Konstitutivní rovnice a konečnoprvková formulace pro anizotropní hyprelastický kompozit, založené na svázané Cosseratově teorii kontinua

Constitutive equations and finite element formulation for anisotropic hyperelastic composites based on constrained Cosserat continuum

conference paper

en

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.

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.

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.

Anizotropie; Hyperelasticita; Vláknový kompozit; Cosseratovo kontinuum; Metoda konečných prvků.

hyperelasticity, anisotropy, fibre composite, Cosserat continuum, finite element method

2012

04.09.2012

Elsevier

Vienna

978-3-9502481-9-7

ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers

3379–3389

11