THE APPLICATION OF THE UNIFIED HOMOGENEOUS PERIODICAL BOUNDARY CONDITIONS TO THE PREDICTION OF EFFECTIVE ELASTIC STIFFNESS IN A WIDESPREAD FIELD

Periodical boundary conditions (PBC) are important for the prediction of effective elastic stiffness of composites by applying the macro-microscopic asymptotic expansion homogenization method (HM). In this paper, two kinds of homogeneous periodical boundary conditions are proposed to satisfy the improved expression for the homogenized effective stiffness with the homogeneous characteristic function, and one is the relaxed periodical boundary condition, and the other is a precise polynomial derived from the first one. A typical example of the off-axis short-fiber reinforced composites is analyzed by the described procedure. The results show that the periodical boundary condition is not unique, and the relaxed periodic boundary condition is the simplest and most convenient method to guarantee periodical displacement and anti-periodical traction boundary conditions simultaneously in a widespread field with a unified form.