A distributed order viscoelastic model for small deformations

In this work we discuss the connection between classical, fractional and dis- tributed order viscoelastic Maxwell models, presenting the basic theory supporting these constitutive equations, and establishing some background on the admissibility of the dis- tributed order Maxwell model. We derive the storage and loss modulus functions for the distributed order viscoelastic model and perform a fitting to experimental data. The fitting results are compared with the Maxwell and Fractional Maxwell models.L.L. Ferr´as would also like to thank FCT for financial support through projects UIDB/ 00013/2020 and UIDP/00013/2020. M.L. Morgado aknowledges funding by FCT through project UID/Multi/04621/2019 of CEMAT/IST-ID, Center for Computational and Stochastic Mathematics, Instituto Su perior T´ecnico, University of Lisbon. This work was partially supported by the Funda¸c˜ao para a Ciˆencia e a Tecnologia (Por tuguese Foundation for Science and Technology) through the project UIDB/00297/2020 (Centro de Matem´atica e Aplica¸c˜oes). The authors also acknowledge financial support from COST Action CA15225, a network supported by COST (European Cooperation in Science and Technology)