This open access book gathers authoritative contributions concerning multiscale problems in biomechanics, geomechanics, materials science and tribology. It is written in memory of Sergey Grigorievich Psakhie to feature various aspects of his multifaceted research interests, ranging from theoretical physics, computer modeling of materials and material characterization at the atomic scale, to applications in space industry, medicine and geotectonics, and including organizational, psychological and philosophical aspects of scientific research and teaching as well. This book covers new advances relating to orthopedic implants, concerning the physiological, tribological and materials aspects of their behavior; medical and geological applications of permeable fluid-saturated materials; earthquake dynamics together with aspects relating to their managed and gentle release; lubrication, wear and material transfer in natural and artificial joints; material research in manufacturing processes; hard-soft matter interaction, including adhesive and capillary effects; using nanostructures for influencing living cells and for cancer treatment; manufacturing of surfaces with desired properties; self-organization of hierarchical structures during plastic deformation and thermal treatment; mechanics of composites and coatings; and many more. Covering established knowledge as well as new models and methods, this book provides readers with a comprehensive overview of the field, yet also with extensive details on each single topic.

This application-oriented book introduces readers to the associations and relationships between contact mechanics and friction, providing them with a deeper understanding of tribology. It addresses the related phenomena of contacts, adhesion, capillary forces, friction, lubrication, and wear from a consistent point of view. The author presents (1) methods for rough estimates of tribological quantities, (2) simple and general methods for analytical calculations, and (3) the crossover into numerical simulation methods, the goal being to convey a consistent view of tribological processes at various scales of magnitude (from nanotribology to earthquake research). The book also explores the system dynamic aspects of tribological systems, such as squeal and its suppression, as well as other types of instabilities and spatial patterns. It includes problems and worked-out solutions for the respective chapters, giving readers ample opportunity to apply the theory to practical situations and to deepen their understanding of the material discussed. The second edition has been extended with a more detailed exposition of elastohydrodynamic lubrication, an updated chapter on numerical simulation methods in contact mechanics, a new section on fretting in the chapter on wear, as well as numerous new exercises and examples, which help to make the book an excellent reference guide.

This book describes for the first time a simulation method for the fast calculation of contact properties and friction between rough surfaces in a complete form. In contrast to existing simulation methods, the method of dimensionality reduction (MDR) is based on the exact mapping of various types of three-dimensional contact problems onto contacts of one-dimensional foundations. Within the confines of MDR, not only are three dimensional systems reduced to one-dimensional, but also the resulting degrees of freedom are independent from another. Therefore, MDR results in an enormous reduction of the development time for the numerical implementation of contact problems as well as the direct computation time and can ultimately assume a similar role in tribology as FEM has in structure mechanics or CFD methods, in hydrodynamics. Furthermore, it substantially simplifies analytical calculation and presents a sort of "pocket book edition" of the entirety contact mechanics. Measurements of the rheology of bodies in contact as well as their surface topography and adhesive properties are the inputs of the calculations. In particular, it is possible to capture the entire dynamics of a system - beginning with the macroscopic, dynamic contact calculation all the way down to the influence of roughness - in a single numerical simulation model. Accordingly, MDR allows for the unification of the methods of solving contact problems on different scales. The goals of this book are on the one hand, to prove the applicability and reliability of the method and on the other hand, to explain its extremely simple application to those interested.

This book describes for the first time a simulation method for the fast calculation of contact properties and friction between rough surfaces in a complete form.

In contrast to existing simulation methods, the method of dimensionality reduction (MDR) is based on the exact mapping of various types of three-dimensional contact problems onto contacts of one-dimensional foundations. Within the confines of MDR, not only are three dimensional systems reduced to one-dimensional, but also the resulting degrees of freedom are independent from another. Therefore, MDR results in an enormous reduction of the development time for the numerical implementation of contact problems as well as the direct computation time and can ultimately assume a similar role in tribology as FEM has in structure mechanics or CFD methods, in hydrodynamics. Furthermore, it substantially simplifies analytical calculation and presents a sort of pocket book edition of the entirety contact mechanics.

Measurements of the rheology of bodies in contact as well as their surface topography and adhesive properties are the inputs of the calculations. In particular, it is possible to capture the entire dynamics of a system beginning with the macroscopic, dynamic contact calculation all the way down to the influence of roughness in a single numerical simulation model. Accordingly, MDR allows for the unification of the characteristic methods of solving contact problems on different scales.

The goals of this book are on the one hand, to prove the applicability and reliability of the method and on the other hand, to explain its extremely simple application to those interested."

