1. Multiscale Modelling Mateusz Sitko
Faculty of Metals Engineering and Industrial Computer Science Department of Applied Computer Science and Modelling  Kraków

2. Mateusz Sitko
B5*607
consultation:
Tuesday 13:00 – 14:00

3. Classes calendar nr Date Issues 1 4-03 Organizational class 2 11-03
Modification of cellular automata grain growth algorithm- inclusions (at the beginning/end of the simulation) 3
18-03
Modification of CA grain growth algorithm - influence of grain curvature 4
25-03
Modification of CA grain growth algorithm - substructures CA 5
1-04
Monte Carlo grain growth algorithm - algorithm modification (only cells on grain boundaries, ...) 6
8-04
Modification of MC grain growth algorithm - substructures CA, MC 7
15-04
MC static recrystallization – homogeneous nucleation -
22-04 8
29-04
MC static recrystallization algorithm - homogeneous energy distribution 9
6-05
MC static recrystallization algorithm - heterogeneous nucleation 10
13-05
MC static recrystallization algorithm - heterogeneous energy distribution 11
20-05
Morphology after deformation in Abaqus - energy interpolation 12
27-05
Using grid Infrastructure in static recrystallization simulation 13
3-06
Compare sequential and parallel static recrystallization algorithm computation time 14
10-06
Reports 15
17-06
Grading, Reports.

4. Final degree will be positive if each report gets min 3.0
2 reports:
1st – Grain growth algorithm modification (Cellular automata, Monte Carlo)
2nd – Monte Carlo static recrystallization algorithm + grid infrastructure
Final degree will be positive if each report gets min 3.0
2 unexcused absences (remainder – medical leave)

5. CA method
The main idea of the cellular automata technique is to divide a specific part of the material into one-, two-, or three-dimensional lattices of finite cells, where cells have clearly defined interaction rules between each other. Each cell in this space is called a cellular automaton, while the lattice of the cells is known as cellular automata space.
CA space - finite set of cells, where each cell is described by a set of internal variables describing the state of a cell.
Neighborhood – describes the closest neighbors of a particular cell. It can be in 1D, 2D and 3D space.
Transition rules - f, the state of each cell in the lattice is determined by the previous states of its neighbors and the cell itself by the f function
where
N(i) – neighbours of the ith cell, i – state of the ith cell

6. Simple Grain Growth CA algorithm
2 grains
Von Neumann neighborhood
Initial space
1st step
2nd step
last step

7. Boundary conditions
• absorbing boundary conditions – the state of cells located on the edges of the CA space are properly fixed with a specific state to absorb moving quantities.
• periodic boundary conditions – the CA neighborhood is properly defined and take into account cells located on subsequent edges of the CA space.

8. Inclusions
1. At the beginning of simulation (square diagonal d and circle with radius r).
2. After simulation (square with diagonal d and circle with radius r).
Initial space
1st step
2nd step
last step