Runge–Kutta methods in elastoplasticity Original Research Article

Runge–Kutta methods for the constitutive equations of elastoplasticity are presented. These equations form a differential–algebraic equation (DAE) of index 2 with unilateral constraints. For the numerical solution, implicit Runge–Kutta methods are combined with the return mapping strategy of computational plasticity. It turns out that the convergence order depends crucially on the switching point detection. Furthermore, it is shown that algebraically stable Runge–Kutta methods preserve the contractivity of the elastoplastic flow.