a b s t r a c tIn finite element calculations the constitutive model plays a key role. The evaluation of the stress response of the constitutive relation for a given strain increment, which is a time integration in the case of models of the rate type, is a typical sub task in such calculations. Adaptive behaviour of the time integration is essential to assure numerical stability and to control the accuracy of the solution. An adaptive second order semi-implicit method is developed in this paper. Its numerical behaviour is compared with an adaptive second order explicit scheme. The two proposed methods control the local error and guarantee numerical stability of the time integration. We include several numerical geotechnical element tests using hypoplasticity with intergranular strain. The element tests simulate the behaviour of a finite element method based on the displacement formulation.