constitutive modelling of concrete in plasticity

7/26/2019 constitutive modelling of concrete in plasticity

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Presentation on

Constitutive Models for Concrete InPlasticity

DEPARTMENT OF APPLIED MECHANICS

GOVERNMENT COLLEGE OF ENGINEERING

AURANGABAD

2015-16

Presented By

Ansari Abu Usama

Guided By

Dr. M. G. Shaikh


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C!"#!"

Introduction

b$ectives

%iterature survey System Develo&ment

Performance Analysis

'eferences


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Introduction

Constitutive modelin( of concrete.

"heory of Plasticity

)ield criteria

*ardenin( rule+lo, rule


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b$ective

"o study the elasto&lastic behavior of concrete

under different loadin( conditions and to simulate

the same by com&utational model.


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%iterature surveyHan and Chen 1!"5#

In this ,ork- the five&arameter model of /illam/arnke- and

the four&arameter model of *sieh"in(Chen ,as ado&ted.

+or the /illam/arnke five&arameter model

In ,hich rc and rt are the com&ressive and tensile deviatoric

len(ths at the meridians 01 and 201 res&ectively and are related

to by


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,here- are material constants- and the constants satisfy the condition

+or the *sieh"in(Chen four&arameter model

,here a- b- c and d are material constants.


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+i(ure 3.3. )ield Surface and +ailure

Surface in the Model+i(ure 3.4. A non uniform

hardenin( &lasticity model


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*ere a DruckerPra(er ty&e of &lastic &otential function is assumed

,here 5 constant- 6 re&resents the &lastic dilatation factor

"he incremental elastic&lastic constitutive relation is (iven by

,here the &lastic stiffness tensor has the form

in ,hich


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+i(ure 3.7. Com&arison for com&ressioncom&ression loadin(s to

8u&fer9s data :8u&fer et al.- 4;2;< :a< Com&arison for unia=ial andbia=ial com&ressive loadin(s to 8u&fer9s data. :b< Com&arison for

bia=ial com&ressive loadin( to 8u&fer9s data


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+i(ure 3.>. Com&arison for com&ressiontension loadin(s to 8u&fer9s data

:8u&fer et al.- 4;2; Model res&onse under

unia=ial com&ression ,ith unloadin(

com&ared to e=&erimental results re&orted

by 8arsan and irsa.

Th(ee *)n' 7end)n, 'e'


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Th(ee-*)n' 7end)n, 'e'

"he material &arameters are #530 GPa J5 03

ft53.> MPa fc 5 3> MPa 50.00403? and As 5 3 and ' 53? mm and

m 5 4

+i(ure 3.3?-3.32 Geometry- loadin( setu& and finite element mesh for the three&oint bendin(

test. Com&arison of the analysis of the test on the fine mesh ,ith the e=&erimental bounds


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+i(ure 3.3@ Com&arison of the analyses of the three&oint bendin( test on three

different meshes

Author sho,s that the nonlocal dama(e&lastic model for concrete

can &rovide a mesh inde&endent descri&tion of various

combinations of tensile and com&ressive failure.

"o kee& the number of &arameters limited- only one scalar dama(e

variable ,as considered.

Va)) 8 Paan)4*a*. e' a 200%# &


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Va)) 8$ Paan)4*a*. e' a$200%# &

Aim to describe the stren(th and deformational behaviour of both

normal and hi(hstren(th concrete under multia=ial com&ression.

A three&arameter hydrostatic&ressure sensitive loadin( surface,as selected

"he hardenin( &arameter is define as

A softenin( function :c< is assumed to have follo,in( form


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A softenin( function :c< is assumed to have follo,in( form

Plastic &otential function taken here is


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+i(ure 3.3 Com&arison bet,een

analytical and e=&erimental results

:8u&fer et al.- 4;2;< for concrete under

unia=ial com&ression in both a=ial and

lateral directions

+i(ure 3.3; Com&arison bet,een

analytical and e=&erimental results

:8u&fer et al.- 4;2;< for normal concrete

under euibia=ial com&ression


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+i(ure 3.70 Com&arison bet,een analytical and e=&erimental results :Imran- 4;;>< for

normal concrete under tria=ial com&ression and various confinement levels

Author concluded that the model &erformance ,as evaluated a(ainst

e=&erimental results and it ,as verified that the ultimate stren(th-

deformation ca&acity and residual stren(th of confined concrete ,ere

&ro&erly ca&tured.

Model follo,s an o&en structure- allo,in( easy recalibration usin( selected

e=&erimental datasets

9)an, :. e' a 201;# &


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9)an, :. e' a$ 201;# &

In this study- a four&arameter yield function &ro&osed by *sieh

et al. :4;7< is ado&ted.

"he elasto&lastic dama(e constitutive euation can be ,ritten

as

"he material &arameter used for numerical simulation are fKc543.


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"he material &arameter used for numerical simulation arefc 43.

MPa- E532.@ GPa- 50.3?. "he &arameters a- b- c- and d, are

3.0002- 0.;4>- ;.4743- and 0.33430- res&ectively- and w54L402.

