A study of lower-order strain gradient plasticity theories by the method of characteristics

The lower-order strain gradient plasticity theory retains the essential structure of classical plasticity theory, and does not seem to require additional, non-classical boundary conditions. We study the well-posedness of lower-order strain gradient plasticity theory by the method of characteristics for nonlinear partial differential equations. For Niordson and Hutchinsonʹs (2003) problem of an infinite layer in shear, we have obtained the “domain of determinacy” for Bassaniʹs (2001) lower-order strain gradient plasticity theory. It is established that, as the applied shear stress increases, the “domain of determinacy” shrinks and eventually vanishes. The additional, non-classical boundary conditions are needed for Bassaniʹs (2001) lower-order strain gradient plasticity in order to obtain the solution outside the “domain of determinacy”. Within the “domain of determinacy”, the present results agree well with Niordson and Hutchinsonʹs (2003) finite difference solution. Outside the “domain of determinacy”, the solution may not be unique.