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

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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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

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

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

+0+O+@"+P

CAC

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

H 1+"V B0 >:"OBPVO+PP+PH 0 //+0 &=30' ,WECF&XWA.X64' CAA,H CXCH H H B]VYO( @( HH @OV+@P:V+ D=V+P :@ :OB@9P+( ==B]PH (>0 60 6++.:0' 4AE6F&RSA.RRA' CA,4H @7=:P8 VO@P=V:B@& &=30 60 6++0' 4A&CWC.C6_' CA,4H CXXH H H B]VYO( @( H =YVP<+OH 8+O>B(]@>:" 8]PV+O+P:P B0 D8P+ VO@P0BO9 >V:B@ :@ PB=:(PH &=3( ' XWW&WA_.WAS' CAARH CXWH H H B]VYO( @( H =YVP<+OH +0BO>V:B@ B0 (DV:Z+ >V+O:=PH OV H B@9 PVO:@+( (+0BO>V:B@ B0 DB=](B>:@ "O]PV=PH 0 &0 &=30 .+(3' 6R&XXAA. XWXA' CAAAH CX6H H H B]VYO( @( H =YVP<+OH +0BO>V:@ B0 (DV:Z+ >V+O:=PH OV

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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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