The existence of a symmetric stress tensor in a non-local description of continuum mechanics

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Among the foundations of continuum mechanics is the description of the constitutive forces in terms of a symmetric tensor. Noll showed that this is a consequence of the axiom of material frame indifference, what in turn means a local invariance of the system under the Euclidean group. Here we will prove, in order to obtain the same result, that the assumption of locality in this axiom is redundant. We model a non-local system by means of a virtual work principle. Under the global demand that the corresponding functional does not respond on rigid infinitesimal motions, we show the existence of a symmetric stress tensor as a local result.