Modeling viscoelastic materials using internal variables

The purpose of this paper is to present a short review on how internal variables are employed to model highly damped materials in linear structural dynamics. A background discussion is included that provides a reference to literature containing additional technical details. The classical constitutive models of Voigt, Kelvin-Voigt, and the standard linear solid are briefly reviewed. A number of recently proposed internal variable formulations are reviewed in one-dimensional form to highlight their similarities. Displacement-based finite element formulations for the Voigt, Kelvin-Voigt, and standard linear solid materials are presented. Reference is given to numerical methods employed to solve the finite element equations of motion.