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Micropolar elastoplasticity and its role in localization. (English) Zbl 0794.73004
Summary: 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 the second order. The expanded localization conditions are studied with two constitutive models – micropolar Rankine and micropolar von Mises $$J_ 2$$-flow theories of elastoplasticity – for which definite statements are derived with regard to their regularization properties.

##### MSC:
 74A35 Polar materials 74C99 Plastic materials, materials of stress-rate and internal-variable type 74A20 Theory of constitutive functions in solid mechanics
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