Homogenization of a pressurized tube made of elastoplastic materials with discontinuous properties

In this paper we present the homogenization of a periodic multilayered pressurized tube made of very dissimilar elastoplastic materials. We focus on some aspects of technological importance, such as the effective properties, the behavior of the homogenized displacements and stresses, the discontinuities of hoop and longitudinal stresses, the homogenization-induced anisotropy. We conclude that the problem needs to be reformulated in order to be stable by homogenization and we define the effective elastic and incremental stress corrector matrices for the incremental stress–total strain matrix law. Finally, we present the numerical simulation for both the non-homogeneous and the homogenized material and two numerical examples confirming the theoretical results.