Submacroscopic Disarrangements Induce a Unique, Additive and Universal Decomposition of Continuum Fluxes

Refinements of the geometrical settings employed to describe deformations of continuous bodies are widely known to lead to refinements in the fields that describe how parts of the body interact with each other and with the exterior of the body. These refined fields can be defined universally and the relations among them may be regarded as universal, in the sense that the definitions and their consequences do not rest on particular constitutive assumptions, i.e., are independent of the specific material comprising the body. In this article we show that the two terms \(w_{\backslash }\) and \(w_{d}\) appearing in a universal, additive decomposition of fluxes \(w\), previously studied in the field theory “elasticity with disarrangements,” are unique and may be described as the parts of \(w\) with and without disarrangements. The universal consistency relation satisfied by \(w_{\backslash }\) and \(w_{d}\) provides a field relation that connects geometrical changes at different length scales and, when supplemented by additional constitutive relations, permits the determination of the “disarrangement phases” available to a given material body.