Continuum Mechanics and Thermodynamics

, Volume 31, Issue 6, pp 1795–1803 | Cite as

Surface elasticity effect on diffusional growth of surface defects in strained solids

  • Sergey KostyrkoEmail author
  • Gleb Shuvalov
Original Article


This paper presents a theoretical approach that allows to predict the nucleation of surface topological defects under the mechanical loading taking into account the thermodynamic and elastic properties of solid surface as well as its geometrical characteristics. Assuming that the surface atomic layers are thermodynamically unstable under the certain conditions, we obtain the evolution equation describing the kinetics of the relief formation in the case of diffusion mass transport activated by the stress field. The rate of growth of surface defects depends on the field of bulk and surface stresses, which vary with the shape and size of the considered defects. To find the stress state, we use the first-order perturbation solution of a 2D boundary value problem formulated in the terms of the constitutive equations of bulk and surface elasticity. The solution of linearized evolution equation gives the critical values of the ridges size and the initial level of stresses, which stabilize surface profile.


Surface diffusion Surface stress Evolution equation Boundary perturbation method 


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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.St. Petersburg State UniversitySt. PetersburgRussia

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