Acta Mechanica

, Volume 230, Issue 10, pp 3457–3475 | Cite as

Energy and volume changes due to the formation of a circular inhomogeneity in a residual deviatoric stress field

  • Marinos A. KattisEmail author
  • Elli Gkouti
  • Paraskevas Papanikos
Original Paper


An inclusion of purely dilatational eigenstrain in an infinitely extended isotropic elastic matrix, independently of its shape, causes a deviatoric stress field around it. The present paper analyses the energy and volume changes due to the formation of a circular inhomogeneity in a deviatoric stress field coming from a circular inclusion of dilatational eigenstrain. It is found that the elastic stress inside the inhomogeneity remains deviatoric and the inhomogeneity formation does not change the volume of the inclusion-matrix system; it is argued that the same occurs for any inclusion shape and non-uniform eigenstrain. The elastic energy changes occurring in the domains occupied by matrix, inhomogeneity, and inclusion are calculated, and its dependence on the elastic properties and geometrical parameters of inhomogeneity and matrix is numerically investigated. Strengthening effects of the matrix-inhomogeneity system are examined by means of the energy force and expanding moment acting on the inhomogeneity.



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Copyright information

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

Authors and Affiliations

  • Marinos A. Kattis
    • 1
    Email author
  • Elli Gkouti
    • 1
  • Paraskevas Papanikos
    • 2
  1. 1.School of Rural and Surveying EngineeringNational Technical University of AthensZographou, AthensGreece
  2. 2.Department of Product and Systems Design EngineeringUniversity of the AegeanErmoúpolisGreece

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