Asymptotic models for curved rods derived from nonlinear elasticity by Gamma-convergence

Details Asymptotic models for curved rods derived from nonlinear elasticity by Gamma-convergence Asymptotic models for curved rods derived from nonlinear elasticity by Gamma-convergence

2008-03-06

arxiv.org/abs/0803.0927v1

Physics

Mathematical Physics

25 pages

Scientific paper

We study the problem of the rigorous derivation of one-dimensional models for a thin curved beam starting from three-dimensional nonlinear elasticity. We describe the limiting models obtained for different scalings of the energy. In particular, we prove that the limit functional corresponding to higher scalings coincides with the one derived by dimension reduction starting from linearized elasticity. Finally we also address the case of thin elastic rings.

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