Transcript and came the rains

Coupled Atomistic and
Discrete Dislocation method
(CADD)
Peipei Li - Civil Engineering [email protected]
Shule Hou - Civil Engineering [email protected]
Jiaqi Qu - Civil Engineering [email protected]
Topics
 Background
 What is CADD
 Model of CADD
 1D Model
 1D Model Example
 Implementation
 How to run the code
 Results
Background
• Some phenomena (dislocation nucleation, cross-slip,
crack formation and growth) involving plastic
deformation and fracture of ductile materials are
intrinsically atomistic.
• Atomistic studies are usually unable to address largescale deformation except with supercomputers.
• So multi-scale methods are introduced in which certain
key regions are modeled atomistically while most of the
domain is treated with an approximate continuum
model(such as FEM) and able to reduce computational
cost.
What is CADD
• Coupled atomistic and discrete dislocation
method(CADD)
• CADD is one of the multi-scale methods.
• CADD minimizes the number of atoms and replaces
atomic degrees of freedom by continuum DOFS
describing the continuum elastic displacements and the
dislocation lines with little or no loss of accuracy.
Model of CADD
• Ⅰ: contain all the
singularities and
discontinuities
(Discrete dislocation)
• Ⅱ: smooth,
continuous and
ideally suited to FE
(Linear elastic body
bvp)
• Ⅲ: atomistic region
Model of CADD
• Pad:
• Passing of dislocations
• Ensure that real atoms
at and near the interface
are properly coordinated
• Mitigate the effect of the
free surface that would
be created on the
atomistic region during
the cutting process
1D Model
• The total potential energy of CADD:
• Where
is the energy functional for chain of atoms,
is the total continuum energy.
• Where k1 is the stiffness for first-neighbour
interaction, k2 is the stiffness for second –neighbour
interactions.
1D Model
• The total potential energy of CADD:
• Where
is the energy functional for chain of atoms,
is the total continuum energy.
• Where kc is the effective stiffness for the element.
• For a proper value for kc in a state of uniform
deformation,
1D Model Example
• A chain of 101 atoms,
• The displacement of
atom 0 is fixed,
• A force f =1 applied to
atom 100,
• K1=1,K2=1,Kc=6,
• Interface I = 50,
• Considering inhomogeneous deformation, apply
additional force of magnitude f = 0.1 to atoms/nodes I2, I-1, I.
• The distance a between atoms is constant, the value
is 1.
1D Model Example
• Using MATLAB to solve this problem,
[K]{d}={ f }
Ka: Stiffness of atoms part
Kc: Stiffness of continuum part
1D Model Example
Point Force at Interface: FE solution
0.25
Strain
0.2
0.15
0.1
46
47
48
49
50
51
Atom/Node Number
52
53
54
W A Curtin and Ronald E Miller
Our MATLAB solution
Atomistic/continuum coupling
in computational materials science
Implementation
We get the code
package from
http://qcmethod.
org/
(This website serves
as a clearinghouse
for multi-scale
method-related
information.)
Unzipped the
package
Download the terminal
(Cygwin under windows)
How to run the code
Commands:
% cd ~/QC/GB-example
% Make QCCOMPILER=gnu
(gFortran compiler)
After compile, we'll get
executable—gb.
Use commands
% cd ~/QC/GB-example/Shear
%../gb<gb_shear.in>gb_shear.out
Run gb, we’ll get outputs.
Finally, we need some
tools to visualize the
outputs. Here we used
Tecplot to get the plots
and even videos.
Example
• This example builds an Al bi-crystal consisting of two
face-centered cubic (fcc) crystals separated by a (111)
twin plane.
• The twin plan has a step,
the height of which is
equal to three (111)
interplanar spacings.
• The bi-crystal is subjected
to an increasing uniform
shear which causes the
twin boundary to migrate
in the direction perpendicular
to the twin plane.
Code: FEM part
• The example presented here uses three-node linear elements with
one Gauss point at the centroid of each element. The iso-parametric
formulation is used.
• A utility routine that can be used
by the user_mesh routine to generate
regular or symmetric meshes.
• Eg. Set SymmetricMesh=.true, We get
the finite mesh for the continuum
region as:
The element, local node numbering and shape functions
Results
• Final mesh
• Video
Final mesh in atom shape
Thank you !