A Variational Framework For Nonlinear Viscoelastic And Viscoplastic Models In Finite Deformation Regime

Abstract

The goal of this work is to provide a general framework for constitutive viscoelastic and viscoplastic models based on the theoretical background proposed in Ortiz and Stainier, Comput. Meth. App. Mech. Engng., Vol. 171, 419-444 (1999). Thus, 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 thus employs, according to the specific model chosen, multiplicative decomposition of strain in elastic and irreversible components. Inserted in the same theoretical framework, the present approach for viscoelasticity shares the same technical procedures used for analogous models of plasticity or viscoplasticity, say, the solution of a minimization problem to identify inelastic updates and the use of exponential mapping for time integration. Spectral decomposition is explored in order to accommodate, into analytically tractable expressions, a wide set of specific models. Moreover, it is shown that, through appropriate choices of the constitutive potentials, the proposed formulation is able to reproduce results obtained elsewhere in the literature. Finally, different numerical examples are included to show the characteristics of the present approach and to compare results with others found in literature when possible.