A time adaptiv finite-element procedure applied to creep and relaxation processes

In this paper we interpret the finite-element method applied to constitutiv e 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. Th is proceeding doesn't affect already developed FE-implementations which are based on the Backward Euler method. Furthermore, the meaning of the consis tent tangent operator becomes more obvious. The paper ends with so-me examp les in creep and relaxation tests, where step size control should always be used conditioned by the different time scales.