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Ä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
(&&0&UDFRZ3RODQG $QH[SUHVVLRQIRUWKHHIIHFWLYHVWUHVVWHQVRUKDVDVVXPHGWKHIROORZLQJIRUP S ( ) = ' e e ZKHUH ' LV WKH IRXUWK RUGHU OLQHDUHODVWLF FRQVWLWXWLYH PDWUL[ e LV WKH VHFRQG RUGHU VWUDLQ WHQVRUe S LVWKHSODVWLFVWUDLQWHQVRU 7KHIROORZLQJIRUPRI+HOPKROW]IUHHHQHUJ\SRWHQWLDOKDVEHHQDGRSWHG Yee S G + G = G + Y + ee S + G Y ee S 7KHHODVWLFIUHHHQHUJLHVDUHGHILQHGDVIROORZV Y Y = = ' + + ' + G G DUHWKHGDPDJHYDULDEOHVDVVLJQHGUHODWLYHO\WRFRPSUHVVLRQDQGWHQVLRQ7KHLUYDOXHV DUHRIWKHUDQJH!,QRUGHUWRFKDUDFWHULVHWKHGDPDJHDFRQFHSWRIHIIHFWLYHFRPSUHVVLYHDQGWHQVLOHVWUHVVKDV EHHQLQWURGXFHG,QWKHSUHVHQWZRUNWKH\ZLOODVVXPHWKHIROORZLQJIRUPV U = + + + ' U =. + t RFW RFW.LVDPDWHULDOSURSHUW\DQGWKH RFW t RFW DUHWKHRFWDKHGUDOQRUPDOVWUHVVDQGWKHRFWDKHGUDO VKHDUVWUHVVFDOFXODWHGIURP 2Q WKH EDVLV RI FDOFXODWHG HIIHFWLYH HTXLYDOHQW VWUHVVHV WZR GDPDJH FULWHULD KDV EHHQ LQWURGXFHGDFFRUGLQJWR6LPRDQGX>@ + + + + J U U = U + U Ê J U U = U U Ê ZKHUH WKH HQWLWLHV U DQGU DUH FXUUHQW GDPDJH WKUHVKROGV DQG FRQWURO WKH VL]H RI GDPDJH VXUIDFHV 7KHUDWHVRIWHQVLOHDQGFRPSUHVVLYHYDULDEOHDUHGHILQHGDVIROORZV + + & * U + G & + U & + = + = * Ë U & * U G & U *& = = Ë U * * DUHWKHDSSURSULDWHPRQRWRQLFDOO\LQFUHDVLQJIXQFWLRQVLQRUGHUWRREWDLQWKHYDOXHV RIGDPDJHYDULDEOHVLQWKHUDQJHRI!
.&LFKRFNL05XFKZD 6LPLODUO\ WR WKH GDPDJH YDULDEOHV WKH UDWH RI SODVWLF VWUDLQ WHQVRU KDV EHHQ LQWURGXFHG LQWKHIRUPRI e& S & < e & > = b (+ G ' ZKHUH ( LV D <RXQJ PRGXOXV b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
(&&0&UDFRZ3RODQG /RDG SURGXFHG E\ WKH H[SORVLRQ ZDV VLPXODWHG DV D ILHOG RI SUHVVXUH YDULDEOH LQ VSDFH DQG WLPH DFFRUGLQJ WR HTXDWLRQV JLYHQ E\ +HQU\FK >@,Q WKLV GHVFULSWLRQ WKH YDOXH RI PD[LPXP LQFLGHQW SUHVVXUHV DS f DW WKH GLVWDQFH 5 >P@ IURP WKH FHQWUH RI 717 FKDUJH :>NJ@GHSHQGVRQWKHSDUDPHWHU DFFRUGLQJWRWKHIROORZLQJHTXDWLRQV 5 5 = : DS DS DS f f f = + + [ NS FP ] 5 5 5 5 Ê 5 Ê = + [ NS FP ] 5 5 5 Ê 5 Ê = + + [ NS FP ] 5 5 5 Ê 5 Ê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
(&&0&UDFRZ3RODQG 5HIHUHQFHV >@ '.UDXV DQG )5RHW]HU 3URFHHGLQJV RI WKH,QWHUQDWLRQDO &RQIHUHQFH RQ &RPSXWDWLRQDO 0RGHOOLQJ RI &RQFUHWH 6WUXFWXUHV Ä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
ECCM2001, Cracow, Poland Fig.1. Vertical diplacement Fig.2. Platic equivalent train 8
K. Cichocki, M.Ruchwa Fig.3. Final configuration of lab Energy [J] Diipated Kinetic Strain Inelatic Time [] Fig.4. Energie veru time 9