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A Decomposition Approach for the Numerical Solution of Frictional Contact Problems in Nonlinear Elasticity

Titel Englisch A Decomposition Approach for the Numerical Solution of Frictional Contact Problems in Nonlinear Elasticity
Gesuchsteller/in Krause Rolf
Nummer 132198
Förderungsinstrument Projektförderung (Abt. I-III)
Forschungseinrichtung Facoltà di scienze informatiche Università della Svizzera italiana
Hochschule Università della Svizzera italiana – USI
Hauptdisziplin Informatik
Beginn/Ende 01.10.2010 - 30.09.2013
Bewilligter Betrag 158'418.00
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Keywords (9)

frictional contact problems; nonlinear elasticity; self contact; nonsmooth minimization; nonlinear domain decomposition methods; nonlinear multiscale strategies; nonconforming domain decomposition; nonconvex minimization; nonsmooth mechanics

Lay Summary (Englisch)

Lead
Lay summary
Contact problems occur in almost all situations of our life and they are usually connected to the touching of elastic bodies. Examples are gear boxes, tires, moving machine parts or prostheses. Simulation tools, which provide reliable predictions for the behavior of elastic bodies in contact, are therefore of high importance for many applications in engineering, industry and life sciences.There is a at least two-dimensional gap between the need of efficient simulation tools for contact problems and the availability of reliable and efficient simulation methods and their implementations. The first dimension of this gap can be found to be the still relatively low number of inherently nonlinear and nonsmooth decomposition methods, which can deal with the effects at the interfaces between the contacting bodies as well as with the nonconvexity arising from nonlinear material laws. The second dimension of this gap is the fact that many modern and mathematically sound methods are not implemented in a way, which makes them usable for the simulation of demanding applications.Even worse, many new methodological developments are tested only for simple model problems, and the robustness of new methods with respect to varying geometries, material laws, boundary conditions is often not investigated. It is the aim of this project to narrow this gap in both dimensions by developing, implementing and providing new solution strategies for frictional contact problems in nonlinear elasticity.This project is concerned with the development of highly efficient and reliable smooth and nonsmooth decomposition based discretization and solution strategies, which are applicable to frictional contact problems in nonlinear elasticity. To this end, we will exploit the power of state of the art ideas from nonlinear domain decomposition, optimization and nonsmooth minimization for the development of new tools for numerical simulations in frictional contact mechanics; we will also put considerable emphasis on the implementation of these methods, in order to make them applicable to real world problems.By providing theoretically well designed and modern solution methods, which are moreover implemented in a flexible framework and tested along realistic problems, we will provide a sound basis for improving the quality of numerical simulation in many important application areas, ranging from engineering over medicine to life sciences.
Direktlink auf Lay Summary Letzte Aktualisierung: 21.02.2013

Verantw. Gesuchsteller/in und weitere Gesuchstellende

Mitarbeitende

Publikationen

Publikation
A Numerical Remark on the Time Discretization of Contact Problems in Nonlinear Elasticity
Groß Christian, Krause Rolf, Poletti Valentina (2013), A Numerical Remark on the Time Discretization of Contact Problems in Nonlinear Elasticity, in Numerical Mathematics and Advanced Applications 2011, Proceedings of ENUMATH 2011, Leicester.

Zusammenarbeit

Gruppe / Person Land
Formen der Zusammenarbeit
University of Ostrava Tschechische Republik (Europa)
- vertiefter/weiterführender Austausch von Ansätzen, Methoden oder Resultaten
- Publikation
- Austausch von Mitarbeitern
University Research Programm Ford Deutschland (Europa)
- Industrie/Wirtschaft/weitere anwendungs-orientierte Zusammenarbeit
Universitaet Bonn Deutschland (Europa)
- vertiefter/weiterführender Austausch von Ansätzen, Methoden oder Resultaten
- Publikation

