Emanuel Willert

Emanuel Willert
Technische Universität Berlin | TUB · Department of Mechanics

Doctor of Engineering

About

66
Publications
16,565
Reads
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364
Citations
Citations since 2016
62 Research Items
344 Citations
2016201720182019202020212022020406080
2016201720182019202020212022020406080
2016201720182019202020212022020406080
2016201720182019202020212022020406080
Additional affiliations
March 2015 - present
Technische Universität Berlin
Position
  • Research Assistant
Education
March 2015 - December 2019
Technische Universität Berlin
Field of study
  • Contact-Impact Mechanics
October 2012 - December 2014
Technische Universität Berlin
Field of study
  • Engineering Physics
October 2008 - September 2012
Technische Universität Berlin
Field of study
  • Engineering Physics

Publications

Publications (66)
Article
Full-text available
The subsurface elastic stress fields in plane and axisymmetric contacts with friction under oscillating tangential loading are calculated via a very robust, high-precision method, which operates with appropriate superpositions of analytic solutions for the respective Hertzian contact problems. Based on the stress fields, two critical plane fatigue...
Article
Full-text available
Fretting wear of axisymmetric contacts is considered within the framework of the Hertz-Mindlin approximation and the Archard law for the linear wear. If the characteristic time scale for the wear is much larger than the duration of a single fretting oscillation, the profile change due to wear during one fretting cycle can be neglected for the conta...
Article
Full-text available
It is shown how the Abel transform solution to the general axisymmetric normal contact problem for homogeneous and power-law graded elastic materials, which is paramount for the solution of different classes of tribological problems with the help of the method of dimensionality reduction (MDR), can be written in terms of explicit convolutions. Thes...
Preprint
Full-text available
As an improvement to the recently proposed procedure for the determination of the stress state beneath axisymmetric tangential contacts in Hertz-Mindlin approximation via an appropriate superposition of solutions for the respective flat-punch problem, the determination via the superposition of solutions for parabolic contact is demonstrated. It has...
Article
Full-text available
The contact problem for an elastic third-body particle between two elastic half-spaces is considered. The contact is assumed to consist of three Hertzian contact spots. The normal and tangential contact problems are analyzed analytically considering partial slip in the contacts and the influence of third-body weight. Self-consistency conditions bet...
Preprint
Full-text available
The transition between two conceptionally different solution procedures for general axisymmetric tangential contact problems with arbitrary laoding histories under Hertz-Mindlin assumptions is demonstrated, namely J\"ager's superposition solution and the method of dimensionality reduction. Both finite and ininite superpositions of Cattaneo-Mindlin...
Article
Full-text available
We analyze the onset of plastic yield in the Maugis‐adhesive contact of elastic spheres. Written in proper dimensionless variables, the problem solution depends on Poisson's ratio, the Tabor parameter and a non‐dimensional adhesion strength. The influences of adhesion range and strength are studied in detail. First yield can either occur inside the...
Article
Full-text available
The Hertzian contact theory, as well as most of the other classical theories of normal and tangential contact, provides displacements and the distribution of normal and tangential stress components directly in the contact surface. However, other components of the full stress tensor in the material may essentially influence the material behaviour in...
Preprint
Full-text available
The Hertzian contact theory, as well as most of the other classical theories of normal and tangential contact, provides displacements and the distribution of normal and tangential stress components directly in the contact surface. However, other components of the full stress tensor in the material may essentially influence the material behaviour in...
Article
Full-text available
Impact tests are an important tool to analyze dynamic material properties of viscoelastic media in technology and biology. In this context, rigorous contact mechanical models of the collision problem are necessary to adequately interpret data from impact experiments. It is shown here theoretically that the coefficient of restitution in these types...
Chapter
Full-text available
In diesem sehr umfangreichen Kapitel sind die Methoden und Lösungen der Mechanik von axialsymmetrischen Kontaktproblemen dargelegt, die später zur Behandlung des Stoßproblems herangezogen werden. Ausgehend von der statischen Fundamentallösung der Elastizitätstheorie für einen homogenen elastischen Halbraum werden Schritt für Schritt die später im B...
Chapter
Full-text available
Sehr viele rotationssymmetrische Kontaktprobleme können exakt auf Kontakte zwischen einem entsprechend zu wählenden starren ebenen Profil und einer eindimensionalen Bettung von linearen, unabhängigen verallgemeinerten Federelementen abgebildet werden. Der mathematische und numerische Aufwand zur Behandlung solcher Kontakte ist deutlich geringer als...
Chapter
Full-text available
Basierend auf den geschilderten kontaktmechanischen Grundlagen (teilweise in deren Interpretation durch die MDR) sind in diesem Kapitel die Lösungen des Normalstoßproblems in unterschiedlichen Fällen dargestellt. Betrachtet werden homogene und inhomogene elastische Medien mit und ohne Adhäsion sowie elasto-plastische und viskoelastische Materialien...
Chapter
Full-text available
Nach der Darstellung der dynamischen und kontaktmechanischen Grundlagen und der ausführlichen Untersuchung des Stoßproblems unter verschiedenen Bedingungen stehen in diesem Kapitel Anwendungsbereiche aus Physik, Technik und Medizin im Mittelpunkt, für die die in den früheren Kapiteln gezeigten Ergebnisse von Bedeutung sind. Die Gebiete, in denen di...
Chapter
Full-text available
