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Mathematical Modeling of Phenomena Caused by Surface Stresses in Solids

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Surface Effects in Solid Mechanics

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 30))

Abstract

Interfacial region between two bulk phases and the transition region near the line of contact of three media are considered as a two-dimensional and one-dimensional continuum, respectively. A survey of works on mathematical modeling of phenomena in such systems is presented. The equation of the linear momentum balance for an interface generalizes the classical Laplace equation and that for a contact line generalizes the Young equation of the capillarity theory. The influence of nonuniform surface tension on the stress field in an infinite cylinder is investigated. The anisotropy of wetting is discussed and explained on the basis of the generalized Young equation taking into account the tensor character of surface stresses. Several applications of the results in the theory of surface defects are also discussed.

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  1. Institute of Mathematics and Computer Science, Jan Długosz University in Czȩstochowa, Armii Krajowej 13/15, 42-200 , Czȩstochowa, Poland

    Yuriy Povstenko

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  1. , Lehrstuhl für Technische Mechanik, Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, Magdeburg, 39106, Germany

    Holm Altenbach

  2. St. Petersburg State University, Bibliotechnaya sq. 2, St. Petersburg, 198904, Russia

    Nikita F Morozov

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Povstenko, Y. (2013). Mathematical Modeling of Phenomena Caused by Surface Stresses in Solids. In: Altenbach, H., Morozov, N. (eds) Surface Effects in Solid Mechanics. Advanced Structured Materials, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35783-1_11

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