Transcript CC2013 (FBX_LM_BAI) - Workspace
Slide 1
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
Department of Civil & Environmental Engineering, Imperial College London
Project Funding
Slide 2
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
Slide 3
Numerical Analysis of Masonry Panels
Bed Joint
Brick Unit
Head Joint
Slide 4
Numerical Analysis of Masonry Panels
a) Micro-Model
b) Simplified Micro-Model –
Mesoscale Model
Increasing
Computational
Expense
c) Homogenised Macro-Model
Slide 5
Mesoscale Modelling
20-Noded Solid
Element
Elastic Material
•Brick Units
•Brick-Mortar Interfaces
•“Brick-Brick” Interfaces
16-Noded Interface
Element
Material Nonlinearity,
Mix-Mode Cohesive
Cracking, Crushing,
Damage
Slide 6
Mesoscale Modelling - Drawback
Brick Mortar Interaction Leading to Unit Cracking
e.g.: Masonry Prism – Uniform Compression
Tension
assuming Eb > Em
Compression
Slide 7
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:
z k z
0
0 z
Approximate
Solution
0 x
x 0 k x
0
0 k y y
y
at Interface Material Level
Tension & Shear
x y
2
2
“Crushing” Failure Surface
No Lateral Tension Develops in the Units
z
Slide 8
Enhanced Mesoscale Modelling
Brick-Mortar Interaction
a) Micro-Model
- Typically Captured with Refined
Micro-Models
Modified Interface
Element Kinematics
b) Simplified Micro-Model –
Mesoscale Model
Slide 9
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
Slide 10
Enhanced Mesoscale Modelling
•
Assuming displacements inside the mortar layer as linear
function of top and bottom surfaces:
u ( x, y, z )
1
(u u )
2
•
(u u )
h
A representative average strain vector is obtained as:
h
av
1
h
h
2
dz
h
1
h
2
•
z
2
Lu ( x, y, z )dz
h
2
Introducing a further simplification with regards to shear
strain definition in the x-z and z-y planes:
xz
'
u x
z
; yz
'
u y
z
Slide 11
Enhanced Mesoscale Modelling
•
Assuming displacements inside the mortar layer as linear
function of top and bottom surfaces:
u ( x, y, z )
1
(u u )
2
•
(u u )
h
A representative average strain vector is obtained as:
h
av
1
h
h
2
dz
h
1
h
2
2
•
z
Lu ( x, y, z )dz
h
2
Assemble matrix L as:
x
L 0
0
0
y
0
0
0
z
z
0
0
0
z
0
y
x
0
T
Slide 12
Enhanced Mesoscale Modelling
The strain vector for the enhanced interface
element yields:
x
y
z
'
xz
'
yz
xy av
1 (u x u x )
2
x
1 (u y u y )
2
y
uz uz
h
ux ux
h
uy uy
h
1 (u u ) 1 (u u )
y
y
x
x
x
2
y
2
Considering the conjugate
stress vector:
Average of top and bottom surface
T
engineering
av x strain
y z xz yz xy
The local elastic constitutive
relationship is:
av D av
z
1with:
x
Av
0
0
0
A (1 v ) h A v
Av
A(1 y v)
Av
0
0
0
Av
Av
A (1 v )
0
0
0
Typical Interface displacement
D
0
0
0
Gx
0
0
discontinuities
uniformly smeared over the
0
0
0
0
Gy
0
height of the mortar layer
(1
2
v
)
0
0
0
0
0
A
2
Slide 13
Enhanced Mesoscale Modelling
3D Constitutive matrix:
A (1 v )
Av
Av
D
0
0
0
A
Av
Av
0
0
A (1 v )
Av
0
0
Av
A (1 v )
0
0
0
0
Gx
0
0
0
0
Gy
0
0
0
0
E
(1 v )(1 2 v )
Coupling between interface opening
and normal strains at mid-surface
Interface stiffness to sliding
In-plane shear stiffness
at mid-surface
0
0
0
0
(1 2 v )
A
2
0
Directly obtained with shear test
Slide 14
Enhanced Mesoscale Modelling
Co-rotational Framework
•Large Displacements
Out-of-Plane Response under
Extreme Loading
Slide 15
Enhanced Mesoscale Modelling
Comparison between full continuum and enhanced
interface elastic response at detailed level
Mortar joints
detailed with solid
FE
Masonry prism under uniform compression
Symmetry Boundary
Conditions
•10 mm thick mortar joints
•250x120x55 mm3 units
•Eb>Em
Mortar joints lumped into
zero-thickness enhanced
interfaces
Slide 16
