A Strain Energy Function for Vulcanized Rubbers

Carroll, M. M.

doi:10.1007/s10659-010-9279-0

Cited by 91 publications

(62 citation statements)

References 14 publications

(15 reference statements)

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“…These are two-parameter models, where C 1 and C 2 are the material constants to be found from the best-fit procedure. As noted by Carroll (2011), all three belong to the class of strain energies proposed by Klingbeil and Shield (1964). When these strain energies are expanded up to third order in the powers of the Green-Lagrange strain tensor E, we find that they all give…”

Section: From Small To Moderate Strainsmentioning

confidence: 65%

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Methodical fitting for mathematical models of rubber-like materials

2017

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A great variety of models can describe the non-linear response of rubber to uni-axial tension. Yet an in-depth understanding of the successive stages of large extension is still lacking. We show that the response can be broken down in three steps, which we delineate by relying on a simple formatting of the data, the socalled Mooney transform. First, the small-to-moderate regime, where the polymeric chains unfold easily and the Mooney plot is almost linear. Second, the strainhardening regime, where blobs of bundled chains unfold to stiffen the response in correspondence to the "upturn" of the Mooney plot. Third, the limiting-chain regime, with a sharp stiffening occurring as the chains extend towards their limit. We provide strain-energy functions with terms accounting for each stage, that (i) give an accurate local and then global fitting of the data; (ii) are consistent with weak non-linear elasticity theory; and (iii) can be interpreted in the framework of statistical mechanics. We apply our method to Treloar's classical experimental data and also to some more recent data. Our method not only provides models that describe the experimental data with a very low quantitative relative error, but also shows that the theory of non-linear elasticity is much more robust that seemed at first sight.

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Section: From Small To Moderate Strainsmentioning

confidence: 65%

“…In passing we note that other sets of invariants exist, but that they are equivalent to our choice for all intents and purposes (Saccomandi 2015, Carroll 2011. This form of the strain-energy density leads to the usual representation formula for the Cauchy stress tensor T , due to Rivlin (1996)…”

Section: Choice Of Materials Parametersmentioning

confidence: 99%

Methodical fitting for mathematical models of rubber-like materials

2017

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“…So, if the chains in a particular network are joined at their centres and then affixed to the continuum, which is deformed as before, it should be clear that the stretches and the stored energy will be as before but the number of chains is doubled. The consistent chain counts are (3,6,4) or (6,12,8).…”

Section: (B) Counting Chainsmentioning

confidence: 99%

Molecular chain networks and strain energy functions in rubber elasticity

Carroll

2019

Phil. Trans. R. Soc. A.

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A relatively simple molecular–statistical model for rubber elasticity, similar to the Wang–Guth and the Arruda–Boyce (AB) models, is presented. Discussion of some approximate inverse Langevin functions leads to the selection of a new one as the most attractive balance between accuracy and simplicity. Use of this approximation with the AB model, in particular, yields the logarithmic strain energy introduced by Gent that exhibits limiting chain extensibility. A rather unusual facet of the relationship between the three strain energies is that the new one is the mean of the other two. This article is part of the theme issue ‘Rivlin's legacy in continuum mechanics and applied mathematics’.

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“…Gent and Thomas [16] proposed an empirical model similar to that of Mooney and Rivlin but containing a logarithmic function of the second invariant. Many other strain energy functions in terms of strain invariants are developed for modeling the nonlinear elastic behavior [17][18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Constitutive modeling of isotropic hyperelastic materials using proposed phenomenological models in terms of strain invariants

Bahreman

Darijani

Fooladi

2015

Polymer Engineering & Sci

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Rubber‐like materials deform largely and nonlinearly under loading and preserve their initial configuration after removal of the load. These materials are usually modeled as being homogeneous, isotropic, and incompressible elastic solids that are supported by experimental data. In this article, a general form for the strain energy density of these materials is assumed as the sum of two independent functions of the first and second strain invariants. Applying the essential requirements on the form of the strain energy density, the mathematical form of these functions is obtained as polynomial, logarithmic, and exponential. Then a general form is derived for the strain energy density of compressible materials and its effectiveness is evaluated for hydrostatic compression and uniaxial tension tests. The determination of material parameters and the evaluation of effectiveness of models are done based on the correlation between the values of the strain energy density (rather than the stresses) cast from the theory and the test data. Comparison of the theoretical predictions with the experimental data indicates that the represented models can achieve a satisfactory agreement with the behavior of different materials. POLYM. ENG. SCI., 56:299–308, 2016. © 2015 Society of Plastics Engineers

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A Strain Energy Function for Vulcanized Rubbers

Cited by 91 publications

References 14 publications

Methodical fitting for mathematical models of rubber-like materials

Methodical fitting for mathematical models of rubber-like materials

Molecular chain networks and strain energy functions in rubber elasticity

Constitutive modeling of isotropic hyperelastic materials using proposed phenomenological models in terms of strain invariants

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