A non-second-gradient model for nonlinear elastic bodies with fibre stiffness

被引:2
|
作者
Shariff, M. H. B. M. [1 ]
Merodio, J. [2 ]
Bustamante, R. [3 ]
机构
[1] Khalifa Univ Sci & Technol, Dept Math, Abu Dhabi, U Arab Emirates
[2] Univ Politecn Madrid, Dept Matemat Aplicada TIC, ETS Ingn Sistemas Informat, Madrid 28031, Spain
[3] Univ Chile, Dept Ingn Mecan, Beauchef 851, Santiago, Chile
关键词
FINITE DEFORMATIONS; SOLIDS;
D O I
10.1038/s41598-023-33670-6
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
In the past, to model fibre stiffness of finite-radius fibres, previous finite-strain (nonlinear) models were mainly based on the theory of non-linear strain-gradient (second-gradient) theory or Kirchhoff rod theory. We note that these models characterize the mechanical behaviour of polar transversely isotropic solids with infinitely many purely flexible fibres with zero radius. To introduce the effect of fibre bending stiffness on purely flexible fibres with zero radius, these models assumed the existence of couple stresses (contact torques) and non-symmetric Cauchy stresses. However, these stresses are not present on deformations of actual non-polar elastic solids reinforced by finite-radius fibres. In addition to this, the implementation of boundary conditions for second gradient models is not straightforward and discussion on the effectiveness of strain gradient elasticity models to mechanically describe continuum solids is still ongoing. In this paper, we develop a constitutive equation for a non-linear non-polar elastic solid, reinforced by embedded fibers, in which elastic resistance of the fibers to bending is modelled via the classical branches of continuum mechanics, where the development of the theory of stresses is based on non-polar materials; that is, without using the second gradient theory, which is associated with couple stresses and non-symmetric Cauchy stresses. In view of this, the proposed model is simple and somewhat more realistic compared to previous second gradient models.
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页数:10
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