Interaction of a helical shell with a nonlinear viscous fluid

In recent years a significant progress in synthesis of metamaterials with perspective and unusual functional properties is observed. The properties of these metamaterials highly depend on their microstructure. In particular, helical shell structures have found various applications, for example in MEMS/NEMS, optics and medicine, see e.g. (Delclos et al., 2008, Ghosh and Fischer, 2009, Pendry, 2004). In Girchenko, Eremeyev, and Morozov (2011) we are taken into account the piezoelectric properties of helical shells. Here we analyze the interaction of the elastic helical shell with a non-Newtonian fluid. The interaction of the shell with the environment is highly important for engineering design, e.g. in medical applications when the shell operates in a fluid. The non-Newtonian fluid is assumed to be of pseudoplastic type.