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

Autor: Claire Lestringant, Basile Audoly
Přispěvatelé: 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), Department of Engineering [Cambridge], University of Cambridge [UK] (CAM), Lestringant, Claire [0000-0002-6929-4655], Apollo - University of Cambridge Repository
Jazyk: angličtina
Rok vydání: 2021
Předmět:
Asymptotic analysis
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]
FOS: Physical sciences
02 engineering and technology
Kinematics
Elastic material
Condensed Matter - Soft Condensed Matter
[SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph]
01 natural sciences
010305 fluids & plasmas
Strain energy
Energy methods
0103 physical sciences
High order
Elasticity (economics)
[SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of the solides [physics.class-ph]
Physics
Mechanical Engineering
Mathematical analysis
16. Peace & justice
021001 nanoscience & nanotechnology
Condensed Matter Physics
Longitudinal direction
[SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Mechanics of the structures [physics.class-ph]
Nonlinear system
Mechanics of Materials
[SPI.MECA.STRU]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Structural mechanics [physics.class-ph]
Localization
Finite strain
Soft Condensed Matter (cond-mat.soft)
0210 nano-technology
Low symmetry
Zdroj: Journal of the Mechanics and Physics of Solids
Journal of the Mechanics and Physics of Solids, Elsevier, In press
Journal of the Mechanics and Physics of Solids, Elsevier, 2021, 148, pp.104264
ISSN: 0022-5096
Popis: International audience; 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.
Databáze: OpenAIRE
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