Multiscale Modelling Mateusz Sitko Faculty of Metals Engineering and Industrial Computer Science Department of Applied Computer Science and Modelling  Kraków 11-03-2014

Mateusz Sitko B5*607 msitko@agh.edu.pl consultation: Tuesday 13:00 – 14:00

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.

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)

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

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

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 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