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Fibre-reinforced composites with fibre-bending stiffness under azimuthal shear – Comparison of simulation results with analytical solutions

Asmanoglo, Tobias and Menzel, Andreas LU (2017) In International Journal of Non-Linear Mechanics 91. p.128-139
Abstract

In Ref. [1], Spencer and Soldatos proposed an enhanced modelling approach for fibre-reinforced composites which accounts for the fibre-bending stiffness in addition to the directional dependency induced by the fibres. Although analytical solutions for simple geometries have been derived over the past years, often subject to specific assumptions such as small deformation kinematics, the application to more general and non-academic boundary value problems is desirable. Motivated by the latter, the numerical solution of the general system of partial differential equations by means of a multi-field finite element approach is proposed in Ref. [2] and the principal model properties are studied for a specific form of the elastic energy... (More)

In Ref. [1], Spencer and Soldatos proposed an enhanced modelling approach for fibre-reinforced composites which accounts for the fibre-bending stiffness in addition to the directional dependency induced by the fibres. Although analytical solutions for simple geometries have been derived over the past years, often subject to specific assumptions such as small deformation kinematics, the application to more general and non-academic boundary value problems is desirable. Motivated by the latter, the numerical solution of the general system of partial differential equations by means of a multi-field finite element approach is proposed in Ref. [2] and the principal model properties are studied for a specific form of the elastic energy potential. In the present contribution a comparison of the numerical solution by means of the multi-field finite element approach against the analytical solution is presented for the azimuthal shear deformation of a tube-like structure. To this end, the general deformation pattern and especially the distribution of the stress and couple stress tensor are taken into account. We find that, although the analytical solution is derived subject to the assumption of small deformations, whereas the numerical solution is based on the finite strain counterpart of the theory, the simulation results are quasi identical, which verifies the numerical framework proposed.

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organization
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Contribution to journal
publication status
published
subject
keywords
Comparison of finite element simulations with analytical solutions, Fibre-reinforced composites with fibre-bending stiffness, Generalised continuum, Multi-field mixed-type finite element approach
in
International Journal of Non-Linear Mechanics
volume
91
pages
12 pages
publisher
Elsevier
external identifiers
  • scopus:85014165481
  • wos:000401384100012
ISSN
0020-7462
DOI
10.1016/j.ijnonlinmec.2017.01.001
language
English
LU publication?
yes
id
5108a2e0-5fc6-4a1f-8c4d-0eba4a91b474
date added to LUP
2017-03-14 10:48:42
date last changed
2018-01-07 11:55:06
@article{5108a2e0-5fc6-4a1f-8c4d-0eba4a91b474,
  abstract     = {<p>In Ref. [1], Spencer and Soldatos proposed an enhanced modelling approach for fibre-reinforced composites which accounts for the fibre-bending stiffness in addition to the directional dependency induced by the fibres. Although analytical solutions for simple geometries have been derived over the past years, often subject to specific assumptions such as small deformation kinematics, the application to more general and non-academic boundary value problems is desirable. Motivated by the latter, the numerical solution of the general system of partial differential equations by means of a multi-field finite element approach is proposed in Ref. [2] and the principal model properties are studied for a specific form of the elastic energy potential. In the present contribution a comparison of the numerical solution by means of the multi-field finite element approach against the analytical solution is presented for the azimuthal shear deformation of a tube-like structure. To this end, the general deformation pattern and especially the distribution of the stress and couple stress tensor are taken into account. We find that, although the analytical solution is derived subject to the assumption of small deformations, whereas the numerical solution is based on the finite strain counterpart of the theory, the simulation results are quasi identical, which verifies the numerical framework proposed.</p>},
  author       = {Asmanoglo, Tobias and Menzel, Andreas},
  issn         = {0020-7462},
  keyword      = {Comparison of finite element simulations with analytical solutions,Fibre-reinforced composites with fibre-bending stiffness,Generalised continuum,Multi-field mixed-type finite element approach},
  language     = {eng},
  month        = {05},
  pages        = {128--139},
  publisher    = {Elsevier},
  series       = {International Journal of Non-Linear Mechanics},
  title        = {Fibre-reinforced composites with fibre-bending stiffness under azimuthal shear – Comparison of simulation results with analytical solutions},
  url          = {http://dx.doi.org/10.1016/j.ijnonlinmec.2017.01.001},
  volume       = {91},
  year         = {2017},
}