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Journal of Elasticity

, Volume 111, Issue 1, pp 41–65 | Cite as

Derivation of the Linear Elastic String Model from Three-Dimensional Elasticity

  • Maroje Marohnić
  • Josip TambačaEmail author
Article

Abstract

We derive a one-dimensional model for the displacement and torsion of an elastic string starting from a cylindrical three-dimensional linearized prestressed elastic body with small diameter. The prestress is due to the prior elastic deformation of an isotropic, homogenous, elastic body. We deduce the scaling of forces by a formal asymptotic expansion. Then we prove that the family of solutions of three-dimensional problems converges to a limit that is the unique solution of the string model. Coefficients of the string model depend on the three-dimensional elasticity coefficients and the tension due to the predeformation.

Keywords

Elastic string Prestress Linearized elasticity Singular perturbation 

Mathematics Subject Classification (2010)

74K05 74B10 

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Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ZagrebZagrebCroatia

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