Zhang Wei, Lu Xiao, Kassab Ghassan S
Department of Biomedical Engineering, IUPUI, Indianapolis, IN 46202, USA.
Biomaterials. 2007 Nov;28(31):4733-8. doi: 10.1016/j.biomaterials.2007.07.025. Epub 2007 Jul 31.
To simplify the stress-strain relationship of blood vessels, we define a logarithmic-exponential (log-exp) strain measure to absorb the nonlinearity. As a result, the constitutive relation between the second Piola-Kirchhoff stress and the log-exp strain can be written as a generalized Hooke's law. In this work, the shear modulus of porcine coronary arteries is determined from the experimental data in inflation-stretch-torsion tests. It is found that the shear modulus with respect to the log-exp strain can be viewed as a material constant in the full range of elasticity, and the incremental shear modulus for Cauchy shear stress and small shear strain at various loading levels can be predicted by the proposed Hooke's law. This result further validates the linear constitutive relation for blood vessels when shear deformation is involved.
为简化血管的应力-应变关系，我们定义了一种对数-指数（log-exp）应变度量来吸收非线性。因此，第二皮奥拉-基尔霍夫应力与对数-指数应变之间的本构关系可写为广义胡克定律。在这项工作中，猪冠状动脉的剪切模量由充气-拉伸-扭转试验中的实验数据确定。结果发现，相对于对数-指数应变的剪切模量在整个弹性范围内可视为材料常数，并且所提出的胡克定律可预测不同加载水平下柯西剪应力和小剪应变的增量剪切模量。这一结果进一步验证了涉及剪切变形时血管的线性本构关系。
