IMPLEMENTATION, VERIFICATION AND APPLICATION OF THREE DIMENSIONAL HISS MODEL IN ABAQUS.pdf

8/11/2019 IMPLEMENTATION, VERIFICATION AND APPLICATION OF THREE DIMENSIONAL HISS MODEL IN ABAQUS.pdf

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31 ! 1 " Vol.31 No.1 # $ % &

2014 ' 1 ( Jan. 2014 ENGINEERING MECHANICS 160

)*+", 2012-09-13 -./+", 2013-02-250123,45678&0123 (50908123) -9:;&6?23 (2010THZ0)@ABC,D E (1974 F )GHGIJKLMGN=OPGQRGSTUV#$=O (E-mail: [email protected]).BCWX,YZ[ (1986 F )GHG\]^_MG`RaGSTbcde#B=O (E-mail: [email protected]).

!"#$% 1000-4750(2014)01-0160-06

&'( )*+,-./01234YZ[ 1GD E 1,2

(1. 9:;&fg#$hGij 100084 - 2. 9:;&fg#$klmnopqrstuvwGij 100084)

5 6% xyz{|} (HISS) ~ {|} ! z "#$ %& G '()*+,- ~ ./ & & 0123456

7 X 8) HISS ~ 9:;?@ABCDEF 1d ~ GH < IJ&K {|} LM G NO MATLAB K

"PQRS xt TUVWX vG YZ)/VW[ $ 9\ % ]^G {|} _F -0 ` ABAQUS abc $ def

ghijkl Gmhno) f p HISS ~ qrOstu, $ d5NO ABAQUS vw67ij Os, $ d

~ x) Leighton Buzzard y f 4 zq{X v |} (~ L X v !" q{ # X v q{ # X v $ q{ %& X

v )G '( > | )* \ % -\_; h $ pS_F muv YZ +, K - G~> | +, muv +,./01 Gv

2 ) HISS ~ O`y f D 345 6 OD G '( ~ O` x 7 x 8 ] 0 k 9 W : X v 5 HISS ~ qr, $ d

u ;< ABAQUS x 7 qr f p => D34ef)"z ? @A ; h 5

789% xyz{|}~- ABAQUS - qrOstu, $ d - q{X v-x 8 ] 0

):;?@% A doi: 10.6052/j.issn.1000-4750.2012.09.0666

IMPLEMENTATION, VERIFICATION AND APPLICATION OF THREEDIMENSIONAL HISS MODEL IN ABAQUS

WANG Ming-qiang 1 , YANG Jun 1,2

(1. Department of Civil Engineering, Tsinghua University, Beijing 100084, China;

2. Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry, Beijing 100084, China)

Abstract: The yield surface of a hierarchical single surface (HISS) model is a single smooth function, whichovercomes the singularity of the so-called cap model. The HISS 1d model with non-associated flow rule and

isotropic hardening was introduced, and the influence of main parameters on the yield surface was alsoinvestigated. Tests on one Gauss Point were produced by MATLAB, and the stress path and yield surface weremeasured during a loading process. Based on the further development platform provided by ABAQUS, the HISSmodel was programmed into a three dimensional user-material subroutine (UMAT). Four kinds of triaxial tests(HC, CTC, TC and TE) of Leighton Buzzard sand were simulated by ABAQUS with the developed model. Thestress-strain relationship and volumetric change obtained by ABAQUS were compared with experiments results.The numerical predictions showed a good agreement with the observed behaviours in experiments, which provedthe applicability of a HISS model to sands. The model was used to simulate the plate loading test of a layered road

bed. The three dimensional implementation of an HISS model in ABAQUS provides the commercial FEM codewith a new optional constitutive law for the elasto-plastic problems in soil mechanics.Key words: HISS model; ABAQUS; three dimensional UMAT; triaxial tests; layered road bed

f%& 9 BC {|~ a Mohr-Coulomb $

Drucker-Prager ~G D 7 EF z ~ GHIJKK f p [ L LM G MNO =>?@ PQ G EF

z ~ " R j a > D\_ STU a 0 ; > DpS VW G /X v 9 'X aYZ *E z YZ j [ 0P\] p W;^ G _`a< !i _ b }G ~ L