Die dreidimensionale Dynamik allgemeiner, zusammenstoßender Körper ist kompliziert und erlaubt im Zusammenhang mit der jeweiligen Kontaktmechanik des Stoßes in der Regel weder eine analytische Behandlung noch eine auch nur ansatzweise überschaubare Darstellung der vollständigen Lösung.
Chapter
Full-text available
In diesem Kapitel werden zwei Aspekte genauer untersucht, deren Einflüsse bei der Vereinfachung der Bewegungsgleichungen zweier räumlich zusammenstoßender Kugeln in Abschn. 2.2.1 als vernachlässigbar klein verworfen wurden. Dies betrifft einerseits einige dynamische Effekte durch die Rotation der Stoßachse (und deren Einfluss auf die Kontaktmechani...
Chapter
Full-text available
In diesem Kapitel werden zunächst die Lösungen einiger Tangentialkontaktprobleme, basierend auf der elastischen Fundamentallösung, hergeleitet. Außerdem ist eine kurze Übersicht der im Buch verwendeten mathematischen Spezialfunktionen und eine einfache Implementierung des MDR-Modells zur Untersuchung des ebenen Stoßes mit Reibung einer starren Kuge...
Chapter
Full-text available
Nach der Behandlung des reinen Normalstoßproblems ist das folgende Kapitel dem allgemeinen Stoßproblem von Kugeln gewidmet. Im Rahmen der im zweiten und dritten Kapitel beschriebenen Annahmen ist diese Aufgabe äquivalent zu dem ebenen Stoß einer starren Kugel auf einen deformierbaren Halbraum (siehe Abb. 2.2).
Book
Full-text available
Dieses Open Access Buch widmet sich dem Problem der Mechanik des Zusammenstoßes zweier makroskopischer Körper. Falls die Dynamik der Körper als Ganzes dies erlaubt, ohne in unüberschaubare Komplexität zu verfallen (in der Regel ist das nur für das reine Normalstoßproblem der Fall), werden allgemeine axialsymmetrische Stoßpartner betrachtet. Für das...
Article
Full-text available
We consider fretting wear in elastic frictional contact under influence of oscillations of small amplitude and investigate the question, how wear damage can be influenced by the introduction of material gradients. To achieve a general understanding we restrict our consideration to media with a power-law dependency of the elastic modulus on depth. I...
Data
Look through the index of the "Handbook of Contact Mechanics"! Find out the details of the history of contact mechanics from 1860 to 2018, from Abramian to Zhupanska.
Chapter
Full-text available
Normal contact Problem is solved both for frictionless contacts (Boussinesq problems) and complete sticking (Mossakovskii problems) for the following contact shapes: - The cylindrical flat punch - The cone - The paraboloid - The sphere - The ellipsoid - The profile which generates constant pressure - The profile in the form of a power law - The tru...
Book
Full-text available
This open access book contains a structured collection of the complete solutions of all essential axisymmetric contact problems. Based on a systematic distinction regarding the type of contact, the regime of friction and the contact geometry, a multitude of technically relevant contact problems from mechanical engineering, the automotive industry a...
Article
Full-text available
Percussive and erosive wear by repetitive impacting of solid particles damages surfaces even at low impact velocities. As the impact wear is often directly related to the energy loss during the collision and therefore to the coefficients of normal and tangential restitution, in the present study the oblique low-velocity impact of a rigid sphere ont...
Article
The application of the Method of Dimensionality Reduction (MDR) to frictionless normal contacts of compressible linear‐viscoelastic materials is presented. The mapping rules within the framework of MDR are given, strictly proven and illustrated by examples. The application of the Method of Dimensionality Reduction (MDR) to frictionless normal conta...
Book
Full-text available
This is a practical guide to the Method of Dimensionality Reduction with application illustrations. The Method of Dimensionality Reduction (MDR) is a method of calculation and simulation of contacts of elastic and viscoelastic bodies. It consists essentially of two simple steps: (a) substitu-tion of the three-dimensional continuum by a uniquely de...
Article
Full-text available
Until recently the analysis of contacts in tribological systems usually required the solution of complicated boundary value problems of three-dimensional elasticity and was thus mathematically and numerically costly. With the development of the so-called Method of Dimensionality Reduction (MDR) large groups of contact problems have been, by sets of...
Article
Until recently the analysis of contacts in tribological systems usually required the solution of complicated boundary value problems of three-dimensional elasticity and was thus mathematically and numerically costly. With the development of the so-called Method of Dimensionality Reduction (MDR) large groups of contact problems have been, by sets of...
Preprint
Full-text available
The influence of compressibility on the coefficient of restitution in the normal impact of a rigid sphere onto a linear-viscoelastic compressible standard solid under quasi-static conditions is studied using a numerical solution procedure for the contact-impact problem based on the Method of Dimensionality Reduction. We find that the influence of c...
Preprint
Full-text available
We study analytically and numerically the process of indentation of cylindrical rigid indenter with concave face in form of a power-law function. In the well-known case of a parabolic concave indenter, the contact starts at sharp edges of the indenter and spreads inwards with increasing indentation depth. For all profiles with the exponent larger t...
Preprint
Full-text available
We propose an approach to describe the propagation of a crack (or boundary of an adhesive contact) in a viscoelastic material which is only based on the consideration of the rheology of the material without the introduction of any additional dependency of the separation energy on the velocity of crack propagation. The suggested idea is illustrated...
Article
Full-text available
