cc2013: analysis, modelling and design of masonry structures
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CC2013: Analysis, Modelling and Design of Masonry Structures. Mesoscale Modelling of Masonry Structures Accounting for Brick-Mortar Interaction. Francisco B. Xavier, Lorenzo Macorini, Bassam A. Izzuddin. Project Funding. Department of Civil & Environmental Engineering, Imperial College London. - PowerPoint PPT PresentationTRANSCRIPT
CC2013: Analysis, Modelling and Design of Masonry Structures
Francisco B. Xavier, Lorenzo Macorini, Bassam A. Izzuddin Project Funding
Mesoscale Modelling of Masonry Structures Accounting for Brick-Mortar Interaction
Department of Civil & Environmental Engineering, Imperial College London
Outline
Introduction
- Standard Mesoscacle Modelling
- Importance of Brick-Mortar Interaction
Enhanced Meoscale Modelling
- Interface FE Formulation
Verification Examples under Uniaxial Compression
- Elastic Analysis of Single Prism
- Crack Initiation on Masonry Wall
Closure
- Ongoing Work
Numerical Analysis of Masonry Panels
Brick Unit
Bed Joint
Head Joint
Numerical Analysis of Masonry Panels
a) Micro-Model
b) Simplified Micro-Model – Mesoscale Model
c) Homogenised Macro-Model
Increasing
Computational Expense
Mesoscale Modelling
20-Noded Solid Element
Elastic Material
16-Noded Interface Element
Material Nonlinearity, Mix-Mode Cohesive Cracking, Crushing, Damage
• Brick Units
• Brick-Mortar Interfaces
• “Brick-Brick” Interfaces
Brick Mortar Interaction Leading to Unit Cracking
Mesoscale Modelling - Drawback
e.g.: Masonry Prism – Uniform CompressionTension
Compressionassuming Eb > Em
Mesoscale Modelling - Drawback
Brick Mortar Interaction Leading to Unit Cracking
e.g.: Masonry Prism – Uniform Compression
assuming Eb > Em
However, with standard interface modelling there is no coupling between in-plane and normal deformations:
0 0
0 0
0 0
z z z
x x x
y y y
k
k
k
z
2 2x y Tension & Shear
“Crushing” Failure Surface
No Lateral Tension Develops in the Units
Approximate Solution at Interface Material Level
Enhanced Mesoscale Modelling
a) Micro-Model
b) Simplified Micro-Model – Mesoscale Model
Brick-Mortar Interaction
- Typically Captured with Refined Micro-Models
Modified Interface Element Kinematics
Enhanced Mesoscale Modelling
Considering interface finite elements representing an actual volume, in which one of the dimensions is considerable smaller than the other two – in this case the mortar joint thickness h
It is possible to introduce triaxial stresses and deformations into a zero-thickness interface, while maintaining its capabilities for cohesive crack modelling
Enhanced Mesoscale Modelling
1( , , ) ( ) ( )
2
zu x y z u u u u
h
• Assuming displacements inside the mortar layer as linear function of top and bottom surfaces:
• A representative average strain vector is obtained as:
2 2
2 2
1 1( , , )
h h
avh h
dz Lu x y z dzh h
• Introducing a further simplification with regards to shear strain definition in the x-z and z-y planes:
' '; yxxz yz
uu
z z
Enhanced Mesoscale Modelling
1( , , ) ( ) ( )
2
zu x y z u u u u
h
• Assuming displacements inside the mortar layer as linear function of top and bottom surfaces:
• A representative average strain vector is obtained as:
2 2
2 2
1 1( , , )
h h
avh h
dz Lu x y z dzh h
• Assemble matrix L as:
0 0 0
0 0 0
0 0 0 0 0
T
x z y
Ly z x
z
Enhanced Mesoscale Modelling
The strain vector for the enhanced interface element yields:
'
'
( )1
2
( )1
2
( ) ( )1 1
2 2
x x
y y
x
y z z
z
xz x x
yz
y yxy av
y y x x
u u
x
u u
y
u u
h
u u
h
u u
h
u u u u
x y
1z
x
y
h
Typical Interface displacement discontinuities uniformly smeared over the height of the mortar layer
Average of top and bottom surface engineering strain
Considering the conjugate stress vector:
T
av x y z xz yz xy
