8.MASAT 20112-13 SmearedCrackModel MindlinShell

8/11/2019 8.MASAT 20112-13 SmearedCrackModel MindlinShell

1/19

SMEARED CRACK MODEL FOR MATERIAL

NONLINEAR ANALYSIS OF MINDLIN SHELLS

U n i v e r s i t y o f M i n h o

Department of Civil Engineering

Guimares, Portugal

[email protected] www.civil.uminho.pt


2/19

Lighter parts of the panel

Developed Lightweight SFRSCC panel

30 mm thick

Joaquim Barros

Modeling and Advanced Structural Analysis Techniques

University of Minho Department of Civil Engineering

Acess punching resistance

PasteTotal volume

(%)

CementCEM I 42.5R

(kg)

Limestonefiller

(kg)

Water

(dm3)

Super-plasticizer

*

(dm3)

Finesand

(kg)

Coarsesand

(kg)

Crushedaggregates

(kg)

0.34 364.28 312.24 93.67 6.94 108.59 723.96 669.28

T50 = 4.6 seconds; fcm= 52 MPa; Ecm= 31GPa


3/19

RESEARCH AIMS

Propose a model for simulating the behavior

of cement based laminar structures failing inbending and in shear

Use Reissner-Mindlin theory in the context of

Joaquim Barros



layered shell

Propose a strain-stress softening diagram forthe out-of-plane shear

Compare the proposed model withexperimental punching tests in SFRSCC panels


4/19

Numerical Model

Reissner-Mindlin theory was selected

damage due to crack formation andpropagation was simulated by discretizing the

Joaquim Barros



0

0

crco

mf mf mf

crco

s ss

D

D

=

For the case of cracked concrete theconstitutive law is:


5/19

Numerical Model

In-plane components

z

xy

x

x

Joaquim Barros



y

x x

y

y

yxxy


6/19

z

yz

xz

Numerical Model

Out-of-plane components

Joaquim Barros



y

xdistribuio real

distribuio aproximada

yz

xz

real distribution

approximatedistribution


7/19

Numerical Model

In-plane cracked concrete constitutive matrix

( ), ,1

, ,

ccrco co co co

mf e mf e mf e mf

T Tcrco cr cr r r

mf

c

eT T T T DD D D DD

= +

Joaquim Barros



x1

x2

t

Crack

n

cr

n

cr

t

cr

tcr

n w

s

0

0

crcr I

cr

II

DD

D

=

, 2

1 01 0

11

0 02

co cmf e

ED

=


8/19

Numerical Model

Crackconstitutive matrix

n1Dcr

ncr

n,1cr

n,2cr I

fG crcr =

,

cr

n p

Joaquim Barros



0

0

cr

I

cr

I

cr

IDD

D =

n,ucr

cr

D

Dcr

n2

n3

crnn,3crn,2

cr

n,3cr

nsecDcr

bl

1

cr

II cD G

=

1

,

1

pcr

n

cr

n u

=

,,

,2 2 ,

cr cr

n n p =

,1 1 ,

cr cr

n n u = ,2 2 ,cr cr

n n u = ,

cr

n u


9/19

Numerical Model

Out-of-plane

constitutive matrix

23

,sec

31

,sec

0

0

crco IIIs

III

DD

D

=

linear behaviorOP

OP

Joaquim Barros



p

Gc DIII,sec

GIII

f

lb

OP

max OP

OP

uOP

maxOP

p

max-OP

-OPu

-OPmax

-OPp

p-OPShear stress-strain

diagram


10/19

Inverse Analysis

Fracture mode I

8 node serendipityplane stress elements2 2 inte ration oints

8 node serendipityplane stress elements1 2 inte ration oints

(a)5

10

15

20

25

scatter of experimental results

experimental average results

numerical simulation

(b)

Load[kN]

Joaquim Barros



x

y

elastic behaviour

elastic-cracked behaviour

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0

Deflection[mm]

i i fG

Fracture parameters


11/19

Panels failing in bending

Model appraisal

Joaquim Barros




12/19

30

40

50

60

oad

[kN]

Joaquim Barros



0.0 0.5 1.0 1.5 2.0

0

10

20

Average Displacement [mm]


13/19

Panels failing in shear

150 150

150

150

300

300

Steel Plate

(100x100x10)

Q Q'

Panel Prototype

Joaquim Barros



SFRSCC

Steel Plate (100x100x10)

Actuator

150 150300(x300)

80

30

Q-Q'

Polystyrene

500

Test setup


14/19

Numerical Simulation

FEM Mesh

+

Point load

m

x2

Joaquim Barros



65

0mm

+

6 50 mm

T

hickness-111

0

x1

Line springs

T

hickness-310

m


15/19

Numerical SimulationRelationship between the force and the

deflection at the center of the test panel

50

60

Joaquim Barros



0

10

20

30

40

0 2 4 6 8 10

Displacement (mm)

Force(kN

)

SFRSCC - experimental

SFRSCC - linear out-of-plane shear

SFRSCC - softening out-of-plane shear

Plain concrete


16/19

Numerical Simulation

Vertical displacement field

Joaquim Barros



Punching critical contour


17/19

Conclusions

A softening diagram was proposed to model,

after crack initiation, both out-of-plane shearstress-strain constitutive laws

Joaquim Barros



The developed model is based on FEM and wasimplemented in the FEMIXcomputer program.

A very good agreement between theexperimental results and the proposed modelis observed.


18/19


19/19

19

Joaquim Barros



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8.MASAT 20112-13 SmearedCrackModel MindlinShell