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In this work we propose and analyze an abstract parameter dependent modelwritten as a mixed variational formulation based on Volterra integrals ofsecond kind. For the analysis, we consider a suitable adaptation to the classicmixed theory in the Volterra equations setting, and prove the well posedness ofthe resulting mixed viscoelastic formulation. Error estimates are derived,using the available results for Volterra equations, where all the estimates areindependent of the perturbation parameter. We consider an application of thedeveloped theory in a viscoelastic Timoshenko beam, and report numericalexperiments in order to assess the independence of the perturbation parameter.

A mixed parameter formulation with applications to linear viscoelasticity