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Continuum Mechanics and Thermodynamics

, Volume 31, Issue 6, pp 1615–1625 | Cite as

On the correspondence between two- and three-dimensional Eshelby tensors

  • Victor A. Eremeyev
  • Violetta Konopińska-ZmysłowskaEmail author
Open Access
Original Article

Abstract

We consider both three-dimensional (3D) and two-dimensional (2D) Eshelby tensors known also as energy–momentum tensors or chemical potential tensors, which are introduced within the nonlinear elasticity and the resultant nonlinear shell theory, respectively. We demonstrate that 2D Eshelby tensor is introduced earlier directly using 2D constitutive equations of nonlinear shells and can be derived also using the through-the-thickness procedure applied to a 3D shell-like body.

Keywords

Eshelby tensor Nonlinear elasticity Nonlinear shell Phase transformations Through-the-thickness integration 

Notes

Acknowledgements

Authors are grateful to Prof. Arkadi Berezovski for the fruitful discussions.

V. Konopińska-Zmysłowska acknowledges the support from the National Centre of Science of Poland with the grant DEC-2012/05/D/ST8/02298.

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Authors and Affiliations

  1. 1.Gdańsk University of TechnologyGdańskPoland

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