Random Tessellation and It's Application at Mechanics of Microstructures

The concept of random tessellation is extensively used in wide area of natural sciences, especially material sciences. In this paper a simple but complete explanation of the random tessellation and mathematical tools requirements is presented. Then introducing the algorithm and the program for display random tessellation diagram was written. This program, with high speed and simple algorithm for random tessellation has the ability to change the level of statistical parameters such as number, mean, variance of the area of the grain. The ability to model microstructures of metals and grains for mechanical application, such as estimation of mechanical properties and crack propagation model at microstructure scale in FEM software is very important. More, an application of random tessellation for finding of equivalent mechanical properties was mentioned. In this paper by increasing the number of grains, in other words, decreasing the size of the grain, property’s values were changed and approached to the experimental global values and isotropic properties.