### Abstract

Original language | English |
---|---|

Pages (from-to) | 474-489 |

Number of pages | 16 |

Journal | Mathematics and Mechanics of Solids |

Volume | 14 |

Issue number | 5 |

Early online date | 11 Mar 2008 |

DOIs | |

Publication status | Published - 2009 |

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### Keywords

- biaxial testing
- anisotropic material
- elastic material
- soft tissue mechanics
- constitutive modeling

### Cite this

*Mathematics and Mechanics of Solids*,

*14*(5), 474-489. https://doi.org/10.1177/1081286507084411

**On planar biaxial tests for anisotropic nonlinearly elastic solids.** / Holzapfel, Gerhard ; Ogden, Raymond W.

Research output: Contribution to journal › Article

*Mathematics and Mechanics of Solids*, vol. 14, no. 5, pp. 474-489. https://doi.org/10.1177/1081286507084411

}

TY - JOUR

T1 - On planar biaxial tests for anisotropic nonlinearly elastic solids

AU - Holzapfel, Gerhard

AU - Ogden, Raymond W.

PY - 2009

Y1 - 2009

N2 - The mechanical testing of anisotropic nonlinearly elastic solids is a topic of considerable and increasing interest. The results of such testing are important, in particular, for the characterization of the material properties and the development of constitutive laws that can be used for predictive purposes. However, the literature on this topic in the context of soft tissue biomechanics, in particular, includes some papers that are misleading since they contain errors and false statements. Claims that planar biaxial testing can fully characterize the three-dimensional anisotropic elastic properties of soft tissues are incorrect. There is therefore a need to clarify the extent to which biaxial testing can be used for determining the elastic properties of these materials. In this paper this is explained on the basis of the equations of finite deformation transversely isotropic elasticity, and general planar anisotropic elasticity. It is shown that it is theoretically impossible to fully characterize the properties of anisotropic elastic materials using such tests unless some assumption is made that enables a suitable subclass of models to be preselected. Moreover, it is shown that certain assumptions underlying the analysis of planar biaxial tests are inconsistent with the classical linear theory of orthotropic elasticity. Possible sets of independent tests required for full material characterization are then enumerated.

AB - The mechanical testing of anisotropic nonlinearly elastic solids is a topic of considerable and increasing interest. The results of such testing are important, in particular, for the characterization of the material properties and the development of constitutive laws that can be used for predictive purposes. However, the literature on this topic in the context of soft tissue biomechanics, in particular, includes some papers that are misleading since they contain errors and false statements. Claims that planar biaxial testing can fully characterize the three-dimensional anisotropic elastic properties of soft tissues are incorrect. There is therefore a need to clarify the extent to which biaxial testing can be used for determining the elastic properties of these materials. In this paper this is explained on the basis of the equations of finite deformation transversely isotropic elasticity, and general planar anisotropic elasticity. It is shown that it is theoretically impossible to fully characterize the properties of anisotropic elastic materials using such tests unless some assumption is made that enables a suitable subclass of models to be preselected. Moreover, it is shown that certain assumptions underlying the analysis of planar biaxial tests are inconsistent with the classical linear theory of orthotropic elasticity. Possible sets of independent tests required for full material characterization are then enumerated.

KW - biaxial testing

KW - anisotropic material

KW - elastic material

KW - soft tissue mechanics

KW - constitutive modeling

U2 - 10.1177/1081286507084411

DO - 10.1177/1081286507084411

M3 - Article

VL - 14

SP - 474

EP - 489

JO - Mathematics and Mechanics of Solids

JF - Mathematics and Mechanics of Solids

SN - 1081-2865

IS - 5

ER -