2/7

# $ % & 161

VW cd 0 T {| 5 Drucker [1]e eGHfgIJ fpD 3 {|} \6!/ Mohr-Coulomb hijk

i _ l V"P*+,-5 NOE P*+,- m?j [e ) no ~G } pqr ~ $ Sandler ~

5 Es *+,- ~ tGHIJ f p/ uK vw V xy \ % z{ pS VW;^|GIJ /QK vw V xy \ % z{ pS #};^ G M !*+,- ~{|} ~ !a F P C o P } !"

G / Es } # kl ? k $ B0 % " G 0 G %" & > > D=> $ B GS _ 0 G % " ' e > D\_j [ $ B G /& &> | ( 0 H 12 G ) I *+l , 5 Desai [2

F 3]e e )"z xyz{|} (HISS) ~G tGIJxW - GIJx# G _` {|} ! z"#$ G{|} ( A t ? k $ B ~ ! % " Gn1 '()*+,- ~ ./ & & 012345

ABAQUS [4]!" ./ G [; 0 `abc $ ?#$~ x 0 w G 1 P 2 '( S 3 K Wz k D x

7* 4567 D : k D ~ x 8 Az345 19 ef) ; : Os, $ dw _B < ghijkl5H9Os 6e ; tu, $ d UMAT S !ef < Ose ; 6 = tu > D ghijw _ 5 UMAT D\_j [ G @ 7 YSTV O:;?@ ABCDEF 1 ~ 5 Desai [7

F 8]e e

HISS ~ {| %& < , 2

0.52 1 12

a aa

(1 )n

r J I I

F S P P P

a g b - = - - + -

(1)

Z 9 , 2 / 2ij ji J s s= - 1 ii I s = - S r < \ % - G r S = 1.5

3 23 3 / 2 J J - G 3 / 3ij jk ki J s s s= - a 101kPa P = < [

W ; \ - ! " < 4 bJ& - n < 3 _J& - # D\_1/2(d d ) p pij ijx e e = - ^_ x : 1/2(d d ) p p D ij ije ex = -

pS x : 1/2(d d / 3) p pkk iix e e = 5 ST :;


3/7

162 # $ % &

4 bJ& ! < ILM 4 b {|} xy G 3 _J& n < ILM xW m x# z{ t |} G F C |~G LM {|} ; } G ks 3 wu 5

0 50 100 150 200 250 3000

10

20

30

40

50

60

70

80

q

/ k P a

p / kPa

2.5, 0.102n g = = 3.0, 0.102n g = =4.0, 0.102n g = = 2.5, 0.08n g = =

2.5, 0.05n g = =

s 3 / p-q k } q ! $ n K {|} LM

Fig.3 Influences of parameter ! and n on F in p-q space

2 MNOPQ7R

~ \_ C: D\_ C: $ ,

d d de pij ij ije e e = + (4)= D\ % C: m \_ C: ; h ! H e "

' e, d de eij ijkl kl s e = C (5)

g # =>?@ ,

d pijij

Qe ls =

(6)

" # D vw ,

d d d d 0ij Dij D

F F F F s x x

s x x

= + + =

(7)

( Z (4)~ Z (7)< $ K ' P) ,

deijkl ijkl ij

e pqrs Q QD

pq rs D

F

F Q F F

e s

lg g

s s x x

= - -

C

C (8)

Z 9 , 1/21/2

;Q QDij ijij ij D D

Q QQ Qg g

s s s s

= =

)*=> D @A ; h, d depij ijkl kl s e = C (9)

