Deformation and compatibility for elasto-plastic micropolar materials with application to geomechanical problems

The consideration of empty porous solid materials (e.g. granular skeletons) naturally falls into the macroscopic continuum mechanical concept of the Theory of Porous Media (TPM). It is well known from Various experiments that granular materials tend to localization phenomena (e. g. shear bands) as a result of local concentrations of plastic strains. The numerical simulation of these phenomena generally reveals an ill-posed problem with the consequence that the shear band width strongly depends on the chosen spatial discretization. To overcome this problem, an internal length scale must be introduced, which, in the present article, is a result of the inclusion of micropolar degrees of freedom in the sense of the Cosserat brothers. Based on this approach, the contribution of the present article is to show that the micropolar compatibility condition of the geometrically linear approach is a direct consequence of the general finite micropolar theory. Furthermore, as a result of the micropolar compatibility condition applied to elasto-plastic problems, there is no independent evolution equation for the rate of curvature tensor, since this quantity is uniquely determined by the the gradient of the plastic strain rate. Proceeding from the fact that micropolar theories are downward compatible to the usual standard approach, the numerical example is carried out on the basis of a model adaptive strategy, where an automatic switch between the standard and the micropolar approach guarantees that the additional micropolar degrees of freedom are only taken into consideration in those domains, where micropolar rotations occur, i.e. in the shear band zone.     «

The consideration of empty porous solid materials (e.g. granular skeletons) naturally falls into the macroscopic continuum mechanical concept of the Theory of Porous Media (TPM). It is well known from Various experiments that granular materials tend to localization phenomena (e. g. shear bands) as a result of local concentrations of plastic strains. The numerical simulation of these phenomena generally reveals an ill-posed problem with the consequence that the shear band width strongly depends o...     »