Asymptotic homogenization, domain decomposition and finite elements combined for calculating effective elastic properties of periodic fiber-reinforced composites with imperfect interfaces

Resumo

A methodology is presented for calculating the effective elastic properties of periodic multi-phase composites made of an anisotropic linear elastic matrix reinforced with a periodical distribution of unidirectional fibers and exhibiting spring-type imperfect contacts at the interfaces. The periodicity cell contains any finite number of parallel fibers and exhibits arbitrary cross-section. Fibers also exhibit arbitrary cross-sections and are made of a different anisotropic linear elastic material each. The methodology uses asymptotic homogenization (AH) to obtain the mathematical expressions of the effective properties and to formulate the so-called local problems on the periodicity cell on whose solutions the effective properties depend on. In order to deal with the discontinuities arising from the spring-type interfaces, the local problems are then restated via domain decomposition (DD) in a way allowing for an iterative resolution scheme in which the solution of the problem to be solve in each iteration is obtained via finite elements (FE). Results in the examples are obtained via a computational implementation of the methodology based on the FreeFEM open-source software, which allows for the variational formulation of the iteration problem to be dealt with directly.