A semi-analytical approach for the calculation of effective properties of elastic composite materials with imperfect interfaces
J.A. Mesejo-Chiong1; A.M. León-Mecías1; L.D. Pérez-Fernández2; J. Bravo-Castillero1
1 Facultad de Matemática y Computación, Universidad de La Habana; 2 Instituto de Física e Matemática, Universidade Federal de Pelotas
doi:10.20906/CPS/CILAMCE2017-0027
Resumo
This work provides details on a methodology combining the application of three well-known methods for the computation of the effective anisotropic elasticity tensor of matrix-inclusions composite materials provided with a periodic microstructure. Periodicity is the only assumption on the microstructure, which is regarded arbitrary for the number and shapes of the inclusions as well as the shape of the periodic cell. Also, we assume that the interfaces between the constitutive phases are imperfect, and that the mechanical behavior of the constituents is anisotropic. The methodology relies on the asymptotic homogenization method (AHM), the domain decomposition method (DDM) and the finite element method (FEM). The complex cell problems, resulting from the application of the AHM to the analysis of the composite material, are stated in an optimization-based domain decomposition framework that allows finding solutions by FEM. We prove the convergence of the employed domain decomposition framework. Examples of the application of the approach for fibrous composites with several phases, using the free code FreeFEM++, are presented. The benefits of the methodology have been already shown in the computation of the effective conductivity tensor of composite materials [1]. The approach can be easily extended to couple phenomena. [1] A.M. León-Mecías; J.A. Mesejo-Chiong; L.D. Pérez-Fernández and J. Bravo-Castillero1; Computation of the Effective Conductivity of Fibrous Composites with Imperfect Thermal Contact by Combination of Asymptotic Homogenization, Domain Decomposition and Finite Elements Methods, Defect and Diffusion Forum, Vol. 372, 2016, pp. 60-69.
Palavras-chave: Periodic composite materials; Anisotropic constituents; Imperfect interfaces; Arbitrary microstructure; Effective elasticity tensor; Asymptotic homogenization; Domain decomposition; Finite elements