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

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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Zagreb, Zagreb, Croatia

    Maroje Marohnić & Josip Tambača

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  1. Maroje Marohnić
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  2. Josip Tambača
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Correspondence to Josip Tambača.

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Marohnić, M., Tambača, J. Derivation of the Linear Elastic String Model from Three-Dimensional Elasticity. J Elast 111, 41–65 (2013). https://doi.org/10.1007/s10659-012-9394-1

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  • DOI: https://doi.org/10.1007/s10659-012-9394-1

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