Homogenization in Linear Elasticity

Bounding methods of moduli in linear elasticity is introduced using the energetic approach of linear elasticity. Using first classical minimum principles of potential and complementary energy, bounding of tensors of elasticity are bounded for a composite material. Then, polarisation tensors defined on an homogeneous body are introduced in order to take distribution of phases into account. Uniform and non uniform polarisation tensors are used for bounding particulate composite material, Hashin-Shtrickmann type bounds are obtained for isotropic materials, comments on self consistent scheme are made. Extensions to imperfect interfaces between phases for particulate composite material are proposed.