Surface boundary conditions trigger flutter instability in non-associative elastic-plastic solids

Abstract

It is shown that surface flutter instability may be triggered by the simultaneous influence of non-associativity and boundary conditions even if, taken independently, neither the elastic-plastic constitutive law (satisfying deviatoric associativity) nor the boundary conditions (no applied traction rates) would lead to flutter. More specifically, it is shown that, for orthotropic elastic-plastic constitutive tensors with an orthotropy axis tangent to the rate-traction-free boundary, the onset of surface flutter instability coincides with the incipience of plasticity for any non-associative flow rule, whenever the normal to the boundary does not coincide with one of the other two orthotropy axes. In the case of deviatoric associativity and coaxiality between the directions of orthotropy and the normal and tangent to the rate-traction-free boundary, surface flutter instability may also occur, but only for unusual values of material parameters.Additional results and discussion are also presented for the onset of stationary surface waves in associative and non-associative elastic-plastic bodies. In contrast to the onset of surface flutter instabilities, the condition for the onset of stationary surface waves involves material properties only, that is, it does not discriminate among different orientations of the rate-traction-free boundary with respect to the material orthotropy directions.