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 finite 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 effects. 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 different regularization strategies are considered, which are (1) the inclusion of independent rotational degrees of freedom (micropolar formulation) and (2) the inclusion of viscosity effects (standard formulation) by taking into consideration viscoplastic properties of the solid matrix or a viscous pore-fluid, respectively. The numerical treatment furthermore proceeds from time- and space-adaptive strategies to refine 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 efficient 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 efficiency of this procedure is demonstrated by the computation of the biaxial experiment on an empty and a liquid-saturated porous soil material and of the slope failure problem of a fluid-saturated soil. Copyright © 2001 John Wiley & Sons, Ltd.