An implementation of the generalized Maxwell viscoelastic constitutive model

Viscoelastic problems deserve great interest in Computational Mechanics literature. In the last years different approaches have been proposed in order to model viscoelastic problems, as in the case of the generalized Maxwell model and its numerical implementation. In particular Kaliske and Rothert (M. Kaliske and H. Rothert, Comput. Mech., 19(3): 228-239 (1997)) discussed basic reological models and the formulation of a generalized Maxwell model and the corresponding implementation of three dimensional viscoelastic model both for small and large strain cases. The numerical implementation addressed by Kaliske and Rothert is quite simple for small strain case and can be extended to a large strain format amenable to be included in finite element codes SOGDE and Metafor. The implementation of the discussed model in a 1D constitutive model, written in Matlab, is addressed. The well known relaxation and creep tests are simulated and compared with analytical results. Furthermore, the influence of constitutive parameters on the viscoelastic response is discussed. In addition, the model is implemented in Finite Element codes and the obtained results are compared with the 1D ones.