Isotropic hyperelasticity in principal stretches: explicit elasticity tensors and numerical implementation

Research output: Contribution to journalArticle

Abstract

Elasticity tensors for isotropic hyperelasticity in principal stretches are formulated and implemented for the Finite Element Method. Hyperelastic constitutive models defined by this strain measure are known to accurately model the response of rubber, and similar materials. These models may not be available in the library of a Finite Element Analysis software, but a numerical implementation of the constitutive model may be provided by a programmed subroutine. The implementation proposed here is robust and accurate, with straightforward user input. It is presented in multiple configurations with novel features, including efficient definition of isochoric stress and elasticity coefficients, symmetric dyadic products of the principal directions, and development of a stable and accurate algorithm for equal and similar principal stretches. The proposed implementation is validated, for unique, equal and similar principal stretches. Further validation in the Finite Element Method demonstrates the developed implementation requires lower computational effort compared with an alternative, well-known implementation.
LanguageEnglish
Number of pages16
JournalComputational Mechanics
Early online date3 May 2019
DOIs
Publication statusE-pub ahead of print - 3 May 2019

Fingerprint

Hyperelasticity
Stretch
Tensors
Elasticity
Tensor
Constitutive models
Finite element method
Constitutive Model
Subroutines
Dyadic product
Finite Element Method
Rubber
Principal direction
Symmetric Product
Finite Element
Configuration
Software
Alternatives
Coefficient
Model

Keywords

  • hyperelasticity
  • principal stretches
  • finite element method
  • numerical implementation
  • elasticity tensors

Cite this

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title = "Isotropic hyperelasticity in principal stretches: explicit elasticity tensors and numerical implementation",
abstract = "Elasticity tensors for isotropic hyperelasticity in principal stretches are formulated and implemented for the Finite Element Method. Hyperelastic constitutive models defined by this strain measure are known to accurately model the response of rubber, and similar materials. These models may not be available in the library of a Finite Element Analysis software, but a numerical implementation of the constitutive model may be provided by a programmed subroutine. The implementation proposed here is robust and accurate, with straightforward user input. It is presented in multiple configurations with novel features, including efficient definition of isochoric stress and elasticity coefficients, symmetric dyadic products of the principal directions, and development of a stable and accurate algorithm for equal and similar principal stretches. The proposed implementation is validated, for unique, equal and similar principal stretches. Further validation in the Finite Element Method demonstrates the developed implementation requires lower computational effort compared with an alternative, well-known implementation.",
keywords = "hyperelasticity, principal stretches, finite element method, numerical implementation, elasticity tensors",
author = "Connolly, {Stephen John} and Donald MacKenzie and Yevgen Gorash",
year = "2019",
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doi = "10.1007/s00466-019-01707-1",
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T1 - Isotropic hyperelasticity in principal stretches

T2 - Computational Mechanics

AU - Connolly, Stephen John

AU - MacKenzie, Donald

AU - Gorash, Yevgen

PY - 2019/5/3

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N2 - Elasticity tensors for isotropic hyperelasticity in principal stretches are formulated and implemented for the Finite Element Method. Hyperelastic constitutive models defined by this strain measure are known to accurately model the response of rubber, and similar materials. These models may not be available in the library of a Finite Element Analysis software, but a numerical implementation of the constitutive model may be provided by a programmed subroutine. The implementation proposed here is robust and accurate, with straightforward user input. It is presented in multiple configurations with novel features, including efficient definition of isochoric stress and elasticity coefficients, symmetric dyadic products of the principal directions, and development of a stable and accurate algorithm for equal and similar principal stretches. The proposed implementation is validated, for unique, equal and similar principal stretches. Further validation in the Finite Element Method demonstrates the developed implementation requires lower computational effort compared with an alternative, well-known implementation.

AB - Elasticity tensors for isotropic hyperelasticity in principal stretches are formulated and implemented for the Finite Element Method. Hyperelastic constitutive models defined by this strain measure are known to accurately model the response of rubber, and similar materials. These models may not be available in the library of a Finite Element Analysis software, but a numerical implementation of the constitutive model may be provided by a programmed subroutine. The implementation proposed here is robust and accurate, with straightforward user input. It is presented in multiple configurations with novel features, including efficient definition of isochoric stress and elasticity coefficients, symmetric dyadic products of the principal directions, and development of a stable and accurate algorithm for equal and similar principal stretches. The proposed implementation is validated, for unique, equal and similar principal stretches. Further validation in the Finite Element Method demonstrates the developed implementation requires lower computational effort compared with an alternative, well-known implementation.

KW - hyperelasticity

KW - principal stretches

KW - finite element method

KW - numerical implementation

KW - elasticity tensors

UR - https://link.springer.com/journal/466

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