Recursive derivation of one-dimensional models from three-dimensional nonlinear elasticity

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.