Journal
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
Volume 63, Issue 6, Pages 1119-1141Publisher
SPRINGER INT PUBL AG
DOI: 10.1007/s00033-012-0197-9
Keywords
Contact interactions; Generalized continua; Principle of Virtual Powers; Contact K-forces; Hth order stress; Edge and wedge interactions; Transverse distributions; Boundary conditions for Nth order continua
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Navier-Cauchy format for Continuum Mechanics is based on the concept of contact interaction between sub-bodies of a given continuous body. In this paper, it is shown how-by means of the Principle of Virtual Powers-it is possible to generalize Cauchy representation formulas for contact interactions to the case of Nth gradient continua, that is, continua in which the deformation energy depends on the deformation Green-Saint-Venant tensor and all its N - 1 order gradients. In particular, in this paper, the explicit representation formulas to be used in Nth gradient continua to determine contact interactions as functions of the shape of Cauchy cuts are derived. It is therefore shown that (i) these interactions must include edge (i.e., concentrated on curves) and wedge (i.e., concentrated on points) interactions, and (ii) these interactions cannot reduce simply to forces: indeed, the concept of K-forces (generalizing similar concepts introduced by Rivlin, Mindlin, Green, and Germain) is fundamental and unavoidable in the theory of Nth gradient continua.
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