Wissenschaftliche Veranstaltungen

Aktiver Beitrag

Titel Art des Beitrags Titel des Artikels oder Beitrages Datum Ort Beteiligte Personen
22nd International Conference on Domain Decomposition Methods Poster 18.09.2013 Lugano, Schweiz Poletti Valentina; Krause Rolf;
Conference on the Mathematics of Finite Elements and Applications (MAFELAP) Vortrag im Rahmen einer Tagung 03.06.2013 Brunel, Grossbritannien und Nordirland Krause Rolf;
21st International Symposium on Mathematical Programming (ISMP 2012) Vortrag im Rahmen einer Tagung 19.08.2012 Berlin, Deutschland Krause Rolf;
Euromech Colloquium on Contact Problems Vortrag im Rahmen einer Tagung 27.03.2012 Corsica, Frankreich Krause Rolf;
PhD course on Non-smooth Analysis and Multilevel Methods, Einzelvortrag 30.01.2012 University of Copenhagen, Dänemark Krause Rolf; Poletti Valentina;
ENUMATH 2011, 9th European Conference on Numerical Mathematics and Advanced Applications, Leicester Vortrag im Rahmen einer Tagung 05.09.2011 Leicester, Grossbritannien und Nordirland Poletti Valentina;
Euromech Colloquium 516 entitled ”Nonsmooth Contact and Impact Laws in Mechanics” Vortrag im Rahmen einer Tagung 07.07.2011 Grenoble, Frankreich Krause Rolf;
39th Speedup Workshop Einzelvortrag 17.06.2011 Zuerich, Schweiz Poletti Valentina; Krause Rolf;
Oberwolfach Conference “Schnelle Loeser fuer Partielle Differentialgleichungen” Vortrag im Rahmen einer Tagung 20.05.2011 Oberwolfach, Deutschland Krause Rolf;


Selber organisiert

Titel Datum Ort
Minisymposium on “High Performance Methods for Strongly Nonlinear Problems in Computational Science” 19.07.2011 Sydney, Australien
Organization of a Minisymposium on “Optimal algorithms for contact problems” on the International Conference on Domain Decomposition methods 05.02.2011 San Diego, USA, Vereinigte Staaten von Amerika

Kommunikation mit der Öffentlichkeit

Kommunikation Titel Medien Ort Jahr
Medienarbeit: Printmedien, Online-Medien Two pages on ICS reserach, including this project Corriere del Ticino Italienische Schweiz 2014

Abstract

This project "ReAct" is concerned with the development of new discretization and solution strategies for frictional contact problems in nonlinear elasticity. Contact problems occur in almost all situations of our life and they are usually connected to the touching of elastic bodies. Simulation tools, which provide reliable predictions for the behavior of elastic bodies in contact, are therefore of high importance for many applications in engineering, industry and life sciences. The applicant Prof. Dr. Rolf Krause, the director of the new Institute of Computational Science (ICS) of the Faculty of Informatics at Università della Svizzera italiana, is one of the world leading specialists of iterative nonsmooth solution methods, in particular in the field of highly efficient simulations of contact phenomena. The existing skills in his group in applied mathematics and computational science provide an excellent basis for the development of advanced solution techniques for nonlinear problems, especially frictional contact in nonlinear elasticity. There is a at least two-dimensional gap between the need of efficient simulation tools for contact problems and the availability of reliable and efficient simulation methods and their implementations. The first dimension of this gap can be found to be a lack of inherently nonsmooth solution methods, which can deal with the effects at the interfaces between the contacting bodies as well as with the nonconvexity arising from nonlinear material laws. The second dimension of this gap is the fact that many modern and mathematically sound methods are not implemented in a way, which makes them usable for the simulation of demanding applications. Even worse, many new methodological developments are tested only for simple model problems, and the robustness of new methods with respect to varying geometries, material laws, boundary conditions etc. is often not investigated. It is the aim of this project to narrow this gap in both dimensions by developing, implementing and providing new solution strategies for frictional contact problems in nonlinear elasticity. The ReAct project will create new (non-)smooth methodological approaches, which will allow for exploiting the power of state of the art methods from decomposition techniques and optimization for numerical simulations in frictional contact mechanics. To this end, with nonsmooth minimization, ReAct will exploit a modern and not widely used approach for the numerical treatment of contact problems; it will provide efficient solution methods, which are applicable to real world problems; it will close the gap between abstract methodological developments and applications by providing a powerful implementation of the newly developed methods. Although considerable progress has been made during the last decades in the development of fast solution methods for problems in linear elasticity, the underlying ideas and techniques have only slowly or not at all been transferred to more demanding problems. This is due to several intrinsinc difficulties related to contact problems: nonsmooth effects at the interface as the non-penetration condition or friction are hard to deal with analytically and numerically, nonconvex stored energy functions require well elaborated solution strategies, and real word problems need unstructured meshes, efficient data structures and the capability to deal with complex geometries. Within the ReAct project, these challenges will help us in further renfining our new methods. By implementing our methodological indings already during the development phase in the framework of the high-end simulation toolbox ObsLib++, which is developed and maintained in the applicant's group, we will create a feedback loop, which will always keep us close to the quantitative properties of our developments along realistic problems from (bio-)mechanics. It is our belief that this unique combination of modern numerical and analytical techniques and high-end numerical implementations will lead to new, robust, and efficient solution methods, which will be applicable to real world problems - thus providing new theoretical insights as well as a flexible simulation toolbox for contact problems in nonlinear elasticity.
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