FOSSILS AND STRATA Number 66 - August 2021 ISSN 0024-1164

This open access book gathers authoritative contributions concerning multiscale problems in biomechanics, geomechanics, materials science and tribology. It is written in memory of Sergey Grigorievich Psakhie to feature various aspects of his multifaceted research interests, ranging from theoretical physics, computer modeling of materials and material characterization at the atomic scale, to applications in space industry, medicine and geotectonics, and including organizational, psychological and philosophical aspects of scientific research and teaching as well. This book covers new advances relating to orthopedic implants, concerning the physiological, tribological and materials aspects of their behavior; medical and geological applications of permeable fluid-saturated materials; earthquake dynamics together with aspects relating to their managed and gentle release; lubrication, wear and material transfer in natural and artificial joints; material research in manufacturing processes; hard-soft matter interaction, including adhesive and capillary effects; using nanostructures for influencing living cells and for cancer treatment; manufacturing of surfaces with desired properties; self-organization of hierarchical structures during plastic deformation and thermal treatment; mechanics of composites and coatings; and many more. Covering established knowledge as well as new models and methods, this book provides readers with a comprehensive overview of the field, yet also with extensive details on each single topic.

Detailed descriptions of the lingulate brachiopods Within Cambrian-Ordovician Lingulate Brachiopods from Scandinavia, Kazakhstan and South Ural Mountains, the lingulate brachiopods are described from Scandinavia, the South Ural Mountains, and northeastern central and southern Kazakhstan. This publication is Number 35 within the Fossils and Strata series. The series offers monographs and memoirs in palaeontology and stratigraphy. The international Fossils and Strata features systematic and regional monographs with taxonomic descriptions.

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.

Das anwendungsorientierte Buch fuhrt in den Zusammenhang von Kontaktmechanik und Reibung ein und ermoeglicht damit ein tieferes Verstandnis der Tribologie. Es behandelt die eng zusammenhangenden Phanomene Kontakt, Adhasion, Kapillarkrafte, Reibung, Schmierung und Verschleiss unter einem einheitlichen Gesichtspunkt. Der Autor geht ein auf (1) Methoden zur groben Abschatzung von tribologischen Groessen, (2) Methoden zur analytischen Berechnung in einem minimal erforderlichen Umfang und (3) den UEbergang zu numerischen Simulationsmethoden. Damit vermittelt er einen einheitlichen Blick auf tribologische Prozesse in verschiedenen Skalen (von der Nanotribologie bis zur Erdbebenforschung). Auch systemdynamische Aspekte von tribologischen Systemen, wie Quietschen und seine Bekampfung sowie andere Typen von Instabilitaten und Musterbildung werden vermittelt. Aufgaben mit durchgerechneten Loesungen zu einzelnen Kapiteln dienen der Vertiefung und praktischen Anwendung des behandelten Stoffs. Neu an der 3. Auflage sind: eine ausfuhrlichere Darstellung der elastohydrodynamischen Schmierung, ein erweitertes und aktualisiertes Kapitel zu numerischen Simulationsmethoden in der Kontaktmechanik, die Erweiterung des Kapitels "Verschleiss" durch Diskussion und Berechnung von Fretting sowie zahlreiche neue Aufgaben und Fallbeispiele, welche den Wert des Buches als Nachschlagewerk wesentlich erhoehen.

Das Werk beschreibt erstmalig in einer geschlossenen Form eine Simulationsmethode zur schnellen Berechnung von Kontakteigenschaften und Reibung zwischen rauen Oberflachen.

Im Unterschied zu bestehenden Simulationsverfahren basiert die Methode der Dimensionsreduktion (MDR) auf einer "exakten "Abbildung verschiedener Klassen von dreidimensionalen Kontaktproblemen auf Kontakte mit eindimensionalen Bettungen. Innerhalb der MDR wird jedoch nicht nur die Dimension von drei auf eins reduziert, sondern gleichermassen sind voneinander unabhangige Freiheitsgrade gegeben. Die MDR beinhaltet daher eine enorme Reduktion sowohl der Entwicklungszeit fur die numerische Implementierung von Kontaktproblemen als auch der direkten Rechenzeit und kann letztlich in der Tribologie eine ahnliche Rolle einnehmen wie FEM in der Strukturmechanik oder bekannte CFD-Loser in der Hydrodynamik. Daruber hinaus erleichtert sie in hohem Masse analytische Berechnungen und bietet eine Art Taschenausgabe der gesamten Kontaktmechanik.
Messungen der Rheologie der kontaktierenden Korper sowie ihrer Oberflachentopographie und Adhasionseigenschaften finden unmittelbaren Eingang in die Berechnung. Insbesondere ist es moglich, die gesamte Dynamik des Systems beginnend mit der makroskopischen Systemdynamik uber die makroskopische, dynamische Kontaktberechnung bis hin zum Einfluss der Rauheit in" einem" numerischen Simulationsmodell zu erfassen. Die MDR erlaubt demnach die Vereinigung der charakteristischen Ablaufe verschiedener Skalen.

Zielsetzung des Buches ist es, einerseits die Berechtigung und Zuverlassigkeit der Methode zu belegen, andererseits ihre ausserst einfache Handhabung interessierten Praktikern zu erklaren.

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