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Computational Contact and Impact Mechanics

Springer-Verlag Berlin Heidelberg GmbH Engineering ONLlNE LIBRARY http://www.springer.de/engine/

Tod A. Laursen Computational Contact and Impact Mechanics Fundamentals of Modeling Interfacial Phenomena in Nonlinear Finite Element Analysis 1 st ed. 2002, COIT. 2nd printing With 147 Figures and 6 Tables • Springer

Professor Tod A. Laursen Department of Civil and Environmental Engineering Pratt School of Engineering Duke University Box 90287 Durham, NC 27708-0287 USA ISBN 978-3-662-04864-1 (eBook) ISBN 978-3-642-07685-5 DOl 10.1007/978-3-662-04864-1 Cata10ging-in -Publication Data applied for Bibliographic information published by Die Deutsche Bibliothek. Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at . This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in other ways, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer-Verlag. Violations are liable for prosecution under German Copyright Law. http://www.springer.de © Springer-Verlag Berlin Heidelberg 2003 Originally published by Springer-VerJag Berlin Heidelberg New York in 2003. Softcover reprint of the hardcover 1st edition 2003 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: Camera ready by authors Cover-design: Medio, Berlin Printed on acid-free paper 62/3020 hu - 543210 -

To my boys, Orin and Colin, and to my wife, Jennifer

Preface Many physical systems require the description of mechanical interaction across interfaces if they are to be successfully analyzed. Examples in the engineered world range from the design of prosthetics in biomedical engi neering (e.g., hip replacements); to characterization of the response and durability of head/disk interfaces in computer magnetic storage devices; to development of pneumatic tires with better handling characteristics and increased longevity in automotive engineering; to description of the adhe sion and/or relative slip between concrete and reinforcing steel in structural engineering. Such mechanical interactions, often called contact/impact in teractions, usually necessitate at minimum the determination of areas over which compressive pressures must act to prevent interpenetration of the mechanical entities involved. Depending on the application, frictional be havior, transient interaction of interfaces with their surroundings (e.g., in termittent stick/slip), thermo-mechanical coupling, interaction with an in tervening lubricant and/or fluid layer, and damage of the interface (i.e., wear) may also be featured. When taken together (or even separately!), these features have the effect of making the equations of mechanical evolu tion not only highly nonlinear, but highly nonsmooth as well. While many modern engineering simulation packages possess impressive capabilities in the general area of nonlinear mechanics, it can be contended that methodologies typically utilized for contact interactions are relatively immature in comparison to other components of a nonlinear finite element package, such as large deformation kinematics, inelastic material modeling, nonlinear equation solving, or linear solver technology. The result of this situation appears to be that when designers and analysts wish to use "off

viii Preface the shelf' software to characterize a contact/impact system of interest, they either find the contact capability to be considerably less robust and/or accurate than the remainder of the analysis system, or even worse, they find available formulations for contact/impact to be inadequate for their needs. Much of the reason for this situation can be attributed to a simple truth: contact and friction problems are difficult to solve, since they are highly nonlinear and nonsmooth, and the machinations required to treat them in practice are not always aesthetically pleasing. However, as is often the case in computational mechanics, a successful algorithmic strategy for a rather specialized application can usually be achieved if the engineering analyst and the algorithmic developer have significant shared knowledge of the un derlying mathematical structure of the problem, of the issues involved in its computational approximation, and of the physics relevant to the system at hand. The situation is somewhat analogous to that which exists in con stitutive modeling of materials, where practitioner and developer must use the common languages of continuum mechanics and finite element technol ogy to develop a reliable computational description of measured material behavior. The success of this collaborative approach, however, depends crit ically on the existence of a common understanding of the problem at hand, which arguably does not exist for contact interactions to the degree it does, for example, for computational inelasticity. It is to the development of this common "knowledge base," which will enable the advancement of interface science in computational solid and structural mechanics, that this work is dedicated. Accordingly, while this book has been conceptualized as a research mono graph on a rather specialized subject, it became clear during its evolution that it should also contain a useful introduction to computational nonlinear mechanics, such that a non-specialist in computational methods could ac cess the material without the need to consult a multitude of other sources. Accordingly, the book proceeds from a rather terse but reasonably detailed introductory treatment of computational nonlinear solid mechanics; to a thorough description of the continuum mechanics, problem formulation, variational framework, and finite element implementation of modern con tact mechanics algorithms; to a comprehensive presentation of the emerging trends of computational contact mechanics, encompassing such topics as tribological complexity, thermomechanical coupling on interfaces, energy momentum treatment of transient impact events, and new techniques for spatial discretization of contact phenomena. I owe an enormous debt of gratitude to several research sponsors, indus trial and government collaborators, faculty colleagues, and graduate stu dents who have contributed immensely to my understanding of this subject, and who in many cases contributed directly to the results presented in this book. In particular, portions of this work were partially supported by the National Science Foundation under grant numbers MSS-9308486 (Research Initiation Award) and CMS-9703356 (Career Award), and by the Office of

