Abstract
Mathematical idealization of a micro-shear bands system by means of the theory of singular surfaces of order one, related to a physical model of shear strain-rate produced by active micro-shear bands and a certain averaging procedure over the representative volume element, is studied. Theoretical description of small elastic and large plastic deformations within the framework of a two-surface plasticity model, with the internal yield surface connected to kinematic hardening anisotropy and the external surface related to micro-shear banding, is proposed. The idea of the multiple potential surfaces forming a vertex on the smooth external surface is applied to display the connection with the geometric pattern of micro-shear bands. A new physical insight is given into the linear and nonlinear flow laws, in rates of deformation and stress, known in the theory of plasticity.
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