On the mechanical characterization of a class of viscoelastic materials using a dynamic system approach.

Abstract

The present research aims at the use of the dynamic system approach for the characterization of the mechanical response of linear viscoelastic materials. The new and basic idea of the research is to consider the viscoelastic material as a dynamic system. Starting with this concept, the research is carried out according to the following steps: (1) Developing a method for the identification of a general dynamic system. Discrete-time system analysis is introduced to achieve this goal. (2) Extending the method mentioned under (1) above to characterize the creep (or relaxation) function of the viscoelastic material from the measurements of the strain (or stress) output and the corresponding rate of the stress (or strain) input signals. (3) Extending the method further to characterize the creep (or relaxation) function directly from the measurements of the strain (or stress) output and the corresponding stress (or strain) input signals. In this part, the linear viscoelastic material is considered as a dynamic system. From this point of view, a dynamic system identification method is developed for the determination of the creep or relaxation function of the material from dynamic experimental measurements. First, the relation between the creep or relaxation function and the transfer function of the system is established by assuming a model of rational functions of polynomials for the transfer function. Second, a discrete-time system analysis method is introduced to identify the order and parameters of the proposed model from the discrete-time series of both the input and output signals. The numerical examples dealt with in the thesis show that the proposed procedure is reasonable and the models are accurate and efficient.