A closed-form general analytic solution is presented for the adhesive normal contact of convex axisymmetric power-law graded elastic bodies using a Dugdale-Maugis model for the adhesive stress. The case of spherical contacting bodies is studied in detail. The known JKR-and DMT-limits can be derived from the general solution, whereas the transition...
Book
Full-text available
https://link.springer.com/book/10.1007/978-3-662-53011-5 Das Buch beinhaltet eine strukturierte Sammlung der vollständigen Lösungen aller wesentlichen axialsymmetrischen Kontaktprobleme. Es werden Lösungen für klassische Profile wie die Kugel, den Kegel oder den flachen zylindrischen Stempel angegeben, aber auch für eine Vielzahl weiterer technisch...
Article
Full-text available
Collisions of solid bodies are of significant interest for a great variety of physical and engineering applications. This review is devoted to non-elastic collisions of solid bodies when the energy dissipation is caused by the inner or interface friction, plasticity, adhesion, or other damping mechanisms. We consider only two-particle collisions. T...
Article
Full-text available
This paper is the second part of the review on the physics of two-particle collisions of solids. The first one describes theoretical and experimental works on collisions of elastic and elastic-plastic solid bodies in the case when the energy dissipation is caused by the inner or interface friction, plasticity, adhesion, or some other damping mechan...
Article
We study the influence of the adhesive interaction range on the coefficient of restitution in the normal impact of spheres by analytical and semi-analytical means based on a Maugis–Dugdale model for the adhesive stress. It is found, that—depending on the value of the Tabor parameter—the impact may start and end with and without direct contact betwe...
Conference Paper
Full-text available
Zusammenfassung: Basierend auf analytischen und numerischen Modellen mithilfe der Methode der Dimensionsreduktion werden quasistatisch stoßbeanspruchte biologische Systeme aus Gradientenmaterialien mit Reibung und Adhäsion unter-sucht. Je nach der Struktur der Gradierung können eine deutliche Reduktion der auftretenden Kontaktspannungen und der Ene...
Article
Based on the Method of Functional Equations by Lee and Radok we present the application of the Method of Dimensionality Reduction to frictionless axisymmetric normal contacts with a compressible Kelvin-Voigt material. Both the contact between a rigid indenter and a viscoelastic medium and contacts between two viscoelastic bodies are studied. All ma...
Article
Full-text available
Numerical simulations of the dynamics of an elastic collision between a rigid sphere and an elastic half-space are carried out. We assume an Amontons-Coulomb frictional force with a fixed coefficient of friction between the contacting surfaces during the impact. As a result of modeling a dimensionless function, describing the tangential restitution...
Article
Full-text available
We analyse the oblique impact of linear-viscoelastic spheres by numerical models based on the Method of Dimensionality Reduction and the Boundary Element Method. Thereby we assume quasi-stationarity, the validity of the half-space hypothesis, short impact times and Amontons-Coulomb friction with a constant coefficient for both static and kinetic fr...
Article
The low-velocity oblique impact of a rigid sphere on a power-law graded elastic half-space is studied under the assumptions of elastic similarity and a constant coefficient of friction. The normal component of motion is determined analytically. The tangential problem is investigated numerically using the Method of Dimensionality Reduction. We find...
Article
Full-text available
The JKR-adhesive impact of a rigid sphere on a power-law graded half space is studied analytically and numerically under the assumptions of elastic similarity, no-slip and quasi-stationarity. The coefficient of normal restitution is determined analytically. The tangential problem is solved by a numerical algorithm based on the Method of Dimensional...
Article
The JKR-adhesive impact of a rigid sphere on a power-law graded half space is studied analytically and numerically under the assumptions of elastic similarity, no-slip and quasi-stationarity. The coefficient of normal restitution is determined analytically. The tangential problem is solved by a numerical algorithm based on the Method of Dimensional...
Article
Full-text available
The JKR-adhesive frictionless normal contact problem is solved for the flat annular and the conical or spherical concave rigid punch indenting an elastic half space. The adhesive solution can be derived analytically from the non-adhesive one, the latter one being calculated by the boundary element method. It is found that the annular flat punch wil...
Article
An impact of an elastic sphere with an elastic half space with a constant coefficient of friction is studied numerically using the method of dimensionality reduction. It is shown that the rebound velocity, angular velocity and hence the loss of kinetic energy during the impact, if written as proper dimensionless variables, are determined by a funct...
Conference Paper
Full-text available
Es sollen die Geschwindigkeiten nach dem ebenen Stoß zwischen einer starren Kugel und einem linear-elastischen Halbraum bestimmt werden. Dabei werden drei unterschiedliche Fälle getrennt voneinander behandelt: das Auftreten von Coulombscher Reibung im Kontakt, Adhäsion der beiden Kontaktpartner nach der Theorie von Johnson, Kendall und Roberts und...
Article
Full-text available
Recently the method of dimensionality reduction (MDR) has been introduced to solve axisymmetric contact problems easily and exactly. The list of tasks that this method can deal with comprises normal, tangential, adhesive and rolling contacts with simply connected contact areas between elastic or viscoelastic bodies. Due to its simplicity and easy a...
Article
Full-text available
In this work we present a new method to describe movements of stick-slip microdrives. On the microscopic scale we model the contact between actuator and slider as a dynamic tangential contact using the method of reduction of dimensionality. On the macroscopic scale simple one-and three-dimensional equations of motion are derived. An algorithm to so...

