Detail publikace

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

LASOTA, T. BURŠA, J. FEDOROVA, S.

Originální název

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

Anglický název

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

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.

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.

Dokumenty

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.",