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Modeling Rubber and Viscoelasticity with Abaqus

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Modeling Rubber and Viscoelasticity with Abaqus

Motivation

• Rubber materials are found in many components.

• Some of these are illustrated on the following slide.

• Rubber applications include tires, gaskets, and bushings, among

others.

• The vast number of applications that use rubber materials necessitates

a good understanding of the modeling techniques used to analyze

rubber components.

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Modeling Rubber and Viscoelasticity with Abaqus

Motivation

Tires Medical DevicesSeals

Packaging

Bushings, mounts, etc.

keypad spring

Electronics, consumer

products

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Modeling Rubber and Viscoelasticity with Abaqus

Day 1

• Lecture 1 Rubber Physics

• Lecture 2 Introduction to Rubber Elasticity Models

• Lecture 3 Mechanical Testing

• Workshop 1

• Lecture 4 Defining Rubber Elasticity Models in Abaqus

• Lecture 5 Modeling Issues and Tips

• Workshop 2

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Modeling Rubber and Viscoelasticity with Abaqus

Day 2

• Lecture 6 Viscoelastic Material Behavior

• Lecture 7 Time-Domain Viscoelasticity

• Workshop 3

• Lecture 8 Frequency-Domain Viscoelasticity

• Workshop 4

• Lecture 9 Permanent Set in Solid Elastomers

• Lecture 10 Anisotropic Hyperelasticity

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Modeling Rubber and Viscoelasticity with Abaqus

Additional Material

• Appendix 1 Finite Deformations

• Appendix 2 Rubber Elasticity Models: Mathematical Forms

• Appendix 3 Linear Viscoelasticity Theory

• Appendix 4 Harmonic Viscoelasticity Theory

• Appendix 5 Suggested Reading

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Modeling Rubber and Viscoelasticity with Abaqus

Legal Notices

The Abaqus Software described in this documentation is available only under license from

Dassault Systèmes and its subsidiary and may be used or reproduced only in accordance with the

terms of such license.

This documentation and the software described in this documentation are subject to change

without prior notice.

Dassault Systèmes and its subsidiaries shall not be responsible for the consequences of any

errors or omissions that may appear in this documentation.

No part of this documentation may be reproduced or distributed in any form without prior written

permission of Dassault Systèmes or its subsidiary.

© Dassault Systèmes, 2011.

Printed in the United States of America

Abaqus, the 3DS logo, SIMULIA and CATIA are trademarks or registered trademarks of Dassault

Systèmes or its subsidiaries in the US and/or other countries.

Other company, product, and service names may be trademarks or service marks of their

respective owners. For additional information concerning trademarks, copyrights, and licenses,

see the Legal Notices in the Abaqus 6.11 Release Notes and the notices at:

http://www.simulia.com/products/products_legal.html.

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Modeling Rubber and Viscoelasticity with Abaqus

Revision Status

Lecture 1 5/11 Updated for 6.11

Lecture 2 5/11 Updated for 6.11

Lecture 3 5/11 Updated for 6.11

Lecture 4 5/11 Updated for 6.11

Lecture 5 5/11 Updated for 6.11

Lecture 6 5/11 Updated for 6.11

Lecture 7 5/11 Updated for 6.11

Lecture 8 5/11 Updated for 6.11

Lecture 9 5/11 Updated for 6.11

Lecture 10 5/11 Updated for 6.11

Appendix 1 5/11 Updated for 6.11

Appendix 2 5/11 Updated for 6.11

Appendix 3 5/11 Updated for 6.11

Appendix 4 5/11 Updated for 6.11

Appendix 5 5/11 Updated for 6.11

Workshop 1 5/11 Updated for 6.11

Workshop 2 5/11 Updated for 6.11

Workshop 3 5/11 Updated for 6.11

Workshop 4 5/11 Updated for 6.11

Workshop Answers 1 5/11 Updated for 6.11

Workshop Answers 2 5/11 Updated for 6.11

Workshop Answers 3 5/11 Updated for 6.11

Workshop Answers 4 5/11 Updated for 6.11

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Lecture 1

Rubber Physics

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L1.2

Modeling Rubber and Viscoelasticity with Abaqus

Overview

• Solid Rubber

• Molecular Structure

• Material Processing

• Glass Transition Temperature

• Nearly Incompressible Behavior

• Typical Stress–Strain

Response

• Hysteresis and Damping

• Damage

• Anisotropy

• Thermoplastic Elastomers

• Physical Description

• Advantages and Disadvantages

• Rubber Foam

• Physical Description

• Cellular Structure

• Typical Stress–Strain Response

• Poisson’s Effect

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Lecture 2

Introduction to Rubber Elasticity Models

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L2.2

Modeling Rubber and Viscoelasticity with Abaqus

Overview

• Introduction

• Models for Solid Rubber Elasticity

• Mullins Effect

• Model for Foam Rubber Elasticity

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Lecture 3

Mechanical Testing

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L3.2

Modeling Rubber and Viscoelasticity with Abaqus

Overview

• Modes of Deformation

• Uniaxial Tension

• Planar Tension

• Uniaxial Compression

• Equibiaxial Tension

• Confined Compression (for volumetric response)

