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

The four-fibre family constitutive relation has been used to capture the mechanical behaviour of arterial walls under biaxial loading conditions. This study shows that the material parameters of the four-fibre family model can be determined by uniaxial extension data from the arterial walls. Stochastic optimisation methods were used to determine the material parameters based on uniaxial extension data of the strip samples with circumferential and axial orientations from thoracic aortas and pulmonary arteries of two fresh donation bodies. Moreover, we implemented numerical experiments, in which stress–strain data generated according to different constitutive parameters were treated as mechanical experiment data and went through the same methods as mechanical test data to determine the constitutive parameters. 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 applied to demonstrate the feasibility of our method. The material parameters for Chinese thoracic aorta and pulmonary artery were given with \[R ^{2}\geq 0.979\] R2≥0.979, and the minimal estimate–effect ratio in numerical simulations was 97.77%. In conclusion, the four-fibre family model of arterial walls can be determined from uniaxial extension data. Moreover, the four-fibre family six-parameter constitutive model is the best fit to the data from Chinese pulmonary arteries, and the four-fibre family eight-parameter constitutive model is the best fit to the data from Chinese thoracic aortas.