A continuum and computational framework for viscoelastodynamics: III. A nonlinear theory

TL;DR

This paper develops a nonlinear viscoelasticity theory extending previous models, incorporating a Green-Naghdi type kinematic assumption, and demonstrates its effectiveness through numerical examples at large strains.

Contribution

It introduces a novel nonlinear viscoelasticity model based on Hill's hyperelasticity and a Green-Naghdi type assumption, differing from traditional intermediate configuration approaches.

Findings

The model accurately captures large strain viscoelastic behaviors.

The proposed framework enables consistent linearization and modular implementation.

Numerical examples validate the model's effectiveness in complex scenarios.

Abstract

We continue our investigation of viscoelasticity by extending the Holzapfel-Simo approach discussed in Part I to the fully nonlinear regime. By scrutinizing the relaxation property for the non-equilibrium stresses, it is revealed that a kinematic assumption akin to the Green-Naghdi type is necessary in the design of the potential. This insight underscores a link between the so-called additive plasticity and the viscoelasticity model under consideration, further inspiring our development of a nonlinear viscoelasticity theory. Our strategy is based on Hill's hyperelasticity framework and leverages the concept of generalized strains. Notably, the adopted kinematic assumption makes the proposed theory fundamentally different from the existing models rooted in the notion of the intermediate configuration. The computation aspects, including the consistent linearization, constitutive integration, and modular implementation, are addressed in detail. A suite of numerical examples is provided to demonstrate the capability of the proposed model in characterizing viscoelastic material behaviors at large strains.