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.

Determination of the material parameters of four-fibre family model based on uniaxial extension data of arterial walls

“…All three models, including the Holzapfel-Weizsäcker model (H -W model, Li et al 2011), gave good descriptions of the data with R 2 . 0:9, and the other three indices of goodness-of-fit showed similar result (Table 3).…”

“…Although the methods of Holzapfel 2006;Li et al 2011), the novel point of this paper is the approach, by which the four-fibre family model can be determined from uniaxial tests on strip samples with circumferential and axial orientations from aortas and pulmonary arteries. Because of the difficulties to achieve the transverse strain by measurement when the uniaxial tension is applied to a strip sample, in this study we used a polynomial of degree 5 to describe the relationship between strain components in uniaxial extension.…”

“…We recently reported the circumferential and axial stressstrain data in uniaxial tension of the thoracic aortas and pulmonary arteries from two fresh donation bodies: M 1 (male, 49 years, healthy) and M 2 (male, 20 years, healthy) (Li et al 2011). We briefly describe the protocol: each artery was cut along the axial and circumferential direction into three strip samples with the length and width being about 35 and 6 mm on average, respectively.…”

“…Uniaxial stretching tests are commonly conducted in biomechanics, primarily because of the ease of performance, small sample size and commercial devices available. Therefore, persistent efforts have been made to obtain the 2D or 3D constitutive relations from uniaxial data Li and Luo 2001;Holzapfel 2006;Li et al 2011). Another reason for the popularity of uniaxial stretching test is that there are many specimens such as multi-component diseased materials and layered organs (Holzapfel 2006), which allow only (small) strip preparations, hence not applicable for (conventional) biaxial tests.…”

Differences Between Pulmonary Arterial and Aortic Material Properties

“…11 However, persistent efforts have been made to obtain the constitutive relations from uniaxial data. [12][13][14][15] The main reason is that there are many specimens such as multicomponent diseased materials and layered organs, 12 which allow only (small) strip preparations, hence not applicable for (conventional) biaxial tests. In addition, uniaxial tests have been mostly applied to investigate the mechanical characteristics of soft tissue, such as, Refs.…”