Homogenization problems of a hollow cylinder made of elastic materials with discontinuous properties

In this paper, we present the homogenization of an anisotropic hollow layered tube with discontinuous elastic coefficients. We focus on some aspects of technological importance, such as the effective coefficients of anisotropic materials, the behavior of the homogenized displacements and stresses, the discontinuities of in-plane shear, hoop and longitudinal stresses, the homogenization-induced anisotropy in the isotropic case. We conclude that the problem of cylindrically anisotropic tubes under extension, torsion, shearing and pressuring is stable by homogenization and we define the effective tensor of the material elastic coefficients. Some numerical examples confirm the theoretical results.