Mathematical modeling of composite materials leads to the solving PDEs with strongly oscillating coefficients. The problem of large number of equations can be solved using homogenization, that replaces heterogeneous material by an ‘equivalent‘ homogeneous one. This approach assumes periodic structure, which is not often true in reality. The first aim of the paper is to compare results obtained by solving the model problem describing the torsion of a bar applied to the random medium and the periodic one, respectively. The second aim is to present four algorithms generating samples of random structures of a two-component fibre composite material similar to the real one. and Obsahuje seznam literatury
Mathematical modeling of fibre composite materials is very difficult because of their random values of the coefficient describing mechanical properties of their separate phases. For the computational reasons, the real materials, i.e. materials with non-periodic structure are replaced by ‘equivalent‘ structures having almost the same mechanical properties. To the implementation of this, the various algorithms were developed for generating an ‘equivalent‘ structures, which will be similar to the real one as much as possible. Therefore some simple methodology for a statistical comparing of different structures developed by different algorithms is needed. and Obsahuje seznam literatury