Mechanics of Periodically Heterogeneous Structures

An exact solution for micromechanical analysis of periodically layered composites

“…The expressions of effective material properties c * ij are listed here. These results reproduce those of the mathematical homogenization theory in Manevitch et al (2002). When both layers are made of isotropic material, having Lamé properties 1 , 1 for the bottom layer and 2 , 2 for the top layer, the formulas in Eq.…”

“…Backus (1962) considered isotropic or transversely isotropic layered inhomogeneous medium using an averaging technique. Layered composites made of two alternating orthotropic layers were studied using the mathematical homogenization theory (Bensoussan et al, 1978) in Manevitch et al (2002). An authoritative treatment on layered composites was given in Chapter 9 of Milton (2002).…”

Higher order asymptotic homogenization and wave propagation in periodic composite materials

“…Further, application of the volume-integral homogenizing operator provides a link from the micro-to macroscopic behaviour of the material and allows the evaluation of effective properties. Theoretical foundations of the method have been developed by Bakhvalov (1974), Babuska (1976), Bensoussan et al (1978), Sánchez-Palencia (1980) and Bakhvalov & Panasenko (1989); a number of recent applications can be found in the works of Meguid & Kalamkarov (1993), Parton & Kudryavtsev (1993), Jikov et al (1994), Kalamkarov & Kolpakov (1997), Boutin et al (1998), Boutin (2000), Rodríguez-Ramos et al (2001), Andrianov et al (2002aAndrianov et al ( ,b, 2005Andrianov et al ( , 2007a, Manevitch et al (2002), Miehe et al (2002), Périn (2004), Berdichevsky (2005), Berger et al (2005), Guinovart-Díaz et al (2005), Kamiński (2005), Parnell & Abrahams (2006) and Santos et al (2006).…”

Influence of microstructures on temperature distributions for some mixed problem of composite half-space

“…For these reasons it seems to be useful to apply homogenized (approximated) models. These models were derived by the use averaging procedures: the classical asymptotic homogenization [1][2][3][8][9][10]18], on the mixture theory [4]. on some physical assumptions [6], on matrix methods [5], the tolerance averaged procedures [7,19] and the nonasymptotic methods connected with the nonstandard analysis, resulted in the so-called homogenized model with microlocal parameters [11,12,20].…”