Journal of Theoretical
and Applied Mechanics

22, 1-2, pp. 209-233, Warsaw 1984

Dyskretna analiza modeli reologicznych

Romuald Świtka, Bogdan Husiar

The discretization method of the equation of state for the linear visco-elastic materials has been proposed. The time axis has been divided into seperate time intervals; within each time interval the stresses have been approximated by means of the linear or quadratic functions. The constitutive relation for a viscoelastic material has been assumed in the form of a differential relation with the time derivatives at most of the second order. The constitutive relation for the given approximation can be solved in the exact form. As a result the reccurence relation has been obtained for which the state of derfomation at a given instant is determined by the state of stress at the same instant and by the state of the body in the preceding (discrete) time instant. Thus for the linear and parabolic time distributions of stress, the quadratic approximation leads to the exact results for any length of steps. In other cases the length of the step, controlled by the criterion of accuracy, can be rather big; this fact plays an essential role when long time creep processes are considered. A number of test calculations for different rheological models (Kelvin-Voigt, Zener, Burgers) and for different loading programs have been performed. The error analysis for some special approximations
and different step lenghts has been given.