multiscale modelling mateusz sitko faculty of metals engineering and industrial computer science...
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Multiscale Modelling
Mateusz Sitko
Faculty of Metals Engineering and Industrial Computer ScienceDepartment of Applied Computer Science and Modelling
Kraków 11-03-2014
Classes calendar
nr Date Issues1 4-03 Organizational class
2 11-03Modification 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 curvature4 25-03 Modification of CA grain growth algorithm - substructures CA
5 1-04Monte Carlo grain growth algorithm - algorithm modification (only cells on grain boundaries, ...)
6 8-04 Modification of MC grain growth algorithm - substructures CA, MC7 15-04 MC static recrystallization – homogeneous nucleation- 22-04 -8 29-04 MC static recrystallization algorithm - homogeneous energy distribution9 6-05 MC static recrystallization algorithm - heterogeneous nucleation
10 13-05 MC static recrystallization algorithm - heterogeneous energy distribution11 20-05 Morphology after deformation in Abaqus - energy interpolation12 27-05 Using grid Infrastructure in static recrystallization simulation13 3-06 Compare sequential and parallel static recrystallization algorithm computation time14 10-06 Reports15 17-06 Grading, Reports.
• 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)
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
1t ti jf j N iwhere
N(i) – neighbours of the ith cell, i – state of the ith cell
CA method
Simple Grain Growth CA algorithm
Initial space 1st step 2nd step last step
2 grainsVon Neumann neighborhood
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.
Inclusions
Initial space 1st step 2nd step last step
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).