Time- and space-adaptive methods applied to localization phenomena in empty and saturated micropolar and standard porous materials

Localization phenomena, as e.g. shear bands, occur as a result of local concentrations of plastic strains in small bands of 9nite width. The reason for this behaviour lies in the basic properties of elasto-plastic frictional materials, where variations of the Lode angle together with the non-associated plastic dilatation result in local softening e;ects. Proceeding from non-viscous empty porous materials, it is well known that the computation of shear bands reveals an ill-posed problem. To overcome this behaviour, two di;erent regularization strategies are considered, which are (1) the inclusion of independent rotational degrees of freedom (micropolar formulation) and (2) the inclusion of viscosity e;ects (standard formulation) by taking into consideration viscoplastic properties of the solid matrix or a viscous pore->uid, respectively. The numerical treatment furthermore proceeds from time- and space-adaptive strategies to re9ne and to coarsen both the time step and the mesh size. Considering quasi-static problems, the space discretization yields a DAE system of index 1 in the time domain which can be successfully treated by SDIRK methods, thus allowing for an eAcient estimation of the time error and, as a consequence, for an adaptive time-step control. In the space domain, the present investigation proceeds from an error indicator of Zienkiewicz-Zhu type, where smoothened values of the L2-norms of characteristic quantities are compared to the respective discrete values. The eAciency of this procedure is demonstrated by the computation of the biaxial experiment on an empty and a liquid-saturated porous soil material and of theslopefailureproble m of a >uid-saturated soil