Emanuel Willert's Books

Method of Dimensionality Reduction in Contact Mechanics

User’s Manual

By: Valentin L. Popov,Markus Hess,Emanuel Willert

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Method of Dimensionality Reduction in Contact Mechanics

User’s Manual

By: Valentin L. Popov,Markus Hess,Emanuel Willert

The present book is a collection of open-access papers describing the foundations and applications of the Method of Dimensionality Reduction (MDR), first published in the Journal “Facta Universitatis. Series Mechanical Enginerring” in the years 2014-2018. 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) substitution of the three-dimensional continuum by a uniquely defined one-dimensional linearly elastic or viscoelastic foundation (Winkler foundation) and (b) transformation of the three-dimensional profile of the contacting bodies by means of the MDR-transformation. As soon as these two steps are done, the contact problem can be considered to be solved. For axial symmetric contacts, only a small calculation by hand is required which does not exceed elementary calculus and will not be a barrier for any practically-oriented engineer. Alternatively, the MDR can be implemented numerically, which is almost trivial due to the independence of the foundation elements. In spite of its simplicity, all results are exact. The present book brings together papers covering the most important aspects of the MDR and providing a practical guide for its use.

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Page Count

154

Publisher

Technische Universität Berlin, Department of System Dynamics and Friction Physics

Published Date

ISBN 10

3000603824

ISBN 13

9783000603822

Handbook of Contact Mechanics

Exact Solutions of Axisymmetric Contact Problems

By: Valentin L. Popov,Markus Heß,Emanuel Willert

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Handbook of Contact Mechanics

Exact Solutions of Axisymmetric Contact Problems

By: Valentin L. Popov,Markus Heß,Emanuel Willert

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 and medical engineering are discussed. In addition to contact problems between isotropic elastic and viscoelastic media, contact problems between transversal-isotropic elastic materials and functionally graded materials are addressed, too. The optimization of the latter is a focus of current research especially in the fields of actuator technology and biomechanics. The book takes into account adhesive effects which allow access to contact-mechanical questions about micro- and nano-electromechanical systems. Solutions of the contact problems include both the relationships between the macroscopic force, displacement and contact length, as well as the stress and displacement fields at the surface and, if appropriate, within the half-space medium. Solutions are always obtained with the simplest available method - usually with the method of dimensionality reduction (MDR) or approaches which use the solution of the non-adhesive normal contact problem to solve the respective contact problem.

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Page Count

357

Publisher

Springer

Published Date

ISBN 10

3662587092

ISBN 13

9783662587096

Impact Problems in Physics, Technology, and Medicine: Fundamentals and Applications

By: Willert, Emanuel

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Impact Problems in Physics, Technology, and Medicine: Fundamentals and Applications

By: Willert, Emanuel

The book is devoted to the mechanics of the collision of two macroscopic bodies. First, the fundamentals of contact mechanics (elasticity, adhesion, etc.) are presented and then applied to the collision problem. With the method of dimensionality reduction, a tool has been available for a few years which allows the very efficient analytical and numerical treatment of contact-impact problems. The book concludes with application cases from various fields. Das Buch widmet sich der Mechanik der Kollision zweier makroskopischer Körper. Zunächst werden die kontaktmechanischen Grundlagen (Elastizität, Adhäsion u. a.) dargestellt und anschließend auf das Stoßproblem übertragen. Mit der Methode der Dimensionsreduktion steht seit wenigen Jahren ein Werkzeug zur Verfügung, das die sehr effiziente analytische und numerische Behandlung von Stoß-Kontakt-Problemen ermöglicht. Den Abschluss des Buchs bilden Anwendungsfälle aus verschiedenen Gebieten.

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