Z 9 , e eijmn uvkl

ep e mn uvijkl ijkl

e pqrs Q QD

pq rs D

Q F

F Q F F

s s

g g s s x x

= -

- -

C C

C C

C

3 HISS &'+,ST-.

HISS ~ / ABAQUS 9 u ; = $ ks 45 1) > | = D IJ eC - 2) NO ABAQUS AB \_ C: d ie $= D

IJ > |X|\ % d dei is e = C - NO Z (2)> |EFJ& #-

3) NO? \ % EF %& V ' WG ( F ) 0G@


4/7

# $ % & 163

1 11 1T

( , )

{d }

n ni i

n

i

F

F

s ad

s s

- -- -= -

(10)

7 0 1 1i is s - -= G p,1 6

1 1( , ) 10n ni i F s a

- -- - ) G @ 8 < 5

6 ) 9 G :;56 G K )@ + 9 2 = D rx v \_ ,

1d d ( )[ ] dei i n in

e e d s - = - C (11)x < ( ) 9= \ % 1

nis - $ d ie > }" ? Z VW

ab \ % EF 1is - $ \_ C: d ie G */ 7)-

7) \ % C: 1 1dep

i i i is s e - -= +C G> |a ] > D\_ C: 1 di ix x x-= + G ( 1) d Di D i Dx x x-= + G Vix =

( 1) dV i V x x- + G> | ia G%&6( , ) 10 ?i i F s a

-) p,

! G> | epiC G */ 9)- @ @ */ 8)- 8) A \ %. g [10] G ' e is $

epi

C G */ 9)-

9) NO EF _ :i .\ % \_ EFJ&GH h > | ) I : G @ h C: + + B 5

4 UVWXYS)CDE*Z[

NO MATLAB no"P C$ $ d G K"PQRS xtx < TU D b #$ q{ # X v~ x G /VW[ $ 9Y E \ % ]^ j [$ {|}

_F5 VW 0 < QRS xt > }ab K G D b #

$ q{ # ab K x < < 89.6kPa $ 200kPa GYZVW[ $ \ % ]^ $ {|} _F FG k s 5~s 65

s 6~s 7 9 A B F t ! x < K\ G P 2H * A t 0 \ % EF X a p * ab {|}G \ %\_; h l ; DVW-. Ge; ) => D\ % -\_; hGv 2 )/VW[ $ 9 b IJK " # D vw 5

0 200 400 600 8000

50

100

150

200

250 \ % ]^VW + B= {|}VW[ $ 9 {|}ab {|}

q / k P a

p/kPa

s 5 D b # [ $ 9\ % ]^ $ {|} Fig.5 Stress path and yield surface during confined

compression

0 200 400 600 800 10000

50

100

150

200

250

q /

k a

p / kPa

VW + B= {|} VW[ $ 9 {|} ab {|}\ % ]^

A

B

s 6 q{ # [ $ 9\ % ]^ $ {|} Fig.6 Stress path and yield surface during triaxial

compression

0.000 0.001 0.002 0.003 0.004 0.0050

20

40

60

80

100

120

140

A

q /

k P a

B

1e {B\_ s 7 q{ # \ % \_ k

Fig.7 Stress-strain relationship of triaxial compression

5 +\]0*ST01

5.1 ^_+\]0*3`ab q{X v P 2 1 L IJ X MN % _ vr *

hi l [ $G tP B[ L X vG |P B \ % -\_; h X vG 1 P 2 ~ x0C # G G TU" s 0C\% ]^ X vG O z ! O q{X v \ % ]^ ks 8G j P ~ L X v (HC) !" q{ # X v

(CTC) q{ # X v (TC) $ q{ %& X v (TE) 5

s 8 O zq{X v \ % ]^ [11] Fig.8 Stress path of several triaxial tests

5.2 IJKLc]0defg NO ABAQUS vwOs, $ dK 4 zq{X

v TU fz c ~ x G abc ~ V O C3D8 z c5'( > | +, m Hashmi w A X v +, TUK - 5

q

TCTE

CTC

HC

3

1

O p


5/7

164

Hashmi [12] Leighton Buzzard

1

9 10

- ABAQUS

Hashmi

11 12 ABAQUS

-

13

14 ABAQUS

-

0

10

20

30

40

50

60

7080

90

100

0 0.001 0.002 0.003 0.004 0.005

p / k P a

HashmiAbaqus

1 9 -

Fig.9 Comparison of stress-strain relationship of HC test

v

1

10

Fig.10 Comparison of volumetric response of HC test

0( 34.5kPa)

