presentation - Northeastern University

A CZM-based Macro-model for Progressive Collapse
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Analysis of Frame Structures
Tam Nguyen Nguyen, , Jerome Hajjar Hajjar, , Northeastern University
Junho Song, Derya Deniz Deniz, , University of Illinois at Urbana Urbana-Champaign Champaign
06/20/2012

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1. Background Progressive Collapse
2. Cohesive Zone Model
Content
3. CZM-based Macro-model
4. Summary

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Key elements of structural analysis and practice
� Collapse assessment of new and existing seismicresisting
systems: Incremental dynamic analysis
(IDA) for ATC-63 to access collapse prevention of
structural systems in seismic zone.
Incremental dynamic analysis (IDA) of a 5story
steel braced frame for 30 records by
Vamvatsikos and Cornell, 2002
An Integrated Platform for Validated Prediction of Collapse of Structures

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Key elements of structural analysis and practice
� Regional loss assessment to prevent large-scale
disaster: Fragility curve development for regional
loss assessment (Mid-America Earthquake
Center, MAEviz)
�� Collapse prevention in U.S building codes:
Structural integrity provisions in the wake of 9-
11, whereby it is difficult to ascertain the impact of
provisions because we have inadequate capacity as
a profession to model collapse
An Integrated Platform for Validated Prediction of Collapse of Structures

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Existing approaches for collapse modeling
Continuum FEM
� Indirect model fracture by “delete element”
� Khandelwal and El-Tawil (2007): shell elements + Gurson model
� Xu and Ellingwood (2011) brick elements + J2 plasticity
Khandelwal and El-Tawil (2007)
Xu and Ellingwood (2011)

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Existing approaches for collapse modeling
Macro-model FEM
� Fracture using spring elements / critical plastic strain -> “delete element”
� Kanvinde (2003), Rodgers and Mahin (2006), Lee and Foutch (2004)
� Khandelwal et al. (2008), Fu (2009), Szyniszewski (2012)
� Concentrated plasticity: Kaewkulchai and Williamson (2004)
spring model Khandelwal et al. (2008)
Rodgers and Mahin (2006)

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Existing approaches for collapse modeling
Applied Element Method (AEM)
� Elements are connected through nonlinear springs
� AEM: modeling crack initiation, propagation, fracture
� Meguro (2003), Meguro and Tegel-din (2006)
� Challenging to model ductile materials: e.g. Poisson’s ratio effect
Modeling of structure in AEM
AEM element separation
http://www.appliedelementmethod.org

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Existing approaches for collapse modeling
Adaptive shifted integration (ASI) method
� Isobe and Toi (2000), Natahira et al (2008)
� Physical equivalent of a linear Timoshenko beam and rigid bars
connected via rotational spring
� Proposed to shift the integration point in a beam element depending
on the stage of plasticity/facture to handle strong discontinuity in
progressive collapse analysis
Linear Timoshenko beam
and its physical equivalent
Natahira et al (2008)

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Scope of research
This research seeks “to create” effective and practical
computational formulations for collapse modeling of
steel structures
� CZM continuum model + CZM-based macro-model
formulations for structural collapse (Northeastern
Uni.)
� A stochastic framework to identify accurate collapse
limit states and critical damage measures via
incremental dynamic analysis (UIUC)

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Collapse of industrial structure
(Midwest Steel, Inc 2008)
Cohesive Zone Model
Collapse of structure vs. fracture failure using CZM: elements are
disassociated
CZM “has mainly been applied” to brittle materials in continua.
Limited CZM studies for ductile materials “on a structural scale”
Develop CZM-based macro-model
� Efficient
� Cyclic loadings
Fracture failure using Cohesive Zone Model
(CZM) approach (Zhang, 2003)

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Cohesive law
CZM schematics
Intrinsic model
Extrinsic model
Cohesive Zone Model
(Park, 2009)

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Cohesive Zone Model: ductile materials
Scheider and Brocks (2003), Tvergaardand Hutchinson (1992), Needleman, A. (1987)
Load Load-displacement displacement curve Cohesive law for loading
Fracture surface
Cohesive law for unloading

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CZM: PPR cohesive model
Based on potential, fracture energy, mixed-mode (Park et al, 2009)
Wide range of materials including brittle and ductile material
Parameters α, β control the slope, allow
model different materials
tension
shear

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PPR cohesive model implementation
Explicit time integration scheme (Abaqus explicit)
User element subroutine
� Virtual work
� Update displacement
� Update acceleration
� Update velocity
Mesh generation
� Meshing by Abaqus/CAE
� Insert cohesive elements into the mesh

CZM for ductile materials
�� Validate CZM for ductile material using coupon Test
�� CZM using PPR PPR model (Park, 2009) 2009) for mixed mode fracture
�� CZM elements are inserted in critical area
�� Preliminary Preliminary CZM result shows good agreement with experiment CZM elements
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(tests at UIUC)
Force (KN)
60
50
40
30
20
10
0
Buck elements
1/4" Test Number 1
experiment
analysis
0 10 20 30 40 50 60
Displacement (mm)
Simulation vs. Experiment
Exp

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CZM for progressive collapse (3D)
�� CZM using PPR PPR model (park, (park, 2009) for mixed mode fracture
�� CZM elements are inserted in critical areas
�� Abaqus explicit + user element
Park (2009)
PPR CZM model
Insert cohesive
elements
continuum elements
elements Khandelwal and El-Tawil (2007)

N
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A CZM-based macro-model
1 3 3 4 4 2
M
h
3 4
Fiber section
M
The beam element B34 can
be modeled in the same
manner as CZM in
continuum model
N
fiber
δ
Section
Fiber section will follow
modified plasticity model
The stiffness of the fiber
will be degraded (Damage
parameter K = K 0*D)

Modified Multi-surface Kinematic Hardening Plasticity
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K = K 0*D)
The multi-surface kinematic hardening plasticity model (Mroz 1967) is
modified for the fiber of the CZM-based macro-model to model cyclic
loadings, softening and fracture
n – line segments of constant tangent modulii: E 1, E 2, E 3,.., E n
f 0, f 1, f 2 ,…, f n are hyper-surfaces with constant hardening modulii. All surfaces
can translate in space without changing form and orientation
- Loading/unloading ���� cyclic

Modified Multi-surface Kinematic Hardening Plasticity
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Cantilever example
Applied load
Top displacement
(Danevit, Opensees) vs. (macro-model)
Elastic -plastic
Applied load
elastic

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Collapse modeling using CZM-based macro model
Kanvinde (2003):
Analyze using the proposed
CZM-based macro-model
2 3
1
Interface element
spring model
beam
4

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Progressive collapse
� Aim to develop a robust and efficient procedure
Cohesive Zone model
� Continuum mechanics
� Fracture modeling
CZM-based macro model
� Fiber-section, efficient
Summary
� Multi-surface kinematic hardening plasticity
� Cyclic and fracture