• Miranda, Hd
• Marques, At
• Pires, Fma

Abstract

An algorithm to generate random representative volume elements (RVE) of the microstructure of materials with a large number of circular inclusions of constant diameter is described. The type of problem that the algorithm addresses belongs to the class of sphere packing problems, with important industrial and academic applications. In fact, statistical mechanics of hard-sphere systems has generated considerable interest by the scientific community from Boltzman (1898) [20] to the Bernal (1959)[2] works on the model of the structure of liquids using random close packing (RCP), and many researchers have contributed to this subject. In this work, the general propose algorithm developed is able to generate models that define the internal structure of unidirectional fiber reinforced composites and other materials, but can also be used for other types of applications. The proposed algorithm has a linear complexity and it is based on a new and innovative geometric concept to distribute the inclusions. The computational efficiency of this algorithm was compared with the efficiency of other existing algorithm ([18]) revealing the advantages of the method. The generated models have been combined with finite element analysis of materials subjected to periodic boundary conditions and showed transversal isotropy of the material and good agreement with experimental results.

Topics

• impedance spectroscopy
• microstructure
• inclusion
• composite
• random
• finite element analysis
• statistical mechanics