A variational formulation of constitutive models and updates in non‐linear finite viscoelasticity

The purpose of this article is to present a general framework for constitutive viscoelastic models in finite strain regime. The approach is qualified as variational since the constitutive updates obey a minimum principle within each load increment. The set of internal variables is strain‐based and employs, according to the specific model chosen, a multiplicative decomposition of strain into elastic and viscous components. The present approach shares the same technical procedures used for analogous models of plasticity or viscoplasticity, such as the solution of a minimization problem to identify inelastic updates and the use of exponential mapping for time integration. However, instead of using the classical decomposition of inelastic strains into amplitude and direction , we take advantage of a spectral decomposition that provides additional facilities to accommodate, into simple analytical expressions, a wide set of specific models. Moreover, appropriate choices of the constitutive potentials allow the reproduction of other formulations in the literature. The final part of the paper presents a set of numerical examples in order to explore the characteristics of the formulation as well as its applicability to usual large‐scale FEM analyses. Copyright © 2005 John Wiley & Sons, Ltd.