Detail publikace
Konstitutivní rovnice a konečnoprvková formulace pro anizotropní hyprelastický kompozit, založené na svázané Cosseratově teorii kontinua
LASOTA, T. BURŠA, J. FEDOROVA, S.
Český název
Konstitutivní rovnice a konečnoprvková formulace pro anizotropní hyprelastický kompozit, založené na svázané Cosseratově teorii kontinua
Anglický název
Constitutive equations and finite element formulation for anisotropic hyperelastic composites based on constrained Cosserat continuum
Typ
článek ve sborníku ve WoS nebo Scopus
Jazyk
en
Originální abstrakt
The paper deals with computational simulations of composites with hyperelastic matrix and steel fibres. By comparing different models we found out that present anisotropic hyperelastic models are able to give realistic results only if the fibres are tensed without bending. Hence, we followed Spencer and Soldatos who introduced constitutive equations for anisotropic hyperelastic fibre reinforced composites with bending stiffness of fibres, based on constrained Cosserat theory, which is very complex for practical use. Therefore, we applied some simplifications introduced by Spencer and added some others. After derivation of simplified equations, finite element formulation was elaborated. Due to constraint between rotations and displacements, second derivatives of displacements occur in the finite element formulation. To achieve convergence, continuity of displacements and their first derivatives must be satisfied at element boundaries. We proposed formulation based on minimization of the functional with displacements, rotations and Lagrange multiplier as degrees of freedom.
Český abstrakt
Článek se zabývá návrhem konstitutivních rovnic pro kompozity s elastomerovou matricí vyztuženou vlákny s nenulovou ohybovou tuhostí. Navržené konstitutivní rovnice jsou založeny na svázané Cosseratově teorii kontinua. Jaou analyzovány možnosti implementace těchto konstitutivních rovnic do programu pro metodu konečných prvků.
Anglický abstrakt
The paper deals with computational simulations of composites with hyperelastic matrix and steel fibres. By comparing different models we found out that present anisotropic hyperelastic models are able to give realistic results only if the fibres are tensed without bending. Hence, we followed Spencer and Soldatos who introduced constitutive equations for anisotropic hyperelastic fibre reinforced composites with bending stiffness of fibres, based on constrained Cosserat theory, which is very complex for practical use. Therefore, we applied some simplifications introduced by Spencer and added some others. After derivation of simplified equations, finite element formulation was elaborated. Due to constraint between rotations and displacements, second derivatives of displacements occur in the finite element formulation. To achieve convergence, continuity of displacements and their first derivatives must be satisfied at element boundaries. We proposed formulation based on minimization of the functional with displacements, rotations and Lagrange multiplier as degrees of freedom.
Klíčová slova česky
Anizotropie; Hyperelasticita; Vláknový kompozit; Cosseratovo kontinuum; Metoda konečných prvků.
Klíčová slova anglicky
hyperelasticity, anisotropy, fibre composite, Cosserat continuum, finite element method
Rok RIV
2012
Vydáno
04.09.2012
Nakladatel
Elsevier
Místo
Vienna
ISBN
978-3-9502481-9-7
Kniha
ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers
Strany od–do
3379–3389
Počet stran
11
BIBTEX
@inproceedings{BUT97229,
author="Tomáš {Lasota} and Jiří {Burša} and Svitlana {Fedorova},
title="Constitutive equations and finite element formulation for anisotropic hyperelastic composites based on constrained Cosserat continuum",
booktitle="ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers",
year="2012",
month="September",
pages="3379--3389",
publisher="Elsevier",
address="Vienna",
isbn="978-3-9502481-9-7"
}