Index 2 DAEs in Plasticity Theory

The equations of rate‐independent elastoplasticity form a differential‐algebraic equation (DAE) with discontinuities. For the numerical solution, implicit Runge‐Kutta methods are applied and combined with the return mapping strategy of computational plasticity. It turns out that the convergence order depends crucially on the switching point detection. Further, it is shown that algebraically stable Runge‐Kutta methods preserve the contractivity of the elastoplastic flow.