Enhanced Mesoscale Modelling
•Lateral Tensile Stresses in Brick Units
Full Continuum
With Interfaces
Z
X
•Lateral Stresses
in Pattern
Mortar Joint
Similar
in Z-Y Plane
Importance of 3D Modelling
Continuum Mortar Joint
Good Match especially in
the region where tensile
cracks are expected to
develop
Interface Mortar Joint
Slide 17
Enhanced Mesoscale Modelling
Brick-Mortar
Interface
Enhanced Formulation
Full
Continuum
Detailed
with
Interfaces
Mesoscale a)
Symmetry Boundary
Conditions
Brick-Brick
Interface
Standard Formulation
Brick-Mortar
Interface
Brick-Brick
Interface
Slide 18
Enhanced Mesoscale Modelling
Full
Continuum
Detailed
with
Interfaces
Mesoscale a)
Mesoscale b)
Lateral tensile Stresses in the Brick Units
Mesoscale c)
Slide 19
Enhanced Mesoscale Modelling
Comparison in terms of global stiffness
Response obtained
with standard
interfaces
No lateral stresses
Computational Cost
DOFs
Full
Continuu
m
27951
Detailed Mesoscale Mesoscale Mesoscale
w/
a)
b)
c)
interfaces
23535
1440
2880
10560
Slide 20
Enhanced Mesoscale Modelling
Unreinforced Masonry Wall – Uniaxial Compression test
Mesoscale a)
•
Head and Bed mortar joints 10 mm thick
•
Mesocale Model a) – 1 solid element along the height
of brick units
•
Mesocale Model b) – 2 solid elements along the
•
height of brick units
Mesoscale b)
Symmetry Boundary Conditions
Head Mortar Joints Modelled with standard interfaces
Slide 21
Enhanced Mesoscale Modelling
Enhanced Mesoscacle
Elastic
12
Initiation of cohesive cracking in the
Mesoscale model
11
10
Compressive Stress (MPa)
9
Onset of cracking recorded experimentally
8
7
Experimental
6
5
4
3
2
Brick Cracking
Activated
1
0
0
2
4
6
8 10 12
Vertical Strain (x103)
14
Slide 22
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
Slide 23
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
Slide 24
Thank You!
Questions?
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
Department of Civil & Environmental Engineering, Imperial College London
Project Funding
Slide 2
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
Slide 3
Numerical Analysis of Masonry Panels
Bed Joint
Brick Unit
Head Joint
Slide 4
Numerical Analysis of Masonry Panels
a) Micro-Model
b) Simplified Micro-Model –
Mesoscale Model
Increasing
Computational
Expense
c) Homogenised Macro-Model
Slide 5
Mesoscale Modelling
20-Noded Solid
Element
Elastic Material
•Brick Units
•Brick-Mortar Interfaces
•“Brick-Brick” Interfaces
16-Noded Interface
Element
Material Nonlinearity,
Mix-Mode Cohesive
Cracking, Crushing,
Damage
Slide 6
Mesoscale Modelling - Drawback
Brick Mortar Interaction Leading to Unit Cracking
e.g.: Masonry Prism – Uniform Compression
Tension
assuming Eb > Em
Compression
Slide 7
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:
z k z
0
0 z
Approximate
Solution
0 x
x 0 k x
0
0 k y y
y
at Interface Material Level
Tension & Shear
x y
2
2
“Crushing” Failure Surface
No Lateral Tension Develops in the Units
z
Slide 8
Enhanced Mesoscale Modelling
Brick-Mortar Interaction
a) Micro-Model
- Typically Captured with Refined
Micro-Models
Modified Interface
Element Kinematics
b) Simplified Micro-Model –
Mesoscale Model
Slide 9
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
Slide 10
Enhanced Mesoscale Modelling
•
Assuming displacements inside the mortar layer as linear
function of top and bottom surfaces:
u ( x, y, z )
1
(u u )
2
•
(u u )
h
A representative average strain vector is obtained as:
h
av
1
h
h
2
dz
h
1
h
2
•
z
2
Lu ( x, y, z )dz
h
2
Introducing a further simplification with regards to shear
strain definition in the x-z and z-y planes:
xz
'
u x
z
; yz
'
u y
z
Slide 11
Enhanced Mesoscale Modelling
