Identification of memory kernels in thermo-viscoelasticity

Abstract

This paper discusses the possibility of identifying the shear and structure relaxation kernels in glassy materials by means of a single, simple and non-intrusive experiment. The material should be thermorheologically simple and the kernels expressed in the form of Prony series. The experiment considered consists in measuring the thickness variations over time of a flat sample cooled symmetrically from both side from a temperature above the glass transition temperature down to room temperature. The comparison of experimental observations with theoretically calculated responses allows the identification of the coefficients of the Prony series for the shear and structure relaxation kernels using a least-square type method. This paper illustrates the success of the method with `artificially' created experimental observations and with up to two exponential terms in the Prony series for the shear and structure relaxation kernels.