+ All Categories
Home > Documents > Stress fluctuations in jammed granular solids

Stress fluctuations in jammed granular solids

Date post: 08-Aug-2018
Category:
Upload: bdpmax
View: 214 times
Download: 0 times
Share this document with a friend
21
Xtrcss uhtuetdaks dk leggcm saodms< e stetdstdheo ckscg`oc eppraehb ID]^H ' Hagpocx Mykegdhs dk Frekuoer Xystcgs Gey 0>/ 0>58 Mepckf @d Xyrehusc Skdvcrsdty Haooe`aretars Xugektre Xerier "@rekmcds Skdv +$ @uo`uo Hbeire`arty "@rekmcds Skdv+$ Ldc \bekf "Xbekfbed Ldea ]akf Skdv+$ @a` @cbrdkfcr "Muic Skdv+$
Transcript
Page 1: Stress fluctuations in jammed granular solids

8/22/2019 Stress fluctuations in jammed granular solids

http://slidepdf.com/reader/full/stress-fluctuations-in-jammed-granular-solids 1/21

Xtrcss ffuhtuetdaks dk leggcm saodms<e stetdstdheo ckscg`oc eppraehb

ID]^H ' Hagpocx Mykegdhs dk Frekuoer XystcgsGey 0>/ 0>58

Mepckf @d

Xyrehusc Skdvcrsdty

Haooe`aretarsXugektre Xerier "@rekmcds Skdv+$

@uo`uo Hbeire`arty "@rekmcds Skdv+$

Ldc \bekf "Xbekfbed Ldea ]akf Skdv+$

@a` @cbrdkfcr "Muic Skdv+$

Page 2: Stress fluctuations in jammed granular solids

8/22/2019 Stress fluctuations in jammed granular solids

http://slidepdf.com/reader/full/stress-fluctuations-in-jammed-granular-solids 2/21

Page 3: Stress fluctuations in jammed granular solids

8/22/2019 Stress fluctuations in jammed granular solids

http://slidepdf.com/reader/full/stress-fluctuations-in-jammed-granular-solids 3/21

Haggak jceturcs

‣Fredks erc gehrashapdh dk sdzc

‣ ^urcoy Pcpuosdvc "jar mry fredks$/ Hakteht Dktcrehtdaks/ jrdhtdak

‣ Xtetcs haktraoocm `y `aukmerdcs ekm mrdvdkf

‣Haoochtdvc prapcrtdcs< fes/ odqudm/ saodm +++ `ut kat qudtc%

 LT ]ekf/ Muic

Joudm Xaodmgerfdkeo

‟L‗'scfgckt

Mcksdty 

ar eppodcm strcss

Kefco Oe`/ Hbdhefa

Keturc

Page 4: Stress fluctuations in jammed granular solids

8/22/2019 Stress fluctuations in jammed granular solids

http://slidepdf.com/reader/full/stress-fluctuations-in-jammed-granular-solids 4/21

Jer jrag cqudod`rdug

‣ Oerfc scperetdak aj ckcrfy sheocs

‣ Dktcrehtdaks `ctwcck fredks<

jrdhtdak ekm mdssdpetdak

‣ Ckcrfy fcts mdssdpetcm< dktcrkeo vd`retdakeo

gamcs erc cxhdtcm+ Fredks ma kat gavc+

Ma wc bevc ta saovc Kcwtak—s cquetdaks "wdtb mdssdpetdak ekm

mrdvdkf$ jar cvcry hakhcdve`oc gehrashapdh sctup 1

Hek wc hakstruht e stetdstdheo gchbekdhsjregcwari aj frekuoer gcmde 1

Vbet hek wc `arraw jrag cqudod`rdug stet+ gchb+1

Page 5: Stress fluctuations in jammed granular solids

8/22/2019 Stress fluctuations in jammed granular solids

http://slidepdf.com/reader/full/stress-fluctuations-in-jammed-granular-solids 5/21

