It is well known that second-gradient continuum mechanical theories allow for the appearance of concentrated stresses along the edges of piecewise smooth material surfaces, but this is not the sole example of concentrated interaction. Two additional kinds of concentrated interaction are shown to take place in some second-gradient incompressible dissipative fluids: the adherence to one-dimensional immersed bodies and the capability of sustaining concentrated external body forces. These three phenomena turn out to be distinct and independent. This feature is explicitly discussed in two benchmark problems, and the different mathematical origins of each concentrated interaction are explained.
Giusteri, G. G., The multiple nature of concentrated interactions in second-gradient dissipative liquids, <<ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK>>, 2013; 64 (2): 371-380. [doi:10.1007/s00033-012-0229-5] [http://hdl.handle.net/10807/31331]
The multiple nature of concentrated interactions in second-gradient dissipative liquids
Giusteri, Giulio Giuseppe
2013
Abstract
It is well known that second-gradient continuum mechanical theories allow for the appearance of concentrated stresses along the edges of piecewise smooth material surfaces, but this is not the sole example of concentrated interaction. Two additional kinds of concentrated interaction are shown to take place in some second-gradient incompressible dissipative fluids: the adherence to one-dimensional immersed bodies and the capability of sustaining concentrated external body forces. These three phenomena turn out to be distinct and independent. This feature is explicitly discussed in two benchmark problems, and the different mathematical origins of each concentrated interaction are explained.
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