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On chemical reaction planar fronts in an elastic–viscoelastic mechanical framework

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Abstract

A stress-affected chemical reaction front propagation is considered using the concept of a chemical affinity tensor. A reaction between an elastic solid constituent and a diffusing constituent, localized at the reaction front, is considered. As a result of the reaction, the elastic constituent transforms into viscoelastic one. The reaction is accompanied by volume expansion that in turn may result in stresses at the reaction front, which affect the front velocity through the normal component of the chemical affinity tensor. Considering a plane strain problem with a planar chemical reaction front propagation under uniaxial deformation, we focus on the studies of the reaction front kinetics in dependence on external strains and material parameters with the use of the notion of the equilibrium concentration. Then, stress relaxation behind the propagating reaction front is modeled. A standard linear solid model is used for the reaction product, and its particular cases are also considered. Analytical solutions are obtained which allow to study in explicit form the strain influence and material parameters on the front retardation or acceleration and stress relaxation.

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Acknowledgements

ABF greatly appreciates the financial support provided by the Russian Science Foundation (Grant No. 19-19-00552). SP and ECh are grateful for the financial support provided by the Chaire André Citroën between Stellantis and Ecole Polytechnique

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Authors and Affiliations

  1. Laboratoire de Mécanique des Solides (CNRS UMR 7649), Ecole Polytechnique, Institut Polytechnique de Paris, Route de Saclay, 91120, Palaiseau, France

    Svetlana Petrenko & Eric Charkaluk

  2. Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, Bol’shoy pr. 61, V.O., St. Petersburg, Russia, 199178

    Alexander B. Freidin

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  1. Svetlana Petrenko
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  2. Alexander B. Freidin
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  3. Eric Charkaluk
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Correspondence to Alexander B. Freidin.

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Communicated by Andreas Öchsner.

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Petrenko, S., Freidin, A.B. & Charkaluk, E. On chemical reaction planar fronts in an elastic–viscoelastic mechanical framework. Continuum Mech. Thermodyn. 34, 137–163 (2022). https://doi.org/10.1007/s00161-021-01051-x

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