homogenization

Dear All,



Could somebody indicate me some literature about the topic "2D
approximation of heterogeneous 3D media"?



In particular I am interested to address following issues:



1) Under which conditions averaging thermal conductivity and young
modulus (or more general, mechanical behaviour) on multiple 2D crossections of an heterogeneous "random"
material can be a good approximation for the behaviour of the real 3D
microstructure

In a piezoelectric material an applied uniform strain can induce an electric polarization (or vice-versa). Crystallographic considerations restrict this technologically important property to non-centrosymmetric systems. It can be shown both mathematically and physically, that a non-uniform strain can potentially break the inversion symmetry and induce polarization even in non-piezoelectric dielectrics.