Locality and continuity in constitutive theory (Q1115665)

The author studies some different axioms concerning locality properties of constitutive equations: the principle of determinism, the principle of local action and the definition of materials of grade n. From the principle of determinism stated for the resultant force and from the consistency of the resultant force of any subbody with Cauchy's stress condition follows the principle of local action. Further it is proved that the material is of grade n if the body has a limited memory and if the stress depends continuously on the motion. Finally it is shown that the constitutive relation for the stress is continuous with respect to the first n derivatives of the deformation and that it varies also continuously with the material point.