Effective Complex Properties for Three-Phase Elastic Fiber-Reinforced Composites with Different Unit Cells

Federico J Sabina,Reinaldo Rodríguez-Ramos,Raúl Guinovart-Díaz,Yoanh Espinosa-Almeyda,Héctor Camacho-Montes

doi:10.3390/technologies9010012

Abstract

The development of micromechanical models to predict the effective properties of multiphase composites is important for the design and optimization of new materials, as well as to improve our understanding about the structure–properties relationship. In this work, the two-scale asymptotic homogenization method (AHM) is implemented to calculate the out-of-plane effective complex-value properties of periodic three-phase elastic fiber-reinforced composites (FRCs) with parallelogram unit cells. Matrix and inclusions materials have complex-valued properties. Closed analytical expressions for the local problems and the out-of-plane shear effective coefficients are given. The solution of the homogenized local problems is found using potential theory. Numerical results are reported and comparisons with data reported in the literature are shown. Good agreements are obtained. In addition, the effects of fiber volume fractions and spatial fiber distribution on the complex effective elastic properties are analyzed. An analysis of the shear effective properties enhancement is also studied for three-phase FRCs.

Highlights

Multiphase elastic fiber-reinforced composites (FRCs) are still important in applications because their yields exceed those of their constituents and they offer very interesting properties compared to more conventional materials
The elastic effective properties of two-phase elastic FRCs with periodic square [11] and hexagonal [12] cells were found by applying the asymptotic homogenization method (AHM)
The main aim of this work is the estimation by AHM of the effective elastic complexvalues properties for periodic three-phase elastic FRC with complex-valued constituent properties and a parallelogram cell

Summary

Introduction

Multiphase elastic fiber-reinforced composites (FRCs) are still important in applications because their yields exceed those of their constituents and they offer very interesting properties compared to more conventional materials. The effective properties prediction for FRCs by means of micromechanical models and numerical approaches is a useful tool for technological innovation [4,5,6,7,8,9,10]. Periodic multiphase elastic FRCs have found applications related to transport problems (conductivity, shear elasticity, dielectric constant, thermal expansion, and others). In this sense, different micromechanical and experimental models have been developed to analyze elastic FRCs. For example, the elastic effective properties of two-phase elastic FRCs with periodic square [11] and hexagonal [12] cells were found by applying the asymptotic homogenization method (AHM).

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Conclusion