Micropolar elastoplasticity and its role in localization

In this article we focus on micropolar elastoplasticity and the conditions for the formation of spatial discontinuities. After a brief review of micropolar kinematics and balance equations, an augmented localization tensor is developed for elastoplastic constitutive behavior that describes discontinuous bifurcation at the constitutive level. In this context an auxiliary condition is encountered that restricts the jump of the stress rate to remain symmetric across discontinuity surfaces of second order. The expanded localization conditions are studied with two constitutive models — micropolar Rankine and micropolar von Mises J2-flow theories of elatoplasticity — for which definite statements are derived with regard to their regularization properties