A Study of Saint-Venant’s Principle for Composite Materials by Means of Internal Stress Fields

Abstract

It is well known that end effects in a composite material do not always decay as they do in a homogeneous and isotropic material, but there is no unified explanation for this difference. We note that the stress field in a composite material can be resolved into two kinds: one is the stress distribution in an isotropic and homogeneous reference system where Saint-Venant’s principle is satisfied and the other is the internal stress field induced by the incompatibility. Considering that the incompatibility is proportional to the difference between the elastic compliances of the components or to the deviation from isotropy, we propose, based on an argument concerning the dislocations associated with the incompatibility, a reason why end effects may survive to a long distance in a composite material.