Preface ix Naval Research under Young Investigator Award NOOOl4-97-1-0529. These funding sources are gratefully acknowledged. Sandia National Laboratories funded aspects of this work under two contracts, AN-9563 and BD-3742, and also graciously hosted me for a faculty sabbatical in the spring of 2001, during which time some of the work in Chapter 8 was fleshed out in col laboration with Dr. Martin Heinstein of SNL. This support, which includes as a major component Martin's friendship and continued collaboration, is likewise very gratefully acknowledged. I would like to recognize also the collaboration and assistance received from Dr. Michael Puso of Lawrence Livermore National Laboratory, with whom the three dimensional smooth ing algorithms in Chapter 8 were developed, and whose work contributed greatly to the discussion of mortar methods given in that chapter. Several other collaborators and research sponsors should be acknowl edged for similar reasons, including: Dr. Peter Raboin of Lawrence Liver more National Laboratory; Drs. Harold Morgan, Frank Mello, Sam Key and Steven Attaway of Sandia National Laboratories; Dr. Bradley Maker, for merly of Lawrence Livermore and now at LSTC, Inc.; Drs. Joop Nagtegaal and David Fox of Hibbitt, Karlsson and Sorensen, Inc.; Dr. Ric Mousseau, formerly of Ford Motor Company and now at the University of Toledo; Drs. John Melson and Jean-Marc d'Harcourt of Michelin Tire Company; Professors Sanjay Govindjee, Francisco Armero, and Robert Taylor of the University of California at Berkeley; Dr. Todd McDevitt, formerly my post doctoral colleague at Duke University and currently at MDI, Inc.; and Pro fessors Lawrence Virgin, John Dolbow, Lori Setton and Farshid Guilak of Duke University. Current and former students of mine who contributed to this work include Drs. Victor Oancea, Vikas Chawla, Garrett Love, and Xiaonong Meng, as well as Renuka Srinivasan, Vivek Padmanabhan and !linca Stanciulescu-Panea. I am particularly proud of and grateful for the contributions of these participants in my research group over the past few years. I am grateful to the administration of my home institution, Duke Univer sity, for granting my sabbatical during the 2000-2001 academic year, during which most of the work on this project was completed. Additionally, I want to say a special word of thanks to my family, Jennifer, Orin, and Colin, for their patience and understanding during the many evenings and weekends where my attention and time were devoted to this project rather than to other potential family activities. I love them and am proud of them, and they have inspired me in ways they do not fully realize. Finally, I especially wish to acknowledge the extraordinary mentorship, instruction, and friendship I received from the late Juan C. Simo of Stan ford University, from the time I first walked into his office as a beginning Master's student (looking for help with indicial notation!) in September of 1986, until his untimely and tragic death from cancer in October of 1994. As has been extensively documented by many others, Juan's profes sional genius transformed the manner in which our field thinks about such

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