Viscoplastic stratified composites: shear flows and stability

The general formulation of the problem of stability with respect to low three-dimensional disturbances of some space flow of non-homogeneous medium with vector linear constitutive relations but scalar non-linear ones, are given. The main flow may be, in general, unsteady. Non-homogeneity is understood both by density and viscoplastic properties. A presence of rigid zones (“flow kernels”) is taken into account in general formulation; the conditions on surfaces of these zones are written. In cases when (a) kinematic boundary conditions are fixed on all surfaces and (b) rigid zones are absent (“hard wall” approximation), the integral relation method (IRM) is used and developed for obtaining sufficient estimates of disturbance decay or growth. These estimates involve physico-mechanical, rheological, and geometric parameters of non-disturbed flow.