Time- and space-adaptive methods applied to localization phenomena in empty and saturated micropolar and standard porous materials. (Q2763342)

From the conclusion: Time- and space-adaptive methods have been applied to initial-boundary-value problems of empty or saturated elasto-plastic or elasto-viscoplastic problems, where micropolar solid materials have also been taken into consideration. Time-adaptive strategies have been considered within the framework of finite differences in time domain by use of singly diagonally implicit Runge-Kutta method. Using finite elements in the space domain, space-adaptive strategies were based on a modification of Zienkiewicz-Zhu error indicator, where it was shown that it is unnecessary to take into account individual error measures and indicators for the couple stress and the curvature tensor, since these quantities are included in the above procedure by the error measures and indicators for non-symmetric effective stress through the moment of momentum balance and for the plastic strain through the micropolar compatibility condition. The efficiency of the described method was demonstrated by numerical examples on a biaxial experiment and on the slope failure problem.