^ra`e`dodty aj ahhurrckhc aj tbds gdhrastetc<

Jouhtuetdaks dk tbds

su`systcg< e skepsbat aj e gdhrastetc<

^ ⟨  7 cC ⟨!\ " $

Zcry `rdcj rcvdcw aj cqudod`rdugstetdstdheo gchbekdhs

Dsaoetcm/ hakscrvetdvc systcg< "C K / Z  K / K $

⟨ 

 7@ X 

@ C 

 tbcrgeo cqudod`rdug/ segc cvcrywbcrc

Page 6: Stress fluctuations in jammed granular solids

8/22/2019 Stress fluctuations in jammed granular solids

http://slidepdf.com/reader/full/stress-fluctuations-in-jammed-granular-solids 6/21

]eppdkf Egpodtumc

drrcvcrsd`oc

rcvcrsd`oc

J PO^

J PH^

Kak'cqudod`rdug stcemy stetcs

Mrdvdkf suhb es rcpcetcm teppdkf

rcehb e rcvcrsd`oc `rekhbKawei ct eo ^PC "5446$

Ckcrfy mchrcescs muc ta mdssdpetdak

kat e faam stetc verde`oc

Jrccoy Haaodkf Frekuoer Fes<

Gerct ct eo/ ^PO "0>>2$

Page 7: Stress fluctuations in jammed granular solids

8/22/2019 Stress fluctuations in jammed granular solids

http://slidepdf.com/reader/full/stress-fluctuations-in-jammed-granular-solids 7/21

Cmwerms Ckscg`oc

E sdgpoc/ `aom prapaseo<

Mykegdhs haktraoocm y stetdstdhs aj ‟@oahicm Xtetcs‗

‣ @oahicm Xtetc< Cehb fredk ds dk jarhc ekm

tarquc `eoekhc/ stetdh

‣ ]ateo jrcc vaougc rcehbcs stcemy stetcveouc

Aeicsbatt ekm Cmwerms "5424$

^ ⟨  7 cw⟨ R!\ "R $

5

R 7

@ X 

@ Z  R  7 hagpehtdvdty<

Eppodcs dk tbc dkstkdtcoy rdfdm ar lust tauhbdkf odgdt< akoy vaougc gettcrs

Jdxcm "Z/K$ es rcsuot aj teppdkf

Vdtbdk akc rceodzetdak "c+f+/ es rcsuot aj teppdkf$E gdhrastetc wdtb vaougc< %⟨  "{~ rd}$

Page 8: Stress fluctuations in jammed granular solids

8/22/2019 Stress fluctuations in jammed granular solids

http://slidepdf.com/reader/full/stress-fluctuations-in-jammed-granular-solids 8/21

E hakscrvetdak prdkhdpoc jar `oahicm stetcsJarhc Gagckt ]cksar

Jdxcm `aukmery hakmdtdak

⌈ 7

\ X 

mX  7

D @ X 

~ b m~ o

7 ~ r⇣ ~ b

Mdshrctc ‒Bcdfbt gep— jar strcss@eoo * @ougckjcom ^PO 0>>0

Bckics * Hbeire`arty 0>>6

Mcjarge`oc mry fredks

‣ ^urcoy rcpuosdvc hakteht dktcrehtdaks

‣ Dgpascm strcss ds dgpartekt

‣ Jrdhtdakeo jarhcs

Kccm pasdtdaks ekm jarhcs ta spchdjy e

gdhrastetc%

Oaheo jarhc * tarquc `eoekhc

^asdtdvdty aj jarhcs

~ r ¶ 7 > ekm dl 7 ld jar eoo ~ r

dd ; 0

Page 9: Stress fluctuations in jammed granular solids

8/22/2019 Stress fluctuations in jammed granular solids

http://slidepdf.com/reader/full/stress-fluctuations-in-jammed-granular-solids 9/21

