Boundary effects in elasto-plastic Cosserat continua

The argument of discontinuous bifurcation is normally formulated for detecting spatial discontinuities in the interior of an infinite solution domain. This paper expands localization analysis to a finite domain in which the translatory notion of classical continua is enriched by independent microrotations in the spirit of Cosserat continua. The bifurcation condition for the interior is augmented by complementing conditions at the boundaries and at material interfaces. In analogy to the equivalent propagation argument for Rayleigh surface waves and Stoneley waves within the traditional format of elasto-plasticity (see Needleman, A. and Ortiz, M. (1991). Effect of boundaries and interfaces on shear-band localization. Int. J. Solids Struct. 28, 859 877) the current study develops the complementing propagation conditions for the micropolar Cosserat description of elasto-plasticity. To this end, their singularities are examined in terms of stationary Rayleigh surface waves and Stoneley waves at interior interfaces. (C 1997 Elsevier Science Ltd. All rights reserved.