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A generalisation of \(J_ 2\)-flow theory for polar continua. (English) Zbl 0777.73014
The author proposes a pressure-dependent (so-called) \(J_ 2\)-theory of plastic flow within the framework of the Cosserat (also called “micropolar” by A. C. Eringen) continuum. This necessitates the definition of a second invariant of deviatoric stresses which accounts for couple stresses. Similarly, the strain-hardening hypothesis has to account for micro-curvatures, i.e., the kinematic duals of couple stresses. The temporal integration of the resulting system is successfully achieved by using an implicit Euler backward scheme (return- mapping algorithm). As a result of microstructure being taken into account, an internal length scale is naturally incorporated in the theory. This has for consequence, in finite-element simulations of localization phenomena, to yield a finite width of the localization zone. This is exemplified by treating numerically the case of an infinitely long shear layer, as also that of a biaxial specimen composed of strain- softening Drucker-Prager material. This theory of Cosserat elasto- plasticity seems to be relevant to the study of geomaterials such as concrete, rocks and soils.
Reviewer: G.A.Maugin (Paris)

MSC:
74C99 Plastic materials, materials of stress-rate and internal-variable type
74A35 Polar materials
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