The exponentiated Hencky strain energy in modelling tire derived material for moderately large deformations

TL;DR

This paper introduces a hyper-viscoelastic model based on the exponentiated Hencky strain energy to accurately predict the nonlinear response of Tire Derived Material under moderately large deformations, incorporating both micro and macro dissipation mechanisms.

Contribution

The paper develops a novel exponentiated Hencky strain energy model for TDM that improves prediction accuracy for nonlinear deformation behaviors and integrates viscoelastic effects at multiple scales.

Findings

Model accurately predicts TDM response under various deformation modes.

The exponentiated Hencky energy improves large strain behavior prediction.

Model parameters have clear physical interpretations.

Abstract

This work presents a hyper-viscoelastic model based on the Hencky-logarithmic strain tensor to model the response of a Tire Derived Material (TDM) undergoing moderately large deformations. TDM is a composite made by cold forging a mix of rubber fibers and grains, obtained by grinding scrap tires, and polyurethane binder. The mechanical properties are highly influenced by the presence of voids associated with the granular composition and low tensile strength due to the weak connection at the grain-matrix interface. For these reasons, TDM use is restricted to applications concerning a limited range of deformations. Experimental tests show that a central feature of the response is connected to highly nonlinear behavior of the material under volumetric deformation which conventional hyperelastic models fail in predicting. The strain energy function presented here is a variant of the exponentiated Hencky strain energy proposed by Neff et al., which for moderate strains is as good as the quadratic Hencky model and in the large strain region improves several important features from a mathematical point of view. The proposed form of the exponentiated Hencky energy possesses a set of parameters uniquely determined in the infinitesimal strain regime and an orthogonal set of parameters to determine the nonlinear response. The hyperelastic model is additionally incorporated in a finite deformation viscoelasticity framework that accounts for the two main dissipation mechanisms in TDMs, one at the microscale level and one at the macroscale level. The model is capable of predicting different deformation modes in a certain range of frequency and amplitude with a unique set of parameters with most of them having a clear physical meaning. Moreover, by comparing the predictions from the proposed constitutive model with experimental data we conclude that the new constitutive model gives accurate prediction.