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Nonclassical Linear Theories of Continuum Mechanics

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We present a brief survey of nonclassical linear theories of continuum mechanics. Thus, we give a concise characterization of the Eringen–Edelen nonlocal theory of elasticity, theories of polar and micropolar media, Toupin couple-stress theory of elasticity, Eringen–Suhubi–Mindlin micromorphic theory, Mindlin gradient theory of elasticity, and also the local gradient theory of deformation of elastic media that takes into account local mass displacements.

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  1. Institute of Construction and Architecture, Slovak Academy of Sciences, Bratislava, Slovakia

    О. R. Hrytsyna

  2. Center of Mathematical Modeling, Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, National Academy of Sciences of Ukraine, Lviv, Ukraine

    О. R. Hrytsyna

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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 63, No. 3, pp. 85–106, July–September, 2020.

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Hrytsyna, О.R. Nonclassical Linear Theories of Continuum Mechanics. J Math Sci 273, 101–123 (2023). https://doi.org/10.1007/s10958-023-06487-x

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