A mixed parameter formulation with applications to linear viscoelasticity

TL;DR

This paper develops a parameter-dependent mixed variational model for linear viscoelasticity using Volterra integrals, proving well-posedness and error estimates, and applies it to a Timoshenko beam with numerical validation.

Contribution

It introduces a novel mixed formulation for viscoelasticity based on Volterra integrals, with rigorous analysis and practical application to beam modeling.

Findings

The model is well-posed and the error estimates are independent of the perturbation parameter.

Numerical experiments confirm the robustness and applicability of the theory.

The approach extends mixed variational methods to Volterra integral equations in viscoelasticity.

Abstract

In this work we propose and analyze an abstract parameter dependent model written as a mixed variational formulation based on Volterra integrals of second kind. For the analysis, we consider a suitable adaptation to the classic mixed theory in the Volterra equations setting, and prove the well posedness of the resulting mixed viscoelastic formulation. Error estimates are derived, using the available results for Volterra equations, where all the estimates are independent of the perturbation parameter. We consider an application of the developed theory in a viscoelastic Timoshenko beam, and report numerical experiments in order to assess the independence of the perturbation parameter.