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SUMMARYA major problem in using the ÿnite element method for solving numerous engineering problems in the framework of single-and multiphase materials is the assessment of discretization errors and the design of suitable meshes. To overcome this problem, adaptive ÿnite element methods have been developed. Based on the error indicator by Zienkiewicz and Zhu, it is the goal of the present paper to present a new error indicator which is especially designed for multiphase problems. Furthermore, e cient h-adaptive strategies concerning both the generation of new meshes in the framework of independent and hierarchical remeshing strategies and the data transfer between old and new meshes are pointed out. Finally, numerical examples are given to exhibit the e ciency and the quality of the presented h-adaptive methods and to compare the di erent strategies to each other.

SUMMARYLocalization phenomena, as e.g. shear bands, occur as a result of local concentrations of plastic strains in small bands of ÿnite 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 reÿne 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 e cient 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 L 2 -norms of characteristic quantities are compared to the respective discrete values. The e ciency 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 uid-saturated soil.

Abstract:We introduce a general parallel model for solving coupled nonlinear and time-dependent problems in soil mechanics. In particular, we discuss the application to a triphasic porous media model, where we compute the deformation of unsaturated soil together with the porefluid flow of water and air in the soil, and where the material behaviour of the skeleton is assumed to be elasto-viscoplastic. In two large-scale numerical experiments we finally present an extended evaluation of our parallel model for demanding 3-d configurations.References:

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