Assessment of a New Isotropic Hyperelastic Constitutive Model for a Range of Rubberlike Materials and Deformations

Anssari-Benam, Afshin; Bucchi, Andrea; Horgan, Cornelius O.; Saccomandi, Giuseppe

doi:10.5254/rct.21.78975

Cited by 15 publications

(12 citation statements)

References 53 publications

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“…In the present study we have focussed on the versatility of the model (11) in capturing several important aspects of simple shear response. The addition of a term depending on the second invariant to this model would result in a three-parameter model with enhanced modelling capabilities (see, e.g., [14,30,31]) but we will not pursue this here. Finally, we remark that numerous recent investigations in the literature on simple shearing of biological tissues underline the dominant effect of material anisotropy.…”

Section: Discussionmentioning

confidence: 99%

“…When f (κ) > 0 so that f (κ) monotonically increases with κ, we have a shear hardening behaviour. Thus, from (31) we see that for the ranges of N specified by (30), the model will capture a shear hardening response. It is interesting to note that, from Eq.…”

Section: Various Modes Of Shear Stress Responsementioning

confidence: 91%

“…A detailed account of the structural derivation of the limiting chain extensibility model ( 9) based on the kinetic molecular theory of rubber elasticity has been presented in [26] and [28]. The successful application of this model to various finite deformation modes of rubberlike materials including in-plane deformations, inflation, torsion and the ensuing elastic instabilities has been presented in our previous studies [26,[30][31][32][33]. Horgan [34] demonstrated that this model is directly related to the celebrated two parameter Gent model [35], in that the first derivatives of W with respect to I 1 in these two models differ by just a constant.…”

Section: A Model For Simple Shearmentioning

confidence: 99%

“…The experimental data collated from these studies have been tabulated and presented in the Appendix, Tables 10 to 14. Similar to our previous studies [14,26,[30][31][32][33], the fitting process was carried out to obtain the best fit to each dataset by minimising the residual sum of squares (RSS) function defined as:…”

Section: Capturing Various Shear Stress Responsesmentioning

confidence: 99%

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On Modelling Simple Shear for Isotropic Incompressible Rubber-Like Materials

Anssari-Benam

Horgan

2021

J Elast

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In this paper we demonstrate the application of a recently proposed molecular based generalised neo-Hookean strain energy function within the family of limiting chain extensibility models to the simple shear of incompressible isotropic rubber-like hyperelastic materials. The two-parameter model of concern is capable of capturing both linear and highly nonlinear shear stress responses. It provides favourable simultaneous fits to experimental data for various components of the simple shear stress field, such as the shear stress and normal tractions/stresses, with a single set of parameter values. In addition, when used in a phenomenological context, the model also captures shear-softening behaviour and predicts an interesting instability. These modelling results are demonstrated in conjunction with a wide range of extant experimental data involving the simple shearing of biological tissue specimens and polymer and rubber samples. It will also be shown that in all these applications, the proposed model remains stable (convex) over the defined domain of deformation. These results underline the merits of the considered model for addressing some of the outstanding challenges in the constitutive modelling of the complex nonlinear behaviour of rubber-like materials.

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Section: Discussionmentioning

confidence: 99%

Section: Various Modes Of Shear Stress Responsementioning

confidence: 91%

Section: A Model For Simple Shearmentioning

confidence: 99%

Section: Capturing Various Shear Stress Responsesmentioning

confidence: 99%

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On Modelling Simple Shear for Isotropic Incompressible Rubber-Like Materials

Anssari-Benam

Horgan

2021

J Elast

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“…For a structural derivation of this term based on the concept of modelling the molecular chain entanglements as a topological tube constraint, see [33,36]. Other customary I 2 -term adjuncts, including a Mooney–Rivlin term C 2 ( I 2 − 1) or a Gent–Thomas type term C2ln⁡false(I2/3false) [37,38] have been considered previously [33,39] and are not pursued here. In essence, however, we note that all the foregoing adjunct I 2 terms produce a broadly similar contribution to the modelling results.…”

Section: Modelling Frameworkmentioning

confidence: 99%

Modelling brain tissue elasticity with the Ogden model and an alternative family of constitutive models

Anssari-Benam

Destrade

Saccomandi

2022

Phil. Trans. R. Soc. A.

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The Ogden model is often considered as a standard model in the literature for application to the deformation of brain tissue. Here, we show that, in some of those applications, the use of the Ogden model leads to the non-convexity of the strain-energy function and mis-prediction of the correct concavity of the experimental stress–stretch curves over a range of the deformation domain. By contrast, we propose a family of models which provides a favourable fit to the considered datasets while remaining free from the highlighted shortcomings of the Ogden model. While, as we discuss, those shortcomings might be due to the artefacts of the testing protocols, the proposed family of models proves impervious to such artefacts. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'.

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A generalised $${\varvec{W}}\left({{\varvec{I}}}_{1},{{\varvec{I}}}_{2}\right)$$ strain energy function of binomial form with unified applicability across various isotropic incompressible soft solids

Anssari-Benam

2023

Acta Mech

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A generalised $$W\left({I}_{1},{I}_{2}\right)$$ W I 1 , I 2 strain energy function, a generalisation of previously devised response functions $${W}_{1}$$ W 1 and $${W}_{2}$$ W 2 , of binomial form is presented in this work for application to the finite deformation of isotropic incompressible soft solids. It is shown that the proposed model is the parent to many of the well-known existing invariants-based models in the literature. The first-order expansion of the model, with six model parameters, is then applied to extant multiaxial deformation of a wide range of materials, from filled and unfilled rubbers to hydrogels, liquid crystal elastomers and biomaterials. The model captures the experimental data accurately, with typical relative errors below 4%, while favourably modelling various challenging mechanical behaviours such as the asymmetry of compression—tension, high nonlinearity of the simple shear response, deformation softening effects, pronounced Payne effect, the soft elasticity phenomenon, and the reverse Poynting effect. The predictive capabilities of the model are also demonstrated and verified against experimental data. Given the analyses and results presented here, the devised model is proposed to serve as a standard choice for a priori selection for application to the finite deformation of isotropic incompressible soft materials.

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Assessment of a New Isotropic Hyperelastic Constitutive Model for a Range of Rubberlike Materials and Deformations

Cited by 15 publications

References 53 publications

On Modelling Simple Shear for Isotropic Incompressible Rubber-Like Materials

On Modelling Simple Shear for Isotropic Incompressible Rubber-Like Materials

Modelling brain tissue elasticity with the Ogden model and an alternative family of constitutive models

A generalised $${\varvec{W}}\left({{\varvec{I}}}_{1},{{\varvec{I}}}_{2}\right)$$ strain energy function of binomial form with unified applicability across various isotropic incompressible soft solids

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