An approximate homogenization scheme for nonperiodic materials (Q679258)

The author presents error bounds for Briane's homogenization approach to certain nonperiodic materials, and shows how this approach can be used to study particular defects in fibrous composites. This result requires that a uniform bound exists for the gradients of the periodic cell solutions in \( L^p\). In particular, when unexpected local spreading of the fibers occurs in a small region of the material, constituent stress concentrations can increase by almost a factor of three.