Journal of Elasticity

, Volume 128, Issue 1, pp 115–145 | Cite as

On the Stress Field of a Nonlinear Elastic Solid Torus with a Toroidal Inclusion

  • Ashkan Golgoon
  • Arash YavariEmail author


In this paper we analyze the stress field of a solid torus made of an incompressible isotropic solid with a toroidal inclusion that is concentric with the solid torus and has a uniform distribution of pure dilatational finite eigenstrains. We use a perturbation analysis and calculate the residual stresses to the first order in the thinness ratio (the ratio of the radius of the generating circle and the overall radius of the solid torus). In particular, we show that the stress field inside the inclusion is not uniform. This is in contrast with the corresponding results for infinitely-long and finite circular cylindrical bars and spherical balls with cylindrical and spherical inclusions, respectively. We also show that for a solid torus of any size made of an incompressible linear elastic solid with an inclusion with uniform (infinitesimal) pure dilatational eigenstrains the stress inside the inclusion is not uniform.


Finite eigenstrains Geometric mechanics Nonlinear elasticity Elastic torus Inclusion 

Mathematics Subject Classification (2000)

74B20 70G45 70H09 35Q74 74Fxx 



This work was partially supported by ARO W911NF-16-1-0064, AFOSR—Grant No. FA9550-12-1-0290 and NSF—Grant No. CMMI 1130856 and CMMI 1561578.


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Copyright information

© Springer Science+Business Media Dordrecht 2017

Authors and Affiliations

  1. 1.School of Civil and Environmental EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.The George W. Woodruff School of Mechanical EngineeringGeorgia Institute of TechnologyAtlantaUSA

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