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

Abstract

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.

h‐Adaptive FE methods applied to single‐ and multiphase problems

“…Due to the considerably low lateral pressure of 1 = 50 kN=m 2 , the elasto-viscoplastic deformation process leads to a yield point in the brittle or the dilatant regime, cf. Ehlers et al [23]. As a result, the shear band exhibits a porosity increase of approximately 2 per cent in comparison with the surrounding domain.…”

“…In particular, these quantities are the e ective solid stresses A S E , the plastic strains U Sp and the seepage velocity w F , cf. Ehlers and Ellsiepen [3], Ehlers et al [23] and Ellsiepen [4]:…”

Numerical Simulation of Multiphase Hydromechanical Processes Induced by CO2Injection into Deep Saline Aquifers

“…Some general representations of corresponding numerical approaches to solve the problem under consideration can be found in [42,47,61,62]. The method of weighted residuals is applied to derive the weak formulations of all the governing equations given above.…”

A finite element method for poro mechanical modelling of geotechnical problems using local second gradient models

“…The most important works made in this topic have been performed by Ehlers and coworkers who used Cosserat continuum in coupled problems within a large strain elasto plastic framework [27,28]. A gradient-dependent plasticity model has been recently extended in two and three phases porous media by Zhang and Schefler [29].…”