0( 34.5kPa)

0( 89.6kPa)

1

o c t

/ k P a

0( 89.6kPa)

11 - Fig.11 Comparison of stress-strain relationship of CTC test

v

1

0( 34.5kPa)

0( 34.5kPa)

0( 89.6kPa)

0( 89.6kPa)

12

Fig.12 Comparison of volumetric response of CTC test

0( 89.6kPa)

0( 89.6kPa)

0( 137.8kPa)

0( 137.8kPa)

o c t

/ k P a

1

13 -

Fig.13 Comparison of stress-strain relationship of TC test

1

o c t

/ k P a

0( 137.8kPa)

0( 137.8kPa)

0( 89.6kPa)

0( 89.6kPa)

14 -

Fig.14 Comparison of stress-strain relationship of TE test

HISS

6

Praveen Aggarwal [13] Yamuna

700mm

700mm600mm 100mm 15


6/7

# $ % & 165

Yamuna y

L + U M

700

5 0 0

1 0 0

s 15 x 8 ] 0 W : X v~ s

Fig.15 Model of the plate loading test of layered road bed

Praveen Aggarwal @ [ fz c uv [ e ) F ztu ! & c G kl 25

F 2 Yamuna G2ndop*IJKL

Table 2 Material constants for Yamuna sand and WBMtu ! & Yamuna y L + U M

K c 133.3 197.7

% 0.25 0.32= D ! & N ( 0.986 0.922

! 0.06 0.09074 bJ&

" 0.739 0.7403 _J& n 2.9 2.9

a 1 0.03 0.02

$1 550.0 500.0

a 2 0.004 0.001EFJ&

$2 1.08 0.67

:;< a , ' 0.236 0.15

@ h ~ x ST ) f p = D ~ : \] K CV _ _ ; ;^ G V O Janbu [14] e e = D ~ : mK ^ / $ ? G _ ab = D ~ : ! ab K %& ,

3a

ac E K P P

s

=

(12)

Z 9 , E | +, muv +,./01 G a + [ u ) $d/ u i 349 P OD G C g |P H * / j a oztu > D 349 G Q O HISS "z ~ SP 2

45o ztu > D G P 2 klQ j o z ~ R 45 0Ctu > D m R J& jc $ & c > | ]n D5

- 0.06

- 0.05

- 0.04

- 0.03

- 0.02

- 0.01

00 100 200 300 400 500

o B | c / m

: W / kPa

Praveen Aggarwal uv c@ 7 > | c

s 16 VW 9 9 h l : W | c k

Fig.16 Load displacement curve of the center of the load plate

7 dq 67 X 8) xyz{|}~ GH < IJ&

KH {|} LM G ' P O ABAQUS ef Ostu, $ dghijkl G n n ) HISS ~ABAQUS qr, $ d G' K I z0C\ % ]^ q{X v TU& c ~ x G@ [ > | +, m X vu Z +, K -PQ 1 ~ Ky f D 345 6 OD5 @ 79 ( , $ dO` ~ x x 8 ] 0 k 9 W: X vG a+ [ u ), $ d/ u i 349 P OD $ H 45o ztu > D34 Wp D5

67ij qr, $ d/O ABAQUS ~ xq{ #$%& X v g K Gn1 U | ) tu [ L c GM 9 0 G > |\_j [)n ; FG G qr Da seQ5

rs!=%

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IMPLEMENTATION, VERIFICATION AND APPLICATION OF THREE DIMENSIONAL HISS MODEL IN ABAQUS.pdf