Hakscrvetdak aj tbc Jarhc Gagckt ]cksar 

@

E

@ H 

^crdamdh `aukmery hakmdtdak

]rdvdeo oaap H <

Kak'haktrehtd`oc oaap E <

~ J x 7

\ O

>

my

55"x/ y$50"x/ y$

Kak'haktrehtd`oc oaap @ <

~ J y 7

\ O>

mx

50"x/ y$00"x/ y$

\ X 

mX  ~ r ¶ 7

D @ X 

mo ¶ k 7 > + Gctzfcr< ^BTXDHEO

PCZDCV C 66/ >558>6 0>>2

J

J

"Xerier ct eo erxdv<58>3+8=2=$

Page 10: Stress fluctuations in jammed granular solids

8/22/2019 Stress fluctuations in jammed granular solids

http://slidepdf.com/reader/full/stress-fluctuations-in-jammed-granular-solids 10/21

Haersc'fredkcm su`rcfdak<

"g fredks/ jarhc gagckt tcksar $ˊ

⌈g

⌈ 7

Rd?l

~    rdl ⟩ ~    j dl0m7

✘⌈55 ⌈50

⌈50 ⌈00

Xtrcss ckscg`oc

^ ⟨  7 5\ "R/ ↳$

cxp⇨w⟨ 

⌒cxp

⇨↳ < ⌈⟨ 

↳io 7N X "Z/ ⌈$

N ⌈io

Z  

↳ 7

✘↳55 ↳50

↳50 ↳00

Macs dt wari1

 Ekfardhdty ds dkmccm e tcksardeo‟tcgpcreturc‗ 

Page 11: Stress fluctuations in jammed granular solids

8/22/2019 Stress fluctuations in jammed granular solids

http://slidepdf.com/reader/full/stress-fluctuations-in-jammed-granular-solids 11/21

 ^uhictt * Mekdcos/ ^PO "0>58$

Zaougc ffuhtuetdaks←Hagpehtdvdty 

LeggcmSkleggcm

ÌL 

Ì

Odu * Kefco Keturc "5442$

Egarpbaus

saodms

Geky bevc tcstcm tbc dmce/gast rchcktoy<

 Leggdkf `y dsatrapdhhagprcssdak

^ ⟨  7 cw⟨!Rc↳⟨!\ "R/↳$

Page 12: Stress fluctuations in jammed granular solids

8/22/2019 Stress fluctuations in jammed granular solids

http://slidepdf.com/reader/full/stress-fluctuations-in-jammed-granular-solids 12/21

Cquetdak aj Xtetc

^rcssurc ffuhtuetdaks←ekfardhdty 

 ^uhictt * Mekdcos/ ^PO "0>58$

Dsatrapdheooy leggcm stetcs erc dmceo'fes odic%

LeggcmSkleggcm

Ì

Odu * Kefco Keturc "5442$

Egarpbaus

saodms

Page 13: Stress fluctuations in jammed granular solids

8/22/2019 Stress fluctuations in jammed granular solids

http://slidepdf.com/reader/full/stress-fluctuations-in-jammed-granular-solids 13/21

LeggcmSkleggcm

Xbcer

Leggcm

Jrefdoc Ì

ÌX  ÌL 

•  Leggcm stetcs `coaw tbc hrdtdheo mcksdty aj mcksdty'mrdvck leggdkf "tbc veouc aj tbc hrdtdheo mcksdty

hek mcpckm ak pratahao$

• Xtetcs `coaw Ϊ L hek `c hoessdstcm dkta twa typcs aj stetcs< Jrefdoc ekm Xbcer Leggcm "XL$

• XL stetcs rcqudrc e stkdtc egaukt aj eppodcm sbcer strcss ta jarg "sbcer ds kccmcm ta fckcretc

prcssurc%$

• ]bcsc stetcs erc kat es strakf es tbc mcksdty'mrdvck leggcm stetcs "Gerfdkeo!Jrefdoc$

