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Mass Sources and Modeling of Subsurface Heterogeneities in Deformable Solids

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We propose an approach to the description of thermoelastic processes in deformable solids with regard for the structural heterogeneity of the material and the geometric heterogeneity of the surface of the body. In formulating the source relations, we use the methods of thermodynamics of nonequilibrium processes and nonlinear continuum mechanics. We take into account the structure of the material by introducing an irreversible component of the vector of mass flow. The geometric subsurface heterogeneity of the body is taken into account by introducing mass sources modeling its properties and by the dependence of the characteristics of materials, including the moduli of elasticity, on density. We study the equilibrium state of the half space. It is shown that two characteristic sizes correspond to the distributions of stresses and density. One of these sizes is connected with the structural heterogeneity of the material and the other is connected with the geometric heterogeneity of the actual surface of the body. We discuss the limits of applicability of the local gradient approach in the case of linearized approximation.

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Authors and Affiliations

  1. Center of Mechanical Modeling, Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine

    T. S. Nahirnyi

  2. University of Zielona Góra, Zielona Góra, Poland

    T. S. Nahirnyi

  3. Franko Lviv National University, Lviv, Ukraine

    K. A. Chervinka

Authors
  1. T. S. Nahirnyi
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  2. K. A. Chervinka
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 57, No. 4, pp. 84–94, October–December, 2014.

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Nahirnyi, T.S., Chervinka, K.A. Mass Sources and Modeling of Subsurface Heterogeneities in Deformable Solids. J Math Sci 220, 103–115 (2017). https://doi.org/10.1007/s10958-016-3170-x

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