Revisiting the identification of generalized Maxwell models from experimental results

Linear viscoelastic material behavior is often modeled using a generalized Maxwell model. The material parameters, i.e. relaxation times and elastic moduli, of the Maxwell elements are determined from either a relaxation or a Dynamical Mechanical Analysis (DMA) experiments. The underlying mathematical problem is known to be ill-posed, which means that uniqueness of the identification is not assured and that small errors in the initial data will conduct to high discrepancies in the identified parameters. The standard technique to remove the ill-posedness is to chose a priori a series of relaxation times and to identify only the moduli. The aim of this paper is to propose two techniques to identify an optimal series of relaxation times. In the case of the relaxation experiment relaxation times will be optimized from the numerical integration of the measured relaxation spectrum. In the case of the DMA experiments we show that mathematical results obtained by Krein and Nudelmann can be used to determine the complete series of relaxation times. The methods are illustrated by identification examples using both artificial and experimental data. The results show that the methods provide a good match of the identified models in term of relaxation or complex moduli.