The local elastic constitutive relationship is:
av avD
with:
(1 ) 0 0 0
(1 ) 0 0 0
(1 ) 0 0 0
0 0 0 0 0
0 0 0 0 0
(1 2 )0 0 0 0 0
2
x
y
A v Av Av
Av A v Av
Av Av A vD G
G
vA
Enhanced Mesoscale Modelling
(1 ) 0 0 0
(1 ) 0 0 0
(1 ) 0 0 0
0 0 0 0 0
0 0 0 0 0
(1 2 )0 0 0 0 0
2
x
y
A v Av Av
Av A v Av
Av Av A vD G
G
vA
3D Constitutive matrix:
(1 )(1 2 )
EA
v v
Coupling between interface opening and normal strains at mid-surface
Interface stiffness to sliding
In-plane shear stiffness at mid-surface
Directly obtained with shear test
Enhanced Mesoscale Modelling
Co-rotational Framework
• Large Displacements
Out-of-Plane Response under Extreme Loading
Enhanced Mesoscale Modelling
Comparison between full continuum and enhanced interface elastic response at detailed level
Masonry prism under uniform compression
• 10 mm thick mortar joints• 250x120x55 mm3 units• Eb>Em
Mortar joints detailed with solid FE
Mortar joints lumped into zero-thickness enhanced interfaces
Symmetry Boundary Conditions
Enhanced Mesoscale Modelling
Full Continuum With Interfaces
• Lateral Tensile Stresses in Brick Units
• Lateral Stresses in Mortar Joint
Good Match especially in the region where tensile cracks are expected to develop
Continuum Mortar Joint Interface Mortar Joint
Z
X
Similar Pattern in Z-Y PlaneImportance of 3D Modelling
Enhanced Mesoscale Modelling
Full Continuum
Detailed with Interfaces
Symmetry Boundary Conditions
Brick-Brick Interface
Standard Formulation
Brick-Mortar Interface
Enhanced Formulation
Mesoscale a)
Brick-Brick InterfaceBrick-Mortar
Interface
Enhanced Mesoscale Modelling
Full Continuum
Detailed with Interfaces
Mesoscale b) Mesoscale c)
Lateral tensile Stresses in the Brick Units
Mesoscale a)
Enhanced Mesoscale Modelling
Comparison in terms of global stiffness
Response obtained with standard interfaces
No lateral stresses
Full Continuu
m
Detailed w/
interfaces
Mesoscale a)
Mesoscale b)
Mesoscale c)
DOFs 27951 23535 1440 2880 10560
Computational Cost
Enhanced Mesoscale Modelling
Unreinforced Masonry Wall – Uniaxial Compression test
• Head and Bed mortar joints 10 mm thick
Symmetry Boundary Conditions
Mesoscale a) Mesoscale b)
• Mesocale Model a) – 1 solid element along the height of brick units
• Mesocale Model b) – 2 solid elements along the height of brick units • Head Mortar Joints Modelled with standard
interfaces
Enhanced Mesoscale Modelling
Experimental
0 2 4 6 8 10 12 140
1
2
3
4
5
6
7
8
9
10
11
12
Vertical Strain (x103)
Com
pres
sive
Str
ess
(MP
a)
Enhanced Mesoscacle Elastic
Brick Cracking Activated
Onset of cracking recorded experimentally
Initiation of cohesive cracking in theMesoscale model
Closure
Further Improvements on the enhanced interface element:
• Adapt previous cohesive model (Macorini & Izzuddin, 2011) to accommodate new stress components in the new interface, i.e., allow mix-mode fracture (Tension & Shear) in brick-mortar interfaces (bed joints)
• Introduce failure surface at interface level, accounting for triaxial stress state in order to capture the actual failure of confined mortar material
• Non-linear response of masonry prisms by the knowledge of individual components properties, as opposed to composite properties dependent on the prism characteristics
Closure
• Despite mechanically sound, full potential of this enhanced mesoscale modelling strategy is only achieved if realistic material properties for both mortar and brick units are available
• Current published research underlines mortar material properties when part of a masonry assemblage or taken from single specimen to be markedly different
• There is the need to establish procedures to assess the actual mortar material properties, thus enabling the composite behaviour o masonry panels to be characterized by its individual constituents properties
Thank You!
Questions?