Lattice Discrete Particle Model LDPM for Fracture Dynamics and Rate Effect in Concrete

1
Lattice Discrete Particle Model (LDPM) for
Fracture Dynamics and Rate Effect in Concrete

• Gianluca Cusatis1 Andrea Mencarelli2 Daniele
  Pelessone3 James Baylot4
• 1 Rensselaer Polytechnic Institute, Troy, NY
  (USA)
• 2 Rensselaer Polytechnic Institute, Troy, NY
  (USA)
• 3 ES3, Solana Beach, CA (USA)
• 4 US Army ERDC, Vicksburg, MS (USA)
• Structures Congress
• Vancouver, Canada, April 24-26, 2006

2
Acknowledgements

• Andrea Mencarelli
• Daniele Pelessone
• James T. Baylot

3
Presentation Outline

• The Lattice Discrete Particle Model (LDPM)
• Uniaxial Compression on Prisms Fragmentation
  Simulations
• Hopkinson Bar Tests
• Future Outlook

4
Randomly Generated Aggregate Distribution and
Lattice of Connecting Struts
Concrete Properties (w/c, a/c, c, sieve curve)
Geometry of the Specimen
Random Procedure
3D Delaunay Triangulation
5
LDPM General Framework Topology

• A priori volume discretization is performed
  taking into account material heterogeneity at
  the length scale of interest
• Mesh size is associated with the characteristic
  size of the heterogeneity of the material
• For normal concrete mesoscale features are
  introduced through the granulometric distribution
  of coarse aggregates

6
LDPM Topology, Contd

• LDPM is formulated in a three-dimensional setting
• Delaunay triangulation provides volume
  subdivision into tetrahedra starting from
  aggregate centers
• A dual tessellation of the triangulated domain
  defines a set of discrete polyhedral cells
• The external triangular faces are the facets
  through which adjacent cells interact

7
LDPM General Framework Mechanics

• Stresses and strains are defined on a
  tessellation facets and so they are defined on a
  discrete number of orientations
• Stress and strain vectors are used instead of
  tensors
• Discrete compatibility equations (strain vs.
  displacements) are formulated through the
  relative displacements (and rotations) of
  adjacent nodes (particles)
• Discrete equilibrium equations are obtained
  through the equilibrium of each discrete cell

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LDPM Kinematics
Normal strain
Shear strains
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LDPM Vectorial Constitutive Law

• Softening behavior is only associated with
  tensile stresses
• Compressive behavior is always hardening
• Shear behavior simulates cohesion and friction
• The formulation involves a limited number of
  material parameters with clear physical meaning

n
m
l
3D triangular facet
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LDPM with Rate Effect
s
?
s0F(e)
1
s0
1
?
H0F(e)
H0
?
e0F(e)
e0
e
w0/l
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LDPM Elastic Domain with Strain rate
sT
increasing strain rate
shear frictional behavior
shear frictional behavior
Fssdyn
ss
shear cohesive behavior
shear cohesive behavior
-sc
st
F stdyn
sN
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Uniaxial Compression on Prisms Geometry
5163 particles 25188 tets
24 in
6 in
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Rate Effect on Uniaxial Compression
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Uniaxial Compression on PrismsAnimation
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Uniaxial Compression on PrismsFailure modes
Slow (3.310-5 sec-1)
Medium (3.310-3 sec-1)
Fast (210-2 sec-1)
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Example of Calibration and Validation Hopkinson
Bar Tests (Ispra)
mm
17
Parametric analysisHopkinson Bar Tests (Ispra)
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Parametric analysisHopkinson Bar Tests (Ispra)
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Hopkinson Bar Tests (Ispra) Animation
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Rate effect on concrete strenght
21
Blast Simulations
Thickness
Rebar spacing
t
p
charge
W
R
22
Pressures Histories Are Applied to Triangular
Facets
Pressures histories are computed on the impacted
surface using equations that account for charge
size, stand off, angle of reflection.
Kingery, C.N., and Bulmash, G. "Airblast
Parameters from TNT Spherical Air Burst and
Hemispherical Surface Burst, Technical Report
ARBRL-TR-02555, U.S. Army ARDC-BRL, Aberdeen
Proving Ground, MD, April 1984.
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Preliminary Results
Early time
Back face
Front face
Front face
Back face
Late time
24

• THANK YOU!