A study on the conventional theory of mechanism-based strain gradient plasticity for mixed hardening by the method of characteristics

The Conventional Theory of Mechanism-based Strain Gradient Plasticity (CMSG) is of lower-order strain gradient that retains the essential structure of classical plasticity theory. It does not require additional non-classical boundary conditions, thus it can be easily applied in numerical analysis. The constitutive relations of CMSG theory for mixed hardening are established, and its well-posedness is studied by the method of characteristics. For an infinite layer in shear, the domain of determinacy for CMSG theory at different mixed hardening states is determined. Within the domain of determinacy, the presented results agree well with the numerical solution obtained by the finite difference method. Outside the domain of determinacy, the solution may not be unique, in that case, the additional, non-classical boundary conditions are needed for the well-posedness of CMSG theory. As the applied shear stress increases, the domain of determinacy shrinks and eventually vanishes.