Homogenization Method To Calculation Of Effective Properties For Periodic Composite Materials

In this paper, the macroscopic effective properties of composites with periodicity wereevaluated by the two-scale asymptotic homogenization method. And we can get to solve theeffective stiffness in accordance with a series of perturbation equations, which were deducedbased on the displacement expansion of the small parameter epsilon as well as the perturbationtheory combined with finite element theory.The eigen-displacement, which relates the material relationship between macroscopic andmicroscopic displacement, was introduced in the derivation process. On the basis of minimumpotential energy in linear elastic problems, thermal stress method to the eigen-displacement can beobtained via the further deduction of eigen-displacement. The thermal stress method to makeprediction of the mechanical properties of unidirectional fiber reinforced composite materials canbe realized by manipulating ABAQUS. In the research of the effective properties of thesecomposite materials, the effective stiffness coefficient of the representative volume element wascalculated by the thermal stress method and compared with the results of Mori-Tanaka Method andthe self-consistent method respectively to prove the feasibility of this method which predicts theelastic properties of the composite materials.Then, the thermal stress method was used to predict the effective mechanical properties ofSiC particles reinforced aluminum alloy composites, which were selected the two particle crosssection for circular and square unit cell model of the shape of the mental composite materials. Ofunit cell is discussed in terms of finite element mesh as well as single cell type of influence oncalculation of composite macroscopic effective performance. And in view of two types of the unitcell, both fiber elliptical cross section and fiber longitudinal trace of sine curve, whose effectiveperformance are investigated.Finally, the present work deals with the modeling of periodic composites made ofpiezoceramic (PZT) fibers embedded in a soft non-piezoelectric matrix (polymer). We especiallyfocus on predicting the effective coefficients of periodic transversely isotropic piezoelectric fibercomposites using representative volume element method (unit cell method). In this paper the focusis on square arrangements of cylindrical fibers in the composite. Two ways for calculating theeffective coefficients are presented, an analytical and a numerical approach. The analyticalsolution is based on the asymptotic homogenization method (AHM) and for the numerical approach the finite element method (FEM) is used. With the two introduced methods the effectivecoefficients were calculated for different fiber volume fractions, of which the results are comparedand discussed as well. Apart from this, the correlation between fiber volume fraction and effectiveperformance of the multiphase piezoelectric materials is explored by FEM in this dissertation.