ABSTRACT
The reliable computation of the stress response for a given strain increment is an important issue in computational geotechnics. Hypoplasticity (Kolymbas 1985) is a framework for constitutive models of the rate type specialised for soil behaviour. For the comparison of the numerical behaviour of an adaptive second order semi-implicit method (Fellin et al. 2009) and an adaptive second order explicit method (Fellin and Ostermann 2002), we choose the hypoplastic model with the intergranular strain concept (Niemunis and Herle 1997). For single element tests the solutions show a stiff behaviour all over the computational domain (Mittendorfer 2010). Stiffness in the mathematical sense means that certain implicit integrators perform much more efficiently than explicit ones. For adaptive explicit methods applied to stiff problems the product of the time step size with the dominant eigenvalue of the linearised system lies near the border of the stability domain (Hairer and Wanner 1996). This can enforce very small step sizes, already observed in the single element tests in (Fellin et al. 2009).
