Coupled Atomistic and Discrete Dislocation method
This presentation is the property of its rightful owner.
Sponsored Links
1 / 17

Peipei Li - Civil Engineering [email protected] PowerPoint PPT Presentation


  • 84 Views
  • Uploaded on
  • Presentation posted in: General

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

Download Presentation

Peipei Li - Civil Engineering [email protected]

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Peipei li civil engineering pl474 cornell

Coupled Atomistic and Discrete Dislocation method

(CADD)

Peipei Li - Civil Engineering [email protected]

ShuleHou- Civil Engineering [email protected]

JiaqiQu- Civil Engineering [email protected]


Topics

Topics

  • Background

  • What is CADD

  • Model of CADD

  • 1D Model

  • 1D Model Example

  • Implementation

  • How to run the code

  • Results


Background

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 large-scale 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

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

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 cadd1

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

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 model1

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

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 I-2, I-1, I.

  • The distance a between atoms is constant, the value is 1.


1d model example1

1D Model Example

  • Using MATLAB to solve this problem,

    [K]{d}={ f }

  • Ka: Stiffness of atoms part Kc: Stiffness of continuum part


1d model example2

1D Model Example

W A Curtin and Ronald E Miller

Atomistic/continuum coupling

in computational materials science

Our MATLAB solution


Implementation

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

How to run the code

Commands:

% cd ~/QC/GB-example

% Make QCCOMPILER=gnu

(gFortran compiler)

Finally, we need some tools to visualize the outputs. Here we used Tecplotto get the plots and even videos.

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.


Example

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)

    interplanarspacings.

  • 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

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

Results

  • Final mesh Final mesh in atom shape

  • Video


Thank you

Thank you !


  • Login