• Loading History

• Testing at Temperature

• Test Specimens

• Test Data Guidelines

• Testing for Time-Dependent Properties

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Lecture 4

Defining Rubber Elasticity Models in Abaqus

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L4.2

Modeling Rubber and Viscoelasticity with Abaqus

Overview

• Curve-Fitting for Solid Rubber Elasticity

• Material Stability

• Curve-fitting in Abaqus/CAE

• Choosing a Hyperelastic Model

• Defining Hyperelastic Models

• Mullins Effect

• Hyperfoam Model

• UHYPER

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Lecture 5

Modeling Issues and Tips

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L5.2

Modeling Rubber and Viscoelasticity with Abaqus

Overview

• Contact

• Element Selection

• Overview

• First-Order or Second-Order?

• Full or Reduced Integration?

• Regular or Hybrid?

• Incompatible Modes

• Modified Elements

• Complex Geometry

• Meshing Considerations

• Constraints and Reinforcements

• Instability

• Material Instability

• Structural Instability

• Surface Wrinkling and Folding

• Output Variables

• Using Abaqus/Explicit for Rubber

Analyses

• Special Features

• Example: Column Shifter Boot

• Example: Weather Seal

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Lecture 6

Viscoelastic Material Behavior

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L6.2

Modeling Rubber and Viscoelasticity with Abaqus

Overview

• Introduction

• Effects of Viscoelasticity

• Creep

• Stress Relaxation

• Damping and Hysteresis

• Linear Viscoelasticity

• Nonlinear Viscoelasticity

• Temperature Dependence

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Lecture 7

Time-Domain Viscoelasticity

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L7.2

Modeling Rubber and Viscoelasticity with Abaqus

Overview

• Classical Linear Viscoelasticity

• Prony Series Representation

• Finite-Strain Viscoelasticity

• Relaxation and Creep Test Data

• Prony Series Data

• Automatic Material Evaluation

• Time-Temperature Correspondence

• Reduced Time

• Input Data

• WLF Example

• Usage Hints

• Hysteresis in Elastomers

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Lecture 8

Frequency-Domain Viscoelasticity

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L8.2

Modeling Rubber and Viscoelasticity with Abaqus

Overview

• Frequency-Domain Response

• Storage and Loss Moduli

• Classical Isotropic Linear Viscoelasticity

• Isotropic Finite-Strain Viscoelasticity

• Procedures

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Lecture 9

Permanent Set in Solid Elastomers

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L9.2

Modeling Rubber and Viscoelasticity with Abaqus

Overview

• Motivation

• Defining Permanent Set

• Example

• Summary

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Lecture 10

Anisotropic Hyperelasticity

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L10.2

Modeling Rubber and Viscoelasticity with Abaqus

Overview

• Motivation

• Models Available in Abaqus

• Examples

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Appendix 1

Finite Deformations

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A1.2

Modeling Rubber and Viscoelasticity with Abaqus

Overview

• Motions and Displacements

• Extension of a Material Line Element

• The Deformation Gradient Tensor

• Finite Deformations and Strain Tensors

• Decomposition of a Deformation

• Principal Stretches and Principal Axes of Deformation

• Strain Invariants

• Summary

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Appendix 2

Rubber Elasticity Models: Mathematical Forms

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A2.2

Modeling Rubber and Viscoelasticity with Abaqus

Overview

• Energy Functions for Solid Rubbers (Isotropic)

• Polynomial Model

• Mooney-Rivlin Model

• Reduced Polynomial Model

• Neo-Hookean Model

• Yeoh Model

• Ogden Model

• Marlow Model

• Arruda-Boyce Model

• Van der Waals Model

• Foam Rubber Model

• Mullins Effect

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Appendix 3

Linear Viscoelasticity Theory

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A3.2

Modeling Rubber and Viscoelasticity with Abaqus

Overview

• Classical Linear Viscoelasticity

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Appendix 4

Harmonic Viscoelasticity Theory

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A4.2

Modeling Rubber and Viscoelasticity with Abaqus

Overview

• Classical Linear Viscoelasticity

• Harmonic Excitation

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Appendix 5

Suggested Reading

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A5.2

Modeling Rubber and Viscoelasticity with Abaqus

Overview

• Suggested Reading