Numerical modelling of 2D composite solids accounting for local fibre bending stiffness

2020 ◽  
Vol 244 ◽  
pp. 112289
Author(s):  
Wajdi Zouari ◽  
Hocine Kebir ◽  
Mustapha Assarar ◽  
Tewfik Ghomari ◽  
Rezak Ayad
Keyword(s):  
Numerical Modelling ◽  
Bending Stiffness ◽  
Fibre Bending Stiffness

Finite deformations of fibre-reinforced elastic solids with fibre bending stiffness

2007 ◽  
Vol 42 (2) ◽  
pp. 355-368 ◽  
Author(s):  
A.J.M. Spencer ◽  
K.P. Soldatos
Keyword(s):  
Bending Stiffness ◽  
Finite Deformations ◽  
Elastic Solids ◽  
Fibre Bending Stiffness

scholarly journals A finite deformation isogeometric finite element approach to fibre-reinforced composites with fibre bending stiffness

2021 ◽  
Vol 128 (1) ◽  
Author(s):  
Carina Witt ◽  
Tobias Kaiser ◽  
Andreas Menzel
Keyword(s):  
Finite Element ◽  
Transverse Isotropy ◽  
Bending Stiffness ◽  
Reinforced Composites ◽  
Fibre Direction ◽  
Finite Element Approach ◽  
Continuity Properties ◽  
Element Approach ◽  
Fibre Reinforced Composites ◽  
Fibre Bending Stiffness

AbstractIt is a common technique in many fields of engineering to reinforce materials with certain types of fibres in order to enhance the mechanical properties of the overall material. Specific simulation methods help to predict the behaviour of these composites in advance. In this regard, a widely established approach is the incorporation of the fibre direction vector as an additional argument of the energy function in order to capture the specific material properties in the fibre direction. While this model represents the transverse isotropy of a material, it cannot capture effects that result from a bending of the fibres and does not include any length scale that might allow the simulation of size effects. In this contribution, an enhanced approach is considered which relies on the introduction of higher-gradient contributions of the deformation map in the stored energy density function and which eventually allows accounting for fibre bending stiffness in simulations. The respective gradient fields are approximated by NURBS basis functions within an isogeometric finite element framework by taking advantage of their characteristic continuity properties. The isogeometric finite element approach that is presented in this contribution for fibre-reinforced composites with fibre bending stiffness accounts for finite deformations. It is shown that the proposed method is in accordance with semi-analytical solutions for a representative boundary value problem. In an additional example it is observed that the initial fibre orientation and the particular bending stiffness of the fibres influence the deformation as well as the stress response of the material.

scholarly journals A coupled finite element approach for the modelling of composites with fibres possessing fibre-bending stiffness

PAMM ◽  
2016 ◽  
Vol 16 (1) ◽  
pp. 299-300
Author(s):  
Tobias Asmanoglo ◽  
Andreas Menzel
Keyword(s):  
Finite Element ◽  
Bending Stiffness ◽  
Finite Element Approach ◽  
Element Approach ◽  
Fibre Bending Stiffness

scholarly journals Finite deformations of fibre-reinforced elastic solids with fibre bending stiffness – Part II: determination of the spherical part of the couple-stress

2021 ◽  
pp. 108128652110615
Author(s):  
KP Soldatos
Keyword(s):  
Couple Stress ◽  
Fibrous Composite ◽  
Couple Stress Theory ◽  
Bending Stiffness ◽  
Theoretical Development ◽  
Theoretical Formulation ◽  
Elastic Deformations ◽  
Spherical Part ◽  
Fibre Bending Stiffness

The indeterminacy of the spherical part of couple-stress is a well-known drawback of any theoretical formulation stemming from the Cosserat couple-stress theory of elasticity. The relevant theory of finite elastic deformations of solids reinforced by a family of fibres that resist bending is not an exception. The present communication extends and completes that theory in a manner that enables it to measure the spherical part of the couple-stress tensor outside the conventional equilibrium considerations. To achieve this, the present study reconsiders an extra piece of information that has surprisingly emerged already but, so far, has been left unexplained and unexploited; namely, the fact that the energy stored in a fibrous composite elastic solid with fibre-bending stiffness involves a couple-stress generated term that does not influence the relevant couple-stress constitutive equation. The thus resulting new theoretical development complements the theory previously presented without dismissing any of the theoretical results detailed or the conclusions drawn there. Its validity embraces boundary value problems concerning both finite and infinitesimal elastic deformations of polar fibrous composites. In the latter case, its applicability is also tested and verified through the successful determination of the spherical couple-stress of a polar transversely isotropic elastic plate subjected to pure bending.

The Use of Array Processors for Numerical Modelling of Tidal Estuary Dynamics

1980 ◽  
Author(s):  
D. Prandle ◽  
E.R. Funke ◽  
N.L. Crookshank ◽  
R. Renner
Keyword(s):  
Numerical Modelling ◽  
Tidal Estuary ◽  
Array Processors
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