Geodesic
Equation of state for S2 glass-fiber reinforced polymer composite
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 12 (2020) no. 3, pp. 48-55

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This article presents the results of building a semi-empirical equation of state for S2 glass-fiber reinforced polymer composite. The equation of state includes the heat and cold elements. To describe the cold element of the equation of state, the substantiation has been performed for the choice of the form ($m$ and $n$) of the intermolecular potential adequately describing the structure of interactions in the composite material's components. To describe the heat element of this equation of state, the Helmholtz free energy has been determined with the Debye approximation. When building the equation of state, it has been shown that the equation of state for S2 glass-fiber reinforced polymer composite can be presented in the form of a Mie-Grüneisen equation. A type of dependency has been suggested between the Grüneisen coefficient and the volume, as well as an approach to determining the Grüneisen coefficient at the initial conditions of holding an experiment on the shock-wave exposure of the composite material. Experimental and calculated shock adiabats have been built for the for S2 glass-fiber reinforced polymer composite. The equality of the first and second derivatives of the experimental and theoretical shock adiabats in the point determining the initial state of the composite material has allowed to determine the coefficients being part of the structure ($m$ and $n$) of the intermolecular potential of the composite material's components. The comparing of the pressures calculated as per the work-determined equation of state for S2 glass-fiber reinforced polymer composite, with an experimental shock adiabat, has shown that those correspond with a difference of less than $1 \%$.
Keywords: equation of state, Helmholtz energy
Mots-clés : Debye approximation, Grüneisen coefficient, Mie-Grüneisen equation. 
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     author = {Yu. M. Kovalev},
     title = {Equation of state for {S2} glass-fiber reinforced polymer composite},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matematika, mehanika, fizika},
     pages = {48--55},
     publisher = {mathdoc},
     volume = {12},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VYURM_2020_12_3_a6/}
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Yu. M. Kovalev. Equation of state for S2 glass-fiber reinforced polymer composite. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematika, mehanika, fizika, Tome 12 (2020) no. 3, pp. 48-55. http://geodesic.mathdoc.fr/item/VYURM_2020_12_3_a6/