A homogenization theory for elastic-viscoplastic composites with point symmetry of internal distributions

The homogenization theory for nonlinear time-dependent composites with periodic internal structures developed by the present authors is rebuilt on the assumption that constituents, stress and strain distribute point symmetrically with respect to the center of each unit cell in periodic composites. It is proved that this symmetry also allows the field of perturbed velocity to satisfy the symmetry with respect to the cell boundary facet centers. The symmetry is then used for imposing the boundary condition on perturbed velocity and for developing the theory in an integral form in which a half of the unit cell is taken as the domain of analysis. As applications of the theory, elastic-viscoplastic elongation of unidirectional composites is analyzed by assuming the square and hexagonal arrays of fibers subjected to either transverse or off-axial loading. It is thus shown that the point symmetry can be used for computing efficiently the inelastic behavior of nonlinear, periodic composites. (C) 2001 Elsevier Science Ltd. All rights reserved.