Abstract
Rubber components are used in almost all areas of industrial applications and are often surrounded by liquid media. Caused by thermodynamical reasons the ambient medium is diffusing into or out of the solid. In consequence, the solid can change in mass, volume and material properties. In this study, the diffusion and swelling behaviour using the example of an application of acrylonitrile-butadiene rubber (NBR) in mesitylene is experimentally investigated. For this purpose, sorption experiments are carried out. Within the framework of continuum mechanical material modelling, a thermodynamically consistent approach is presented, which describes non-linear diffusion of fluids in solids including the swelling phenomenon. Finite strains of the solid as well as an exchange of mass, linear and angular momentum, energy and entropy for open systems are considered. The resulting governing equations of such a multi-field problem are solved using the finite-element method. An optimisation strategy is presented by performing inverse calculations with the numerically converted material model to identify its relevant material parameters. Finally, the swelling of an NBR sealing in mesitylene is simulated.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
The index \(_{\mathrm{SR}}\) denotes the solid reference.
Total Lagrangian Formulation of the model is also conceivable, as Sect. 3.2.2 presents.
The strain rate tensor \(\mathbf{D}_{\mathrm{M}}\) represents the symmetric part of \(\mathbf{L}_{\mathrm{M}}\). To obtain a deviatoric structure of \(\mathbf{T}^{\mathrm{D}}\) an approach described in Lion et al. [14] is used. The relations for the heat flux vector \(\mathbf{q}\) as well as for the specific entropy \(\tilde{s}\) can be seen in the detail by Lion et al. [13].
Both the simulation and the experiments were carried out under isothermal conditions at \(\theta = 293\) K.
References
Achenbach M (2014) Zur simulation der volumenquellung von gummi. NAFEMS Magazin 32:67–73
Aminabhavi TM, Khinnavar RS (1993) Diffusion and sorption of organic liquids through polymer membranes: 10. polyurethane, nitrile-butadiene rubber and epichlorohydrin versus aliphatic alcohols (c1-c5). Polymer 34:1006–1018
Chai A, Andriyana A, Verron E, Johan M (2013) Mechanical characteristics of swollen elastomers under cyclic loading. Mater Des 44:566–572
Chester SA, Anand L (2010) A coupled theory of fluid permeation and large deformations for elastomeric materials. J Mech Phys Solids 58:1879–1906
Crank J et al (1979) The mathematics of diffusion. Oxford University Press, Oxford
Duda FP, Souza AC, Fried E (2010) A theory for species migration in a finitely strained solid with application to polymer network swelling. J Mech Phys Solids 58:515–529
Ehlers EW, Bluhm J (2002) Porous media. Springer, Berlin
Flory PJ (1950) Statistical mechanics of swelling of network structures. J Chem Phys 18:108–111
Flory PJ (1953) Principles of polymer chemistry. Cornell University Press, Ithaca
Greve R (2003) Kontinuumsmechanik. Springer, Berlin
Haupt P (2000) Continuum mechanics and theory of materials. Springer, Berlin
Hutter K, Jöhnk K (2004) Continuum methods of physical modeling. Springer, Berlin
Lion A, Johlitz M (2020) On the thermomechanics of solids surrounded by liquid media: balance equations, free energy and nonlinear diffusion. Continuum Mech Thermodyn 32:281–305
Lion A, Dippel B, Liebl C (2014) Thermomechanical material modelling based on a hybrid free energy density depending on pressure, isochoric deformation and temperature. Int J Solids Struct 51:729–739
Lubliner J (1985) A model of rubber viscoelasticity. Mech Res Commun 12:93–99
Müller I (2001) Grundzüge der Thermodynamik: mit historischen Anmerkungen. Springer, Berlin
Neff F, Lion A, Johlitz M (2019) Modelling diffusion induced swelling behaviour of natural rubber in an organic liquid. ZAMM J Appl Math Mech/Zeitschrift für Angewandte Mathematik und Mechanik 99:e201700280
Weitsman Y (1987) Stress assisted diffusion in elastic and viscoelastic materials. J Mech Phys Solids 35:73–93
Wriggers P (2001) Nichtlineare Finite-Elemente-Methoden. Springer, Berlin
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Dr Michael Johlitz, Guest Editor of this Special Issue [New Challenges and Methods in Experimental Investigations and Modelling of Elastomers] confirms that where he was co-author of a research article in this Special Issue, he was not involved in either the peer review or the decision-making process of that particular article.
Rights and permissions
About this article
Cite this article
Musil, B., Demmel, B., Lion, A. et al. A contribution to the chemomechanics of elastomers surrounded by liquid media: continuum mechanical approach for parameter identification using the example of sorption experiments. J Rubber Res 24, 271–279 (2021). https://doi.org/10.1007/s42464-021-00093-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s42464-021-00093-9