A comparative study on the uniaxial mechanical properties of the umbilical vein and umbilical artery using different stress–strain definitions

The umbilical cord is part of the fetus and generally includes one umbilical vein (UV) and two umbilical arteries (UAs). As the saphenous vein and UV are the most commonly used veins for the coronary artery disease treatment as a coronary artery bypass graft (CABG), understating the mechanical properties of UV has a key asset in its performance for CABG. However, there is not only a lack of knowledge on the mechanical properties of UV and UA but there is no agreement as to which stress–strain definition should be implemented to measure their mechanical properties. In this study, the UV and UA samples were removed after caesarean from eight individuals and subjected to a series of tensile testing. Three stress definitions (second Piola–Kichhoff stress, engineering stress, and true stress) and four strain definitions (Almansi–Hamel strain, Green-St. Venant strain, engineering strain, and true strain) were employed to determine the linear mechanical properties of UVs and UAs. The nonlinear mechanical behavior of UV/UA was computationally investigated using hyperelastic material models, such as Ogden and Mooney–Rivlin. The results showed that the effect of varying the stress definition on the maximum stress measurements of the UV/UA is significant but not when calculating the elastic modulus. In the true stress–strain diagram, the maximum strain of UV was 92 % higher, while the elastic modulus and maximum stress were 162 and 42 % lower than that of UA. The Mooney–Rivlin material model was designated to represent the nonlinear mechanical behavior of the UV and UA under uniaxial loading.