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Recursive Derivation of One-Dimensional Models from Three-Dimensional Nonlinear Elasticity

Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 175 rue du Chevaleret, Paris 75013, France

In this paper, we consider a formal asymptotic study of homogeneous slender cylinders made of a Saint-Venant Kirchhoff material submitted to dead loads. Depending on the order of magnitude of the applied loads, we obtain a hierarchy of four one-dimensional models starting from the nonlinear theory of extensible strings to the nonlinear theory of flexible bars. Our approach is based on the resolution of a sequence of recursive minimization problems.

Key Words: elasticity • rods • strings • asymptotic expansions • variational methods

Mathematics and Mechanics of Solids, Vol. 13, No. 2, 172-194 (2008)
DOI: 10.1177/1081286506075357


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