“…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).…”