Localized failure analysis in elastoplastic Cosserat continua

This paper summarizes our experience with localized failure analysis in micropolar Cosserat continua. The main intent is to examine the regularization properties of discontinuous bifurcation problems when higher grade micropolar materials that exhibit an internal length scale are introduced. Thereby, the key feature is the endowment of micropolar continua with rotational drilling degrees of freedom in addition to the traditional description of motion in terms of displacements. After a brief review of elastoplastic Cosserat continua, we examine recent findings of localization analysis of discontinuous bifurcation [1]. To this end we generalize the strength concept of the Mohr envelope condition to non-symmetric stress states to analyze the localization condition of discontinuous failure [2]. The Mohr representation of stress leads to a geometrical condition which is used to determine critical hardening/softening moduli and localization directions that characterize the particular mode of failure. This geometric interpretation of the localization condition lends itself to a systematic study of regularizing weak discontinuities within elastoplastic Cosserat continua. For illustration of these theoretical findings, numerical failure studies are carried out on a representative volume element made of J(2)-type elastoplastic Cosserat material. The computational failure simulations demonstrate the non-local character of Cosserat continua that depends on an internal length scale and on the degree of non-symmetry in the stress and strain states. The computational results also illustrate the conversion of the underlying failure mode from mixed mode to mode I type failure of decohesion and separation.