+i(ure 3.74 Stressstrain curves of unia=ial

tension :a< and com&ression :b< :unit MPa


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+i(ure 3.73 Dam system and monitorin( &oints

+i(ure 3.77 Ma=imum first &rinci&le

stress distribution of the slice of

dam

+i(ure 3.7> Dama(e factor contour ma& of the slice of dam usin( the dama(e model

&ro&osed in soft,are Abaus


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+i(ure 3.7? Com&arison of horiontal dis&lacement :a< and vertical dis&lacement :b 0.004@ O.

Similarly stress vector for the unia=ial com&ression case ,ere takenfrom the e=&eriment for lateral strain calculation is

5N0 3.00 2.0@>? ;.?3@ 43.7?@3 4?.477 4;.7>033.4@?? 37.@2@?O.

%ateral strain vector obtained as an out&ut of the &ro(ram is5 N 0 0.0704 0.02> 0.40@0 0.4>23 0.4;2@ 0.7>>> 0.?74>0.@;7O.


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+i(ure 7.7 !ormalied stress vEs

lon(itudinal strain curve for unia=ialcom&ression

+i(ure 7.> !ormalied stress vEs

lateral strain curve for unia=ial

com&ression

"able 7. 3. #=&erimental data and constants for Concrete A and B tested by


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%i(ea. N%ite,ka et al.:30033 43.20> 4>.3??

4?.2>20 [email protected]>2? 4.30@0O.

%on(itudinal strain vector obtained as an out&ut of the MA"%AB &ro(ram is

5N 0 0.0004 0.0003 0.0007 0.000? 0.0002 0.000@ 0.004

0.0042 0.0033O.

Constant Unit Concrete A Concrete B

MPa *#!! %!+!!

- !."# !."#

fc MPa -"&.# -+."&

A MPa- &.&%'"!(-% ".+&$'"!(-%

B MPa- %.%%'"!(-& .#*#"'"!(-&

C MPa-" -%.)&$'"!(-) -".&$*$'"!(-)

D MPa-" #.%%+'"!(-) ).!$&'"!(-)

Constant Unit Concrete A Concrete B

MPa *#!! %!+!!

- !."# !."#

fc MPa -"&.# -+."&

A MPa- &.&%'"!(-% ".+&$'"!(-%

B MPa- %.%%'"!(-& .#*#"'"!(-&

C MPa-" -%.)&$'"!(-) -".&$*$'"!(-)

D MPa-" #.%%+'"!(-) ).!$&'"!(-)

Stress vector for the Bia=ial com&ression case ,ere taken from thei f l l i l l i


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e=&eriment Nconcrete AO- for lateral strain calculation are

5N 0 3.4?2@ 7.@4>7 ?.4;30 @.7@ 40.>3>0 43.230@

4>.>4@; 42.0??> [email protected]?72 4.4@34O.

5N 0 4.447 7.4;?4 ?.4;30 @.@4 40.40>? 43.?00;4>.4@7 42.4>3 4@.@@3@ 4.3;4;O.

%ateral strain vectors obtained as an out&ut of the MA"%AB &ro(ramare

5N 0 0.03>4 0.0>33 0.0207 0.0;2 0.4>32 0.4;770.3>@; 0.7>;> 0.>@7? 0.24?3O.

5N 0 0.044? 0.077> 0.0?2; 0.0;4 0.47@> 0.3002 0.3;02

0.?>>@ 0.@2?? 0.272O.


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+i(ure 7.? !ormalied stress vEs lateral strain curve for bia=ial com&ression

+i(ure 7.2 !ormalied stress vEslon(itudinal strain curve for bia=ial

com&ression.

P f A l i


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Performance Analysis

"o validate the &erformance of the model em&loyed in the

MA"%AB- simulated results ,ere com&ared to the

e=&erimental and theoretical results.

Com&arison of the stress strain curves obtained bysimulation in MA"%AB for the s&ecimens of Grou& 4-

Grou& 3 and Grou& 7 ,ith the theoretical as ,ell as

e=&erimental results for concrete under unia=ial

com&ression is sho,n in +i(ure >.4- >.3 and >.7.


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+i(ure >.4. %on(itudinal and transverse

strain for Grou& 4 of the s&ecimen vEs

lon(itudinal com&ressive stress

+i(ure >.3. %on(itudinal and transverse

strain for Grou& 3 of the s&ecimen vEs



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"he above curves sho,s (ood a(reement ,ithe=&erimental and theoretical &rediction for the s&ecimens

under unia=ial com&ression

+i(ure >.7. %on(itudinal and transverse strain for Grou& 7 of the s&ecimen vEs


Com&arison of the stressstrain curves obtained by simulation in


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MA"%AB for bia=ial com&ression ,ith e=&erimental data for

Concrete A and Concrete B tested by %i(a and the relevant

theoretical results is sho,n in +i(ure >.> and >.?.

+i(ure >.>. Stressstrain curves for Concrete A sub$ected to bia=ial com&ression

a< k 5 Q3 E Q7 5 0.?- b< k 5 4.0

:b


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+i(ure >.?. Stressstrain curves for Concrete A sub$ected to bia=ial com&ression

a< k 5 Q3 E Q7 5 0- b< k 5 4.0

b:a

constitutive modelling of concrete in plasticity

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