Handbuch der Kontaktmechanik

Popov, Valentin L.; Heß, Markus; Willert, Emanuel

doi:10.1007/978-3-662-53011-5

Cited by 21 publications

(10 citation statements)

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“…1 we illustrate the action of tangential and normal loading on the changes of the surfaces of joint contact (for simplicity, all changes are shown only on one partner). Tangential loading leads to a typical flattening due to wear under conditions of gross slip [27] (Fig. 1a).…”

Section: A Numerical Model For Wear and Growth Of Joint Materialsmentioning

confidence: 99%

Active Bio Contact Mechanics: Concepts of Active Control of Wear and Growth of the Cartilage in Natural Joints

Popov¹

2019

International Workshop "Multiscale Biomechanics and Tribology of Inorganic and Organic Systems" ; Mezhdunarodnaja Konferencija

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The modern practice of treating patients with impaired motor functions often consists in replacing the natural joints with artificial ones. Currently, more than 1.5 million hip joint replacements are performed annually in the world, with a tendency to grow. Even if the replacement procedure is successful, replacement is often ineffective in the medium or long term, due to various complications. The paper puts forward ideas and discusses how to mechanically load the joint to promote the development of regenerative effects, while minimizing the influence of factors determining wear.

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Section: A Numerical Model For Wear and Growth Of Joint Materialsmentioning

confidence: 99%

Active Bio Contact Mechanics: Concepts of Active Control of Wear and Growth of the Cartilage in Natural Joints

Popov¹

2019

International Workshop "Multiscale Biomechanics and Tribology of Inorganic and Organic Systems" ; Mezhdunarodnaja Konferencija

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“…The first and second derivatives of a discretized indentation profile f n = f(r n ) can be obtained via central differences: 11 2 nn n ff f h…”

Section: Exemplary Numerical Proceduresmentioning

confidence: 99%

“…In the following, only homogeneous elastic material is considered. However, the MDR is applicable also to gradient media [10] and to viscoelastic media [11], which can be treated in a similar manner as described in the present paper.…”

Section: Introductionmentioning

confidence: 96%

Fast Numerical Implementation of the MDR Transformations

Benad¹

2018

FU Mech Eng

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In the present paper a numerical implementation technique for the transformations of the Method of Dimensionality Reduction (MDR) is described. The MDR has become, in the past few years, a standard tool in contact mechanics for solving axially-symmetric contacts. The numerical implementation of the integral transformations of the MDR can be performed in several different ways. In this study, the focus is on a simple and robust algorithm on the uniform grid using integration by parts, a central difference scheme to obtain the derivatives, and a trapezoidal rule to perform the summation. The results are compared to the analytical solutions for the contact of a cone and the Hertzian contact. For the tested examples, the proposed method gives more accurate results with the same number of discretization points than other tested numerical techniques. The implementation method is further tested in a wear simulation of a heterogeneous cylinder composed of rings of different material having the same elastic properties but different wear coefficients. These discontinuous transitions in the material properties are handled well with the proposed method.

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“…x F a = π τ (5) On the other hand, the detachment of the cylinder from the half-space can occur when the normal force exceeds the critical adhesion force [8,9] * 3 ,adh 8 .…”

Section: A Simple Model For Competition Of Sliding and Crackingmentioning

confidence: 99%

“…The critical force of beginning of adhesive detachment can be determined by equating the stress intensity factor to its critical value I 2 K E w * = ∆ [9], thus leading to the critical force 2 ,cr 8 . On the other hand, the critical tangential force can be estimated as ,cr 0 .…”

Section: Generalized Rabinowicz Criterion For Elliptic Contactsmentioning

confidence: 99%

Generalized rabinowicz’ criterion for adhesive wear for elliptic micro contacts

Popov¹

2017

AIP Conference Proceedings

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This paper is devoted to an old idea suggested in 1958 by E. Rabinowicz in his paper "The effect of size on the looseness of wear fragments". Rabinowicz assumed a circular shape for two asperities coming into contact and being destroyed due to relative sliding. We generalize his analysis for the case of non-circular contacts, in particular those having elliptical shape and discuss the general case of arbitrary contact shape.

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Handbuch der Kontaktmechanik

Cited by 21 publications

References 0 publications

Active Bio Contact Mechanics: Concepts of Active Control of Wear and Growth of the Cartilage in Natural Joints

Active Bio Contact Mechanics: Concepts of Active Control of Wear and Growth of the Cartilage in Natural Joints

Fast Numerical Implementation of the MDR Transformations

Generalized rabinowicz’ criterion for adhesive wear for elliptic micro contacts

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