Modeling finite viscoelasticity based on the Green-Naghdi kinematic assumption and generalized strains

TL;DR

This paper introduces a flexible finite viscoelasticity modeling framework based on Green-Naghdi assumptions, avoiding the debated intermediate configuration, and demonstrates its effectiveness through experimental data fitting and finite element analysis.

Contribution

It develops a novel viscoelasticity model using Green-Naghdi kinematic assumptions with generalized strains, offering adjustable kinematic separation and unifying several existing models.

Findings

Models recover classical viscoelastic models with specific strains.

Framework effectively fits experimental data of VHB 4910.

Finite element analysis shows influence of strain choice on behavior.

Abstract

We propose a modeling framework for finite viscoelasticity, inspired by the kinematic assumption made by Green and Naghdi in plasticity. This approach fundamentally differs from the widely used multiplicative decomposition of the deformation gradient, as the intermediate configuration, a concept that remains debated, becomes unnecessary. The advent of the concept of generalized strains allows the Green-Naghdi assumption to be employed with different strains, offering a flexible mechanism to separate inelastic deformation from total deformation. This leads to a constitutive theory in which the kinematic separation is adjustable and can be calibrated. For quadratic configurational free energy, the framework yields a suite of finite linear viscoelasticity models governed by linear evolution equations. Notably, these models recover established models, including those by Green and Tobolsky (1946) and Simo (1987), when the Seth-Hill strain is chosen with the strain parameter being -2 and 2, respectively. It is also related to the model of Miehe and Keck (2000) when the strain is of the Hencky type. We further extend the approach by adopting coercive strains, which allows us to define an elastic deformation tensor locally. This facilitates modeling the viscous branch using general forms of the configurational free energy, and we construct a micromechanical viscoelastic model as a representative instantiation. The constitutive integration algorithms of the proposed models are detailed. We employ the experimental data of VHB 4910 to examine the proposed models, which demonstrate their effectiveness and potential advantages in the quality of fitting and prediction. Three-dimensional finite element analysis is also conducted to assess the influence of different strains on the viscoelastic behavior.