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Interconversion of viscoelastic material functions is a longstanding problem that has received attention since the 1950s. There is currently no accepted methodology for interconverting viscoelastic material functions due to the lack of stability and accuracy of the existing methods. This paper presents a new exact, analytical interconversion method for linearly viscoelastic material functions expressed as Prony series. The new algorithm relies on the equations of the thermodynamics of irreversible processes used for defining linearly viscoelastic constitutive theories. As a result, interconversion is made possible for unidimensional and tridimensional materials for arbitrary material symmetry. The algorithm has been tested over a broad range of cases and was found to deliver accurate interconversion in all cases. Based on its accuracy and stability, the authors believe that their algorithm provides a closure to the interconversion of linearly viscoelastic constitutive theories expressed with Prony series. © 2012 Springer Science+Business Media, B. V.

This paper presents two new strategies for implementing Schapery-type nonlinearly viscoelastic constitutive theories into finite element codes. The first strategy uses the original differential equations that lead to the integral formulation of Schapery-type constitutive theories and Finite Difference (FD) schemes. This strategy is quite different from all the other strategies found in the literature. The second strategy is an improvement of recursive strategies, used by many authors, based on the integral formulation of the constitutive theory. The performances of the new algorithms are compared with those of existing strategies for various load histories and nonlinearities. It is shown that the newly developed strategy based on FD schemes can exhibit quadratic convergence rate when one time step is stored and 4th order convergence rate when two time steps are stored, which is a major improvement over the recursive strategies.

Development of new polyimide formulas has led to an increase of the use of polymer matrix composites by the aerospace industry in critical applications such as aircraft engines. In such an extreme environment, the polymer matrix is likely to exhibit a viscoelastic behavior due to the elevated temperatures. Furthermore, physical ageing is likely to appear during the service life of the material. In order for engineers to design with such materials, constitutive theories able to take into account those effects, must be developed. This paper deals with the mechanical behavior of a new polyimide matrix tested under complex thermo-mechanical histories while accounting for physical ageing. The experimental data obtained was modeled with a newly developed constitutive theory stemming from Schapery’s thermodynamical framework. The model parameters were obtained from creep-recovery data under various temperatures, ageing times, and loads. The model was subsequently validated against independent complex thermo-mechanical histories. An excellent agreement between the experiments and the predictions has been obtained.