M@ ct eo Keturc "0>55$

Xbcer leggcm stetcs

Page 14: Stress fluctuations in jammed granular solids

8/22/2019 Stress fluctuations in jammed granular solids

http://slidepdf.com/reader/full/stress-fluctuations-in-jammed-granular-solids 14/21

Pcm pertdhocs 7 Oerfcst hakkchtcm houstcr wdtb j ; j evf

Ì

ÌX  ÌL 

Dkhrcesdkf stredk

Skleggcm

Jrefdoc

Xbcer'leggcm

Hetcs ct eo/^PO "5442$

M@ ct eo Keturc "0>55$

Xbcer leggcm stetcs< Cvaoutdak aj tbc jarhc kctwari 

Page 15: Stress fluctuations in jammed granular solids

8/22/2019 Stress fluctuations in jammed granular solids

http://slidepdf.com/reader/full/stress-fluctuations-in-jammed-granular-solids 15/21

Xbcer leggcm stetcs< strcss ffuhtuetdaks

^ "⌈g$ 75

\ "↳$cxp

bX g"⌈g$

dcxp

⇨↳ < ⌈g

Kcfocht vaougc ffuhtuetdaks/

"teidkf hagpehtdvdty R←∛ Odgdt$

Hekakdheo mdstrd`utdak jar oaheo strcsscs<

Xegc cvcrywbcrc/ fdvck `y cquetdak aj stetc<↳

oafb^ "⌈g$c

↳<⌈gd7 X g

⇨⌈g

oaf\ "ˊ↳$

↳ !G 

⇨⌈G 

⌒5

7G 

mct

⇨⌈G 

⌒✘⌈00/G  ⌈50/G 

⌈50/G  ⌈55/G 

M@ ct eo/ erRdv<58>0+:245 ta eppcer dk C^O

Page 16: Stress fluctuations in jammed granular solids

8/22/2019 Stress fluctuations in jammed granular solids

http://slidepdf.com/reader/full/stress-fluctuations-in-jammed-granular-solids 16/21

Xtrcss ffuhtuetdaks< Pcmuhcm mdstrd`utdaks

cary

     f   g

              "     x

              $

x

hagpakckt/ cxpt

0hagpakckt/ cxpt

>+> >+3 5+> 5+3 0+> 0+3 8+>>+>

>+3

5+>

5+3

0+>

0+3

g 7 =

>+> >+3 5+> 5+3 0+> 0+3 8+>>+>

>+3

5+>

5+3

0+>

0+3

g 7 53

>+> >+3 5+> 5+3 0+> 0+3 8+>>+>

>+3

5+>

5+3

0+>

0+3g 7 02

>+> >+3 5+> 5+3 0+> 0+3 8+>>+>

>+3

5+>

5+3

0+>

0+3g 7 30

Cxpcrdgckt

cary

       b   g

              "     x              $

x7 ⌈

50/g!p ⌈

55/g⌈00/g

g 7 = g 7 53

g 7 02 g 7 30

'5+> '>+3 >+> >+3 5+>>+>

>+3

5+>

5+3

0+>

0+3

8+>

8+3

'5+> '>+3 >+> >+3 5+>>+>

>+3

5+>

5+3

0+>

0+3

8+>

8+3

'5+> '>+3 >+> >+3 5+>>+>

>+3

5+>

5+3

0+>

0+3

8+>

8+3

'5+> '>+3 >+> >+3 5+>>+>

>+3

5+>

5+3

0+>

0+3

8+>

8+3

Xtrcss ckscg`oc sccgs ta prcmdht tbc mdstrd`utdak aj oaheo strcsscs wcoo

@ut+++++++ M@ ct eo/ erRdv<58>0+:245

⌈ 7 ✘⌈55 ⌈50

⌈50 ⌈00◊⌈ 7 ✘⌈55 ⌈50

⌈50 ⌈00◊

Page 17: Stress fluctuations in jammed granular solids

8/22/2019 Stress fluctuations in jammed granular solids

http://slidepdf.com/reader/full/stress-fluctuations-in-jammed-granular-solids 17/21

g

55hagpakckt

5 hagpakckt

hagpakckt

)))))

