Simulated annealing and finite volume method to study the microstructure isotropy effect on the effective transport coefficient of a 2D unidirectional composite

Abstract

The application of the simulated annealing method (SA) is proposed to agitate a two-phase, two-dimensional (2D) material from a randomly aligned system in unidirectional bars to a randomized mono-dispersed system of particles of diameter D = 1. These theoretical microstructural conditions are analyzed to refer to natural or artificial aligned materials, for example, cellulose nanofibrils, biopolymers-based composites, ordered structure from polysaccharide hydrogel or ordered carbon nanotubes composites. The stages of the SA are selected post-process, to analyze the isotropy response and the effective transport coefficient (ETC). The mean squared deviation of the two-point correlation function of the horizontal axis respect to the vertical axis was proposed for the characterization of the microstructural isotropy. The ETC was determined by the finite volume method. The results show that the proposed methodology can be effectively used to quantify the effect of isotropy on the ETC. The results show two trends in the magnitude of ETC respect to the change in isotropy: a) when the surface fraction is higher than 50 %, ETC decreases linearly at the beginning and exponentially at the end of the change, small changes in isotropy in the particulate material they modify it drastically. b) When the surface fraction is less than 50 %, ETC decreases exponentially at the beginning, and linearly at the end of the change, indicating that small changes in isotropy in the bar-aligned material are drastically modified.