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Asymptotically exact strain-gradient models for nonlinear slender elastic structures: a systematic derivation method

Accepted version
Peer-reviewed

Type

Article

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Authors

Lestringant, Claire  ORCID logo  https://orcid.org/0000-0002-6929-4655
Audoly, Basile 

Abstract

We propose a general method for deriving one-dimensional models for nonlinear structures. It captures the contribution to the strain energy arising not only from the macroscopic elastic strain as in classical structural models, but also from the strain gradient. As an illustration, we derive one-dimensional strain-gradient models for a hyper-elastic cylinder that necks, an axisymmetric membrane that produces bulges, and a two-dimensional block of elastic material subject to bending and stretching. The method offers three key advantages. First, it is nonlinear and accounts for large deformations of the cross-section, which makes it well suited for the analysis of localization in slender structures. Second, it does not require any a priori assumption on the form of the elastic solution in the cross-section, i.e., it is Ansatz-free. Thirdly, it produces one-dimensional models that are asymptotically exact when the macroscopic strain varies on a much larger length scale than the cross-section diameter.

Description

Keywords

physics.app-ph, physics.app-ph

Journal Title

Journal of the Mechanics and Physics of Solids

Conference Name

Journal ISSN

0022-5096

Volume Title

136

Publisher

Elsevier BV

Rights

All rights reserved