Micromechanics of Contact and Interphase Layers (Lecture Notes in Applied and Computational Mechanics 30)

Lecture Notes in Applied and Computational Mechanics Volume 30 Series Editors Prof. Dr.-Ing. Friedrich Pfeiffer Prof. D...

Author: Stanislaw Stupkiewicz

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Lecture Notes in Applied and Computational Mechanics Volume 30 Series Editors Prof. Dr.-Ing. Friedrich Pfeiffer Prof. Dr.-Ing. Peter Wriggers

Lecture Notes in Applied and Computational Mechanics Edited by F. Pfeiffer and P. Wriggers Further volumes of this series found on our homepage: springer.com

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Micromechanics of Contact and Interphase Layers Stanisław Stupkiewicz

Stanisáaw Stupkiewicz Institute of Fundamental Technological Research Polish Academy of Sciences ´ ¸tokrzyska 21 Swie 00-049 Warszawa Poland [email protected] With 76 Figures

Library of Congress Control Number: 2006937129

ISSN 1613-7736 ISBN- 3-540-49716-1 Springer Berlin Heidelberg New York ISBN- 978-3-540-49716-5 Springer Berlin Heidelberg New York

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. Violations are liable to prosecution under German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Springer-Verlag Berlin Heidelberg 2007

Printed in Germany 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: Data conversion by the author. Final processing by PTP-Berlin Protago-TEX-Production GmbH, Germany (www.ptp-berlin.com) Cover-Design: WMXDesign GmbH, Heidelberg Printed on acid-free paper 89/3141/Yu - 5 4 3 2 1 0

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

+0+O+@"+P

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

& B(+=:@7 B0 DB=]"O]PV=PH &0 620' W,&6W_. 6SX' X__SH # RSH H @(' H BZ <' H +(= <' @( H :VV@+OH =VOPB@:" "8O"V+O:^V:B@ B0 Y.=.: P:@7=+ "O]PV=P =VV:"+ PV:=:V] :@ V8+ Z:":@:V] B0 V8+ D8P+ VO@P:V:B@H +623.-(3' 6X&4CA.4XS' X__6H RRH H9 H ++ @( H [B@H PV:>V:B@ B0 :\:= PYO0"+ PVO+PP ] :@PVOY>+@V+( :@(+@VV:B@ [:V8 P8OD :@(+@V+OPH 6 620' 4X&C444.C4SW' X__6H

+0+O+@"+P

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ASH H VBBO' H +O8O(V' @( H +OZ+:==+OH :"OB>+"8@:"= >B(+==:@7 B0 PYD+O+=PV:":V] :@ P8D+ >+>BO] ==B]PH 0 &=3(19 ' C&XRR.XAX' CAASH ARH H VBBO' HH 7BY(P' HH @V"8+Z' HH O:@PB@' @( H BH 8D+ >+>BO] ==B]P' OV & +@+O= DOBD+OV:+P @( >B(+=:@7 B0 P:@7=+ "O]PV=PH &0 620' W,&WAC.6XA' X__SH A,H HH Y< @( H B^@: 0BO 8=09PD"+ [:V8 B9 Y@(O] :>D+O0+"V:B@PH -60 0 .+0 62960' WS&W4SA.W4RA' CAAAH AAH H +(+OP+@H +36((6=-(3.62./= ,(-63H +"8@:"= @:Z+OP:V] B0 +@9 >O<' CAARH C__H HHH +OPPB@H +((-% 2(6(.-H DO:@7+O +O=7' +O=:@' CAA,H C_CH H +VO]+

' D7+P A,R.AA6' B@(B@' CA,RH OB"H

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

+0+O+@"+P

CAC

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

CAX

+0+O+@"+P

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

+0+O+@"+P

CAW

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

&7

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

CXC' CW,' C6_

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

C_W' CC,' C4W

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