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Article Dans Une Revue Journal of the Mechanics and Physics of Solids Année : 2021

Asymptotic derivation of high-order rod models from non-linear 3D elasticity

Basile Audoly
Claire Lestringant

Résumé

We propose a method for deriving equivalent one-dimensional models for slender non-linear structures. The approach is designed to be broadly applicable, and can handle in principle finite strains, finite rotations, arbitrary cross-sections shapes, inhomogeneous elastic properties across the crosssection, arbitrary elastic constitutive laws (possibly with low symmetry) and arbitrary distributions of pre-strain, including finite pre-strain. It is based on a kinematic parameterization of the actual configuration that makes use of a center-line, a frame of directors, and local degrees of freedom capturing the detailed shape of cross-sections. A relaxation method is applied that holds the framed center-line fixed while relaxing the local degrees of freedom; it is asymptotically valid when the macroscopic strain and the properties of the rod vary slowly in the longitudinal direction. The outcome is a one-dimensional strain energy depending on the apparent stretching, bending and twisting strain of the framed center-line; the dependence on the strain gradients is also captured, yielding an equivalent rod model that is asymptotically exact to higher order. The method is presented in a fully non-linear setting and it is verified against linear and weakly non-linear solutions available from the literature.
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Dates et versions

hal-03024975 , version 1 (26-11-2020)
hal-03024975 , version 2 (16-12-2020)
hal-03024975 , version 3 (30-12-2020)

Identifiants

  • HAL Id : hal-03024975 , version 3

Citer

Basile Audoly, Claire Lestringant. Asymptotic derivation of high-order rod models from non-linear 3D elasticity. Journal of the Mechanics and Physics of Solids, 2021, 148, pp.104264. ⟨hal-03024975v3⟩
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