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On the central role of the invariant I2 in nonlinear elasticity

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On the central role of the invariant I2 in nonlinear elasticity. / Anssari-Benam, Afshin; Bucchi, Andrea; Saccomandi, Giuseppe.

In: International Journal of Engineering Science, Vol. 163, 103486, 01.06.2021, p. 1-27.

Research output: Contribution to journalArticlepeer-review

Harvard

Anssari-Benam, A, Bucchi, A & Saccomandi, G 2021, 'On the central role of the invariant I2 in nonlinear elasticity', International Journal of Engineering Science, vol. 163, 103486, pp. 1-27. https://doi.org/10.1016/j.ijengsci.2021.103486

APA

Anssari-Benam, A., Bucchi, A., & Saccomandi, G. (2021). On the central role of the invariant I2 in nonlinear elasticity. International Journal of Engineering Science, 163, 1-27. [103486]. https://doi.org/10.1016/j.ijengsci.2021.103486

Vancouver

Anssari-Benam A, Bucchi A, Saccomandi G. On the central role of the invariant I2 in nonlinear elasticity. International Journal of Engineering Science. 2021 Jun 1;163:1-27. 103486. https://doi.org/10.1016/j.ijengsci.2021.103486

Author

Anssari-Benam, Afshin ; Bucchi, Andrea ; Saccomandi, Giuseppe. / On the central role of the invariant I2 in nonlinear elasticity. In: International Journal of Engineering Science. 2021 ; Vol. 163. pp. 1-27.

Bibtex

@article{2a774e80a8dc44daac7ae55bec7dfd49,
title = "On the central role of the invariant I2 in nonlinear elasticity",
abstract = "The necessity of the inclusion of the second invariant of the left Cauchy-Green deformation tensor B, namely I2, in the strain energy function W of rubber-like materials is analysed. Universal relationships that underline such necessity are revisited, and experimental data are examined to establish the trends in the variation of ∂W/∂I2. Corroborated by the established experimental trends, we consider (meso)structural arguments to devise a plausible approach for incorporation of I2 into the W function. On the basis of the molecular theory of rubbers and considering the entanglements as a topological tube constraint, our analysis confers that a first approximation of W (I1, I2) is of the form W (I1,I2 ) = f (I1 ) + g (I2). The f (I1 ) contribution may be that of any classical generalised neo-Hookean model, and the functional form of g (I2) is directly deduced from the tube model of entangled molecules. An additional logarithmic functional form of I2 is also devised based on the rational approximation of the response function β-1. The ensuing additive-type W (I1,I2 ) models are then compared with experimental datasets. While this additive consideration may not be sufficient to account for all aspects of the mechanics of rubber-like materials, the fitting results demonstrate an eminent improvement in the predictions of the additive-type models compared with generalised neo-Hookean models having the same number of constitutive parameters. These analyses underline the central role of I2 in modelling the finite deformation of rubber-like materials.",
keywords = "Additive split of W ( I 1 , I 2 ), I 2 term, Modelling, Rubber-like materials, Logarithmic I 2 term",
author = "Afshin Anssari-Benam and Andrea Bucchi and Giuseppe Saccomandi",
year = "2021",
month = jun,
day = "1",
doi = "10.1016/j.ijengsci.2021.103486",
language = "English",
volume = "163",
pages = "1--27",
journal = "International Journal of Engineering Science",
issn = "0020-7225",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - On the central role of the invariant I2 in nonlinear elasticity

AU - Anssari-Benam, Afshin

AU - Bucchi, Andrea

AU - Saccomandi, Giuseppe

PY - 2021/6/1

Y1 - 2021/6/1

N2 - The necessity of the inclusion of the second invariant of the left Cauchy-Green deformation tensor B, namely I2, in the strain energy function W of rubber-like materials is analysed. Universal relationships that underline such necessity are revisited, and experimental data are examined to establish the trends in the variation of ∂W/∂I2. Corroborated by the established experimental trends, we consider (meso)structural arguments to devise a plausible approach for incorporation of I2 into the W function. On the basis of the molecular theory of rubbers and considering the entanglements as a topological tube constraint, our analysis confers that a first approximation of W (I1, I2) is of the form W (I1,I2 ) = f (I1 ) + g (I2). The f (I1 ) contribution may be that of any classical generalised neo-Hookean model, and the functional form of g (I2) is directly deduced from the tube model of entangled molecules. An additional logarithmic functional form of I2 is also devised based on the rational approximation of the response function β-1. The ensuing additive-type W (I1,I2 ) models are then compared with experimental datasets. While this additive consideration may not be sufficient to account for all aspects of the mechanics of rubber-like materials, the fitting results demonstrate an eminent improvement in the predictions of the additive-type models compared with generalised neo-Hookean models having the same number of constitutive parameters. These analyses underline the central role of I2 in modelling the finite deformation of rubber-like materials.

AB - The necessity of the inclusion of the second invariant of the left Cauchy-Green deformation tensor B, namely I2, in the strain energy function W of rubber-like materials is analysed. Universal relationships that underline such necessity are revisited, and experimental data are examined to establish the trends in the variation of ∂W/∂I2. Corroborated by the established experimental trends, we consider (meso)structural arguments to devise a plausible approach for incorporation of I2 into the W function. On the basis of the molecular theory of rubbers and considering the entanglements as a topological tube constraint, our analysis confers that a first approximation of W (I1, I2) is of the form W (I1,I2 ) = f (I1 ) + g (I2). The f (I1 ) contribution may be that of any classical generalised neo-Hookean model, and the functional form of g (I2) is directly deduced from the tube model of entangled molecules. An additional logarithmic functional form of I2 is also devised based on the rational approximation of the response function β-1. The ensuing additive-type W (I1,I2 ) models are then compared with experimental datasets. While this additive consideration may not be sufficient to account for all aspects of the mechanics of rubber-like materials, the fitting results demonstrate an eminent improvement in the predictions of the additive-type models compared with generalised neo-Hookean models having the same number of constitutive parameters. These analyses underline the central role of I2 in modelling the finite deformation of rubber-like materials.

KW - Additive split of W ( I 1 , I 2 )

KW - I 2 term

KW - Modelling

KW - Rubber-like materials

KW - Logarithmic I 2 term

U2 - 10.1016/j.ijengsci.2021.103486

DO - 10.1016/j.ijengsci.2021.103486

M3 - Article

VL - 163

SP - 1

EP - 27

JO - International Journal of Engineering Science

JF - International Journal of Engineering Science

SN - 0020-7225

M1 - 103486

ER -

ID: 27538772