Determination of material parameters of the two-dimensional Holzapfel–Weizsäcker type model based on uniaxial extension data of arterial walls

Abstract

Soft tissues are anisotropic materials yet a majority of mechanical property tests have been uniaxial, which often failed to recapitulate the tensile response in other directions. This paper aims to study the feasibility of determining material parameters of anisotropic tissues by uniaxial extension with a minimal loss of anisotropic information. We assumed that by preselecting a certain constitutive model, we could give the constitutive parameters based on uniaxial extension data from orthogonal strip samples. In our study, the Holzapfel–Weizsäcker type strain energy density function (H–W model) was used to determine the material parameters of arterial walls from two fresh donation bodies. The key points we applied were the relationships between strain components in uniaxial tensile tests and the methods of stochastic optimisation. Further numerical experiments were taken. The estimate–effect ratio, defined by the number of data with the precision of estimation less than 0.5% over whole size of data, was calculated to demonstrate the feasibility of our method. The material parameters for Chinese aorta and pulmonary artery were given with the maximum root mean square (RMS) errors 0.042, and the minimal estimate–effect ratio in numerical experiments was 90.79%. Our results suggest that the constitutive parameters of arterial walls can be determined from uniaxial extension data, given the passive mechanical behaviour governed by H–W model. This method may apply to other tissues using different constitutive models.

Keywords:

• strain energy density functions
• uniaxial extension
• arterial tissue

Acknowledgements

The authors would like to thank the National Natural Science Foundation of China (No. 30900288) and Beijing Municipal Education Commission Foundation (No. KM201010025007).

Notes

1. Email: [email protected].

2. Email: [email protected].

3. Email: [email protected].

4. Email: [email protected].

5. Email: [email protected].

6. Email: [email protected].

Additional information

Notes on contributors

Lin Li

1

Xiuqing Qian

2

Songhua Yan

3

Jianfeng Lei

4

Xiyun Wang

5

Haixia Zhang

6