Micro-structure in kinematic-hardening plasticity

A gradient regularization of the classical kinematic-hardening plasticity is presented. The underlying continuum model is formally related to Mindlin's elasticity theory with micro-structure. The evolution law for the back stress is identical to Mindlin's higher order equilibrium equation. For consistency reasons the flow rule of classical plasticity is modified by incorporating the Laplacian of the plastic multiplier. The variational formulation of the problem with appropriate boundary conditions is given and an expression for the dissipated energy is established. Shear-band analysis shows that the theory provides the band thickness, and regularizes the governing equations. Micro-structure introduces a singular perturbation to the classical surface instability analysis, and the internal length l is the perturbation parameter. In addition, micro-structure effects tend to reduce the wavelength at onset of surface instability.