ORDER RELATIONSHIPS FOR BOUNDARY-CONDITIONS EFFECT IN HETEROGENEOUS BODIES SMALLER THAN THE REPRESENTATIVE VOLUME

Previous results by Huet [J. Mech. Phys. Solids 38, 813-841 (1990)] for heterogeneous elastic bodies smaller than the representative volume and submitted to static or kinematic uniform boundary conditions are partly extended to the case of mixed boundary conditions. Apparent elastic modulus and compliance tensors defined through the energetic procedure on a single specimen are considered. Through a variational approach, it is shown that each of them is bounded on one side. For cases fulfilling the Hill condition, these apparent modulus and compliance tensors are reciprocals. This provides two-sided bounds on each one. In this case, for a body smaller than the representative volume, the apparent elasticity tensor for mixed boundary conditions falls between the tensors associated with the static and kinematic uniform boundary conditions. Illustrating examples are studied. Various possible fields of application and other extensions are considered.