A homogenization theory for elastic–viscoplastic materials with misaligned internal structures

In this study, a homogenization theory for non-linear time-dependent materials is rebuilt for periodic elastic–viscoplastic materials with misaligned internal structures, by employing a unit cell defined for the aligned structure as an analysis domain. For this, it is shown that the perturbed velocity fields in such materials possess periodicity in the directions of misaligned unit cell arrangement. This periodicity is used as a novel boundary condition for unit cell analysis to rebuild the homogenization theory. The resulting theory is able to deal with arbitrary misalignment using the same unit cell, avoiding not only geometry and mesh generation of a unit cell for every misalignment, but also the influence of mesh dependence. To verify the theory, an elastic–viscoplastic analysis of plain-woven glass fiber/epoxy laminates with misaligned internal structures is performed. It is shown that the misalignment of internal structures affects viscoplastic properties of the plain-woven laminates both macroscopically and microscopically.