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

Autor: Claire Lestringant, Basile Audoly
Přispěvatelé: Institut Jean le Rond d'Alembert (DALEMBERT), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de mécanique des solides (LMS), École polytechnique (X)-MINES ParisTech - École nationale supérieure des mines de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), Lestringant, Claire [0000-0002-6929-4655], Apollo - University of Cambridge Repository
Jazyk: angličtina
Rok vydání: 2020
Předmět:
Length scale
Asymptotic analysis
A Localization B elastic material
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]
Rotational symmetry
FOS: Physical sciences
Applied Physics (physics.app-ph)
02 engineering and technology
Bending
C energy methods
[SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph]
01 natural sciences
010305 fluids & plasmas
Strain energy
0103 physical sciences
Cylinder
B finite strain
Physics
Mechanical Engineering
Mathematical analysis
C asymptotic analysis
Physics - Applied Physics
021001 nanoscience & nanotechnology
Condensed Matter Physics
Nonlinear system
Mechanics of Materials
[SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph]
Finite strain theory
0210 nano-technology
physics.app-ph
Zdroj: Journal of the Mechanics and Physics of Solids
Journal of the Mechanics and Physics of Solids, Elsevier, 2020, pp.103730. ⟨10.1016/j.jmps.2019.103730⟩
ISSN: 0022-5096
DOI: 10.1016/j.jmps.2019.103730⟩
Popis: International audience; 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 o↵ers 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.
Databáze: OpenAIRE
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