A Time Adaptiv Finite‐Element Procedure Applied to Creep and Relaxation Processes

In this paper we interpret the finite-element method applied to constitutive models with internal variables as the solution of differential algebraic equations (DAE). With this interpretation we can utilize Diagonal Implicit Runge-Kutta methods (DIRK) as well as a corresponding step-size control and a special solution technique for block-structured systems of equations. This proceeding doesn't affect already developed FE-implementations which are based on the Backward Euler method. Furthermore, the meaning of the consistent tangent operator becomes more obvious. The paper ends with some examples in creep and relaxation tests, where step size control should always be used conditioned by the different time scales.