))))

)))))

)))

))))))))))

))))

)))))

¶¶¶¶

¶¶¶¶

¶¶

¶¶¶

¶¶¶

¶¶¶¶

¶¶¶

¶¶¶

¶¶¶¶

¶¶¶¶¶

ÅÅÅÅÅ

ÅÅÅÅ

ÅÅ

ÅÅÅ

ÅÅÅ

ÅÅÅÅ

ÅÅÅ

ÅÅÅ

ÅÅÅÅ

ÅÅÅÅÅ

3 5> 0> 3> 5>>5

3

5>

3>

5>>

3>>

⇠ g5+3

              b              "             ⌈    ↳    ↳

              $        0

              d          !             >

        0

M@ ct eo/ erRdv<58>0+:245

Xtrcss ckscg`oc bes kat teick dkta ehhauktharrcoetdaks

Page 18: Stress fluctuations in jammed granular solids

8/22/2019 Stress fluctuations in jammed granular solids

http://slidepdf.com/reader/full/stress-fluctuations-in-jammed-granular-solids 18/21

~    b0

~    b5 7 ~    b> ) ~    j 5

~    b0 7 ~    b5 ) ~    j 0

~    b8 7 ~    b0 ) ~    j 8

~    b= 7 ~    b8 ) ~    j =

~    b3 7 ~    b8 ) ~    j =

~    j 5

~    j 0

~    j 8

~    j = ~    j 3

~    j :

~    j 3

~    j 5 ~    j :

~    j 8~    j =

~    j 0

~    b5

~    b0

~    b0

~    b8

~    b=

~    b3

7 ~ r⇣ ~ b~ r¶ 7 >

Dktramuhc e bcdfbt stcom<

Fcagctrdh rcprcscktetdak< jarhc tdoc

☃ ]bc hakteht jarhcs jarg e hoascm

paoyfak "Kcwtak—s 8rm oew$

☃ Zcrtdhcs fdvck `y tbc bcdfbts

Xerier ct eo erxdv<58>3+8=2=

Keturc aj armcr ekm harrcoetdaks

Page 19: Stress fluctuations in jammed granular solids

8/22/2019 Stress fluctuations in jammed granular solids

http://slidepdf.com/reader/full/stress-fluctuations-in-jammed-granular-solids 19/21

 Jx

 J y

bx

y

• Oaheo gavcs prcscrvc• Jdxcm hakteht kctwari 

• Akc vcrtcx upmetc pcr gavc ehharmdkf tapasdtdvdty hakstredkt

Cxpoardkf mdjjcrckt hakstfuretdaks dk bcdfbt spehc

~    

J x/~    

J y

^bysdheooy/ tbds ds cqudveockt ta pcrtur`etdak `y odfbtoy teppdkf+

Page 20: Stress fluctuations in jammed granular solids

8/22/2019 Stress fluctuations in jammed granular solids

http://slidepdf.com/reader/full/stress-fluctuations-in-jammed-granular-solids 20/21

JAPHC ]DODKF

"XBCEP'LEGGCM$

Xerier ct eo erxdv<58>3+8=2=

Page 21: Stress fluctuations in jammed granular solids

8/22/2019 Stress fluctuations in jammed granular solids

http://slidepdf.com/reader/full/stress-fluctuations-in-jammed-granular-solids 21/21

XSGGEPT

☃E stetdstdheo ckscg`oc eppraehb waris jar frekuoer saodms

☃E heohuoetdak taao< haoochtdvc `cbevdar/ ukdvcrseodty

☃Macs dt bcop ta ukmcrstekm soawoy mrdvck stetcs 1

☃Pdfdmdty ds eoo e`aut armcr ekm harrcoetdaks dk ‟jarhc spehc‗


Recommended