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)] fo r heterogeneous elastic bodies smaller than the representative volume and submitted to static or kinematic uniform boundary conditions are p artly extended to the case of mixed boundary conditions. Apparent elas tic modulus and compliance tensors defined through the energetic proce dure on a single specimen are considered. Through a variational approa ch, it is shown that each of them is bounded on one side. For cases fu lfilling the Hill condition, these apparent modulus and compliance ten sors are reciprocals. This provides two-sided bounds on each one. In t his case, for a body smaller than the representative volume, the appar ent elasticity tensor for mixed boundary conditions falls between the tensors associated with the static and kinematic uniform boundary cond itions. Illustrating examples are studied. Various possible fields of application and other extensions are considered.