Hybrid continuum model for large elastic deformation of rubber

Abstract

This paper presents a hybrid hyperelastic model for rubbery material combining the Gent–Thomas theory for low stretch deformation and the Ogden theory for large stretch deformation. Any deformation mode of rubbery materials is completely characterized by the studied model. A method for mechanical parameters identification is developed. So, comparison between experimental data and analytical solutions is made permitting discussions on the validity of different strain energy function domains. Good agreement between predicted results and experimental data is shown by the processing of the curves of simple tension and pure shear.

Reconciling the fundamental phenomenological expression of the strain energy of rubber with established experimental facts

“…For a finite number of terms in ( I 2 − 3) k , for which k is greater than or equal to one, the predicting biaxial response remains incorrect because the relative coefficients have different weighting orders in simple and biaxial extensions. 3, 7…”

“…Recently, Beda and Chevalier7 proposed a model combining the invariant‐based and stretch‐based models: the Gent–Thomas model25 for low stretches and that of Ogden11 for large stretches. The strain energy function is expressed as follows: where C , K , μ, and α are material constant parameters.…”

“…A good prediction of the pure shear response is sought. 7 Despite the evident success of the model, it remains a hybrid model derived from a combination of different state‐based models.…”

“…The stress–stretch behavior has been well modeled by statistical mechanic treatments of rubber elasticity and by invariant‐based and stretch‐based continuum mechanics theories (see Boyce and Arruda3 and Treloar4 for reviews). Nearly all the continuum models that fit data well do not consider the second strain invariants I 2 (see Gent5 and Yeoh6), are hybrid (see Beda and Chevalier7), or ignore Johnson et al's8 hypothesis by using, for example, negative weighting coefficients in the Rivlin expression (James and Green9 and Yeoh10), along with other considerations.…”

Characterization of hyperelastic deformation behavior of rubber-like materials

“…The implementation of this kind of materials requires an exprimental [1][2][3] and theoretical characterization behavior. On this subject, several isotropic and incompressible hyperelastic models have been proposed in the litterature during the last eighty years [4][5][6][7][8][9][10][11][12][13][14][15].…”