Publication detail

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

LASOTA, T. BURŠA, J. FEDOROVA, S.

Original Title

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

English Title

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

Type

conference paper

Language

en

Original Abstract

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.

English abstract

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.

Keywords

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

RIV year

2012

Released

04.09.2012

Publisher

Elsevier

Location

Vienna

ISBN

978-3-9502481-9-7

Book

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

Pages from

3379

Pages to

3389

Pages count

11

Documents

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",
annote="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.",