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A finite deformation continuum modelling framework for curvature effects in fibre-reinforced nanocomposites

Asmanoglo, Tobias and Menzel, Andreas LU (2017) In Journal of the Mechanics and Physics of Solids 107. p.411-432
Abstract

Motivated by experimental findings on one-dimensional nano-materials, this contribution focusses on the elaboration of a fibre curvature based higher-order gradient contribution to the stored energy function in a finite deformation setting. The presented approach is based on the fundamental theoretical developments for fibre-reinforced composites presented by Spencer and Soldatos (2007), which take into account the fibre-bending stiffness in addition to the directional dependency induced by the fibres. A mixed-type finite element formulation is then used for the solution of the resulting system of coupled partial differential equations. A specific form of the stored energy function is introduced such that well-interpretable... (More)

Motivated by experimental findings on one-dimensional nano-materials, this contribution focusses on the elaboration of a fibre curvature based higher-order gradient contribution to the stored energy function in a finite deformation setting. The presented approach is based on the fundamental theoretical developments for fibre-reinforced composites presented by Spencer and Soldatos (2007), which take into account the fibre-bending stiffness in addition to the directional dependency induced by the fibres. A mixed-type finite element formulation is then used for the solution of the resulting system of coupled partial differential equations. A specific form of the stored energy function is introduced such that well-interpretable contributions to the stress- and the couple stress tensor are obtained. It is shown that this framework may, in principle, account for fibres of different diameters and induces a natural length scale into the model. Such continuum theory covering size-effects is of special interest since experiments for different materials suggest significant size-effects at small length scales.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
B anisotropic material, B fiber-reinforced composite material, C finite elements, Curvature- and size effects in nanocomposites
in
Journal of the Mechanics and Physics of Solids
volume
107
pages
22 pages
publisher
Elsevier
external identifiers
  • scopus:85025809554
  • wos:000409151500022
ISSN
0022-5096
DOI
10.1016/j.jmps.2017.06.012
language
English
LU publication?
yes
id
41444d2c-42c4-4e50-82f7-b9c7852773ea
date added to LUP
2017-08-02 07:29:04
date last changed
2018-01-16 13:22:09
@article{41444d2c-42c4-4e50-82f7-b9c7852773ea,
  abstract     = {<p>Motivated by experimental findings on one-dimensional nano-materials, this contribution focusses on the elaboration of a fibre curvature based higher-order gradient contribution to the stored energy function in a finite deformation setting. The presented approach is based on the fundamental theoretical developments for fibre-reinforced composites presented by Spencer and Soldatos (2007), which take into account the fibre-bending stiffness in addition to the directional dependency induced by the fibres. A mixed-type finite element formulation is then used for the solution of the resulting system of coupled partial differential equations. A specific form of the stored energy function is introduced such that well-interpretable contributions to the stress- and the couple stress tensor are obtained. It is shown that this framework may, in principle, account for fibres of different diameters and induces a natural length scale into the model. Such continuum theory covering size-effects is of special interest since experiments for different materials suggest significant size-effects at small length scales.</p>},
  author       = {Asmanoglo, Tobias and Menzel, Andreas},
  issn         = {0022-5096},
  keyword      = {B anisotropic material,B fiber-reinforced composite material,C finite elements,Curvature- and size effects in nanocomposites},
  language     = {eng},
  month        = {10},
  pages        = {411--432},
  publisher    = {Elsevier},
  series       = {Journal of the Mechanics and Physics of Solids},
  title        = {A finite deformation continuum modelling framework for curvature effects in fibre-reinforced nanocomposites},
  url          = {http://dx.doi.org/10.1016/j.jmps.2017.06.012},
  volume       = {107},
  year         = {2017},
}