Questions

Question (1)
Question
Dear fellow contact mechanicians,
I just stumbled over a problem in analytic mechanics of plane Cattaneo problems in the presence of bulk stress.
It is said that the Ciavarella-Jäger principle for "small enough bulk stress" applies to this problem in the following form:
q(x) = \mu*(p(x; P, beta = 0) - p(x; P - Q/mu, beta)),
where q(x) is the tangential contact traction distribution, p(x) the pressure distribution, P the normal line load, Q the tangential line load, mu the friction coefficient and beta a "rotation angle" proportional to the bulk stress, which I will discuss in a minute.
The second term on the right side in above equation corresponds to a "fictious" normal contact problem of the same contacting bodies under the load (P - Q/mu) and with a relative rotation by beta.
The condition of "small enough bulk stress" is basically that the contact area for this "fictious" problem (which corresponds to the stick region in the actual Cattaneo problem), completely lies within the actual contact area. Moreover, a non-zero value of beta will increase the contact length on one side and decrease it on the other side. So, e.g., for Q = 0 the condition of "moderate bulk stress" is actually that beta = 0, i.e., there is no bulk stress.
Now, we know that tangential contact problems have a loading history. Even the Cattaneo problem has a history: first the normal load is applied, and then an increasing tangential load. However, when beginning to apply the tangential load, Q equals zero, so any (constant) bulk stress will violate the "moderate bulk stress condition".
Or to put it more generally: For any non-zero constant bulk stress, the "moderate bulk stress condition" is violated at the beginning of tangential loading.
Does that change anything about the final contact configuration at the end of the Cattaneo loading?
Or am I missing something?
Thank you very much for your help!
Kind regards,
Emanuel

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Projects

Projects (5)
Project
Understanding of wear, fatigue and damping in oscillating contacts.
Project
Understanding adhesion of systems with complicated geometry, rough surfaces, gradient media etc.
Project
Summary of all essential results of contact mechanics since Hertz