1 Department of Civil Engineering and Centre for Bioengineering Research and Education, Schulich School of Engineering, University of Calgary , Calgary , Canada.
2 Institute of Biomechanics, Graz University of Technology , Graz , Austria.
J R Soc Interface. 2019 Feb 28;16(151):20190029. doi: 10.1098/rsif.2019.0029.
The paper provides a deepened insight into the role of anisotropy in the analysis of residual stresses in arteries. Residual deformations are modelled following Holzapfel and Ogden (Holzapfel and Ogden 2010, J. R. Soc. Interface 7, 787-799. ( doi:10.1098/rsif.2009.0357 )), which is based on extensive experimental data on human abdominal aortas (Holzapfel et al. 2007, Ann. Biomed. Eng. 35, 530-545. ( doi:10.1007