Use of couple-stress theory in elasto-plasticity

One way to avoid vanishing dissipative energy and localization to zero volume when examining localization and softening problems, is to introduce an internal length scale for the material by means of couple-stress theory. Here, the 'constrained' Cosserat theory is adopted where the displacement field also determines the rotation field. For this 'constrained' Cosserat theory an elasto-plastic theory is derived within a thermodynamic framework and it is shown that the evolution laws for the internal variables can be derived from the postulate of maximum dissipation. A generalization of the classical von Mises material is proposed; both the derivation of the model and the numerical treatment of the integration problem are discussed. The generalized von Mises model is used in finite element calculations where shear band formation is considered and the results turn out to be independent of the mesh spacing.