Characterizing the Plastic Strain Localization in Cosserat Media

The analysis of strain localization is of importance in engineering practice because localization is a precursor to sudden failure. Localized deformations in the form of narrow shear bands are often observed to develop after large inelastic deformation in materials. Within this shear band, the material behaviour is inelastic. The width and orientation of these shear bands depend on material parameters, geometry, boundary conditions and loading conditions. In other words, knowledge concerning the development of the strain localization phenomenon will also lead to insight into failure mechanisms. Numerical simulations of strain localization by means of the finite element method are known to lead to mesh sensitivity when the classical continuum models without enrichment are considered. In order to obtain a meaningful representation of the continuum response in the presence of strain localization, much effort has been devoted in recent years to devise regularization strategies which are able to both, simulate the development of shear band independent of the finite element mesh and, retain the nature of the governing equations, (1988), (1991), (1992). In the Cosserat continuum approach, additional micropolar degrees of freedom is introduced into the solution of the initial value problem as an internal length-scale parameter that can prevent loss of hyperbolicity in dynamic equations or loss of ellipticity in static equations. Mesh independence can then be ensured. In this contribution, the generalized numerical formulations for the case of a 3D el as to-plastic Cosserat continuum have been developed and the Desai hierarchical model has been chosen to generalize to the continuum. The aim of this contribution is to provide insight into the phenomenon of strain localization in Cosserat continuum by means of finite element analyses. In order to investigate the significance of the regularizing effects due to the presence of the micropolar degrees of freedom in Cosserat continuum, numerical analyses on strain localization for sand are carried out. The influences of the evolution of the micropolar parameters on the formation of the shear band are investigated numerically. It is shown that due to the presence of an internal length scale changing in magnitude during the deformation of the material, mesh independence can be ensured.