On the implicit integration of rate-dependent inelastic constitutive models

Although there are many different algorithms for the integration of inelastic constitutive models, the fully implicit backward Euler method has become the most popular one. In this study further investigations on the accuracy of the backward Euler method have been carried out. Also the performance of the discontinuous Galerkin family and some implicit Runge–Kutta time integrators is evaluated. By using a simple scalar model problem accuracy of some integrators is studied when a single finite time step is applied. Conclusions drawn from this scalar model problem has been verified to apply also to a full six-dimensional strain space formulation by numerical means. Special emphasis is placed on rate-dependent inelastic creep models