechanics of anisotropic inhomogeneous materials

Multigrid solution of 2D and 3D stress fields in contact mechanics of anisotropic inhomogeneous materials

Effects of material heterogeneity on surface fatigue for rough lubricated rolling–sliding contacts

Local grid refinement in multigrid method for point contact problems of polycrystalline anisotropic material under dry and lubricated conditions

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