An Efficient 3D Model of Heterogeneous Materials for Elastic Contact Applications Using Multigrid Methods

Boffy, Hugo; Baietto, Marie-Christine; Sainsot, Philippe; Lubrecht, Antonius

doi:10.1115/1.4006296

Cited by 16 publications

(19 citation statements)

References 26 publications

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“…(12) from [40], the maximum difference is 1.3% for E c =E s ¼ 0:05, which shows the curve fit formula to be quite accurate. Boffy et al [27] used a multigrid method to solve the elastic problem combined with a conjugate gradient algorithm to determine the contact pressure for the same problem. The present results are also in very good agreement with those findings, as should obviously be the case.…”

Section: Coated Materialsmentioning

confidence: 99%

“…the equations and unknowns are defined at each point of the grid, see [27,35]. Higher order discretizations can be developed using, e.g., the so-called compact schemes, see [42].…”

Section: Appendix a Discrete Equationsmentioning

confidence: 99%

“…Cai and Bhushan [25] used an FFT based approach and accounted for surface roughness. Watremetz et al [26] and Boffy et al [27] used a finite difference discretization of the equations of elasticity in the material volume and a multigrid solution method to solve for the displacement field and stresses in coatings and functionally graded materials subjected to a surface pressure distribution. This approach was used within the conjugate gradient method for the solution of the contact problem.…”

Section: Introductionmentioning

confidence: 99%

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

Boffy

Venner

2015

Tribology International

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Section: Coated Materialsmentioning

confidence: 99%

“…the equations and unknowns are defined at each point of the grid, see [27,35]. Higher order discretizations can be developed using, e.g., the so-called compact schemes, see [42].…”

Section: Appendix a Discrete Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Boffy

Venner

2015

Tribology International

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“…In Refs. [12,13], Boffy et al applied multigrid method to the 3D stress filed solution in heterogeneous and strong heterogeneous material with given contact pressure distribution. It is proved the developed multigrid algorithm possess high accuracy and efficiency.…”

Section: Introductionmentioning

confidence: 99%

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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“…Boffy et al. performed a contact analysis of deformable bodies loaded normally and tangentially against graded layers bonded to heterogeneous substrates. Recently, Barber and Ciavarella proposed an approximate JKR solution for the adhesive contact of anisotropic materials, and found that the dimensionless degree of anisotropy can significantly increase the pull‐off force.…”

Section: Introductionmentioning

confidence: 99%

The multiple fields created by two perfectly‐conducting punches on piezoelectric/piezomagnetic materials with anisotropy

Lee

Jang

Li³

2017

Z Angew Math Mech

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This article proposes an analytical model of two perfectly conducting punches acting on piezoelectric/piezomagnetic materials with anisotropy. For six types of distinct or repeated roots, related auxiliary function are obtained. The closedform solutions of the reduced integral equations are derived for two electrically-conducting and magnetically-conducting flat punches. The stress, electric displacement and magnetic induction intensity factors at both edges of each punch are given explicitly in terms of the distance between the two punches and the width of each punch. Numerical test is done to demonstrate the contributions of the distances between the two flat punches and various material properties on the contact behaviors. The obtained results delineate that at the outer edges, there has stronger strength for the singularities of the surface contact stress, surface electric displacement and surface magnetic induction compared with that at the inner edges.Most materials exhibit anisotropic behavior [1], either due to crystalline structure or because the material possesses more complex structural composition at the nanoscale. Evolution of anisotropy has a significant impact on material properties [2]. Indentation technique is a powerful tool to study materials properties, which is widely used in the semiconductor, biomedical, and magnetic recording industries [3][4][5][6], and etc. Developing indentation technique needs the solution of contact problem of anisotropic materials, which is an important and interesting subject concerned by many researchers. Clements and Ang [7] solved generalized plane contact problems for an anisotropic half-space and layer in which the elastic moduli vary quadratically with the spatial variables. Kuchytsky-Zhyhailo and Rogowski [8] investigated the rigid spherical indenter contacting with an anisotropic linear elastic layer bonded to a rigid substrate. Boffy et al.[9] performed a contact analysis of deformable bodies loaded normally and tangentially against graded layers bonded to heterogeneous substrates. Recently, Barber and Ciavarella [10] proposed an approximate JKR solution for the adhesive contact of anisotropic materials, and found that the dimensionless degree of anisotropy can significantly increase the pull-off force.The growing application of new and especially anisotropic composite materials in modern engineering gives rise to new challenges in mechanics. For example, because of exhibiting a remarkable cross-coupling between the electric and magnetic ferroic orders [11][12][13], piezoelectric/piezomagnetic materials have great potentials to be widely used in smart materials/intelligent structures. The effect of anisotropy on the performances of piezoelectric/piezomagnetic materials is of interest. Zhao et al. [14] derived the analytical solutions in an anisotropic piezoelectric/piezomagnetic bi-material to reveal the effect of different non-uniform loadings (dislocations and tractions) on the induced fields. Problems of anisotropic piezoelectric/piezomagnetic materials...

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An Efficient 3D Model of Heterogeneous Materials for Elastic Contact Applications Using Multigrid Methods

Cited by 16 publications

References 26 publications

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

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

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

The multiple fields created by two perfectly‐conducting punches on piezoelectric/piezomagnetic materials with anisotropy

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