•
Assuming displacements inside the mortar layer as linear
function of top and bottom surfaces:
u ( x, y, z )
1
(u u )
2
•
(u u )
h
A representative average strain vector is obtained as:
h
av
1
h
h
2
dz
h
1
h
2
2
•
z
Lu ( x, y, z )dz
h
2
Assemble matrix L as:
x
L 0
0
0
y
0
0
0
z
z
0
0
0
z
0
y
x
0
T
Slide 12
Enhanced Mesoscale Modelling
The strain vector for the enhanced interface
element yields:
x
y
z
'
xz
'
yz
xy av
1 (u x u x )
2
x
1 (u y u y )
2
y
uz uz
h
ux ux
h
uy uy
h
1 (u u ) 1 (u u )
y
y
x
x
x
2
y
2
Considering the conjugate
stress vector:
Average of top and bottom surface
T
engineering
av x strain
y z xz yz xy
The local elastic constitutive
relationship is:
av D av
z
1with:
x
Av
0
0
0
A (1 v ) h A v
Av
A(1 y v)
Av
0
0
0
Av
Av
A (1 v )
0
0
0
Typical Interface displacement
D
0
0
0
Gx
0
0
discontinuities
uniformly smeared over the
0
0
0
0
Gy
0
height of the mortar layer
(1
2
v
)
0
0
0
0
0
A
2
Slide 13
Enhanced Mesoscale Modelling
3D Constitutive matrix:
A (1 v )
Av
Av
D
0
0
0
A
Av
Av
0
0
A (1 v )
Av
0
0
Av
A (1 v )
0
0
0
0
Gx
0
0
0
0
Gy
0
0
0
0
E
(1 v )(1 2 v )
Coupling between interface opening
and normal strains at mid-surface
Interface stiffness to sliding
In-plane shear stiffness
at mid-surface
0
0
0
0
(1 2 v )
A
2
0
Directly obtained with shear test
Slide 14
Enhanced Mesoscale Modelling
Co-rotational Framework
•Large Displacements
Out-of-Plane Response under
Extreme Loading
Slide 15
Enhanced Mesoscale Modelling
Comparison between full continuum and enhanced
interface elastic response at detailed level
Mortar joints
detailed with solid
FE
Masonry prism under uniform compression
Symmetry Boundary
Conditions
•10 mm thick mortar joints
•250x120x55 mm3 units
•Eb>Em
Mortar joints lumped into
zero-thickness enhanced
interfaces
Slide 16
Enhanced Mesoscale Modelling
•Lateral Tensile Stresses in Brick Units
Full Continuum
With Interfaces
Z
X
•Lateral Stresses
in Pattern
Mortar Joint
Similar
in Z-Y Plane
Importance of 3D Modelling
Continuum Mortar Joint
Good Match especially in
the region where tensile
cracks are expected to
develop
Interface Mortar Joint
Slide 17
Enhanced Mesoscale Modelling
Brick-Mortar
Interface
Enhanced Formulation
Full
Continuum
Detailed
with
Interfaces
Mesoscale a)
Symmetry Boundary
Conditions
Brick-Brick
Interface
Standard Formulation
Brick-Mortar
Interface
Brick-Brick
Interface
Slide 18
Enhanced Mesoscale Modelling
Full
Continuum
Detailed
with
Interfaces
Mesoscale a)
Mesoscale b)
Lateral tensile Stresses in the Brick Units
Mesoscale c)
Slide 19
Enhanced Mesoscale Modelling
Comparison in terms of global stiffness
Response obtained
with standard
interfaces
No lateral stresses
Computational Cost
DOFs
Full
Continuu
m
27951
Detailed Mesoscale Mesoscale Mesoscale
w/
a)
b)
c)
interfaces
23535
1440
2880
10560
Slide 20
Enhanced Mesoscale Modelling
Unreinforced Masonry Wall – Uniaxial Compression test
Mesoscale a)
•
Head and Bed mortar joints 10 mm thick
•
Mesocale Model a) – 1 solid element along the height
of brick units
•
Mesocale Model b) – 2 solid elements along the
•
height of brick units
Mesoscale b)
Symmetry Boundary Conditions
Head Mortar Joints Modelled with standard interfaces
Slide 21
Enhanced Mesoscale Modelling
Enhanced Mesoscacle
Elastic
12
Initiation of cohesive cracking in the
Mesoscale model
11
10
Compressive Stress (MPa)
9
Onset of cracking recorded experimentally
8
7
Experimental
6
5
4
3
2
Brick Cracking
Activated
1
0
0
2
4
6
8 10 12
Vertical Strain (x103)
14
Slide 22
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
Slide 23
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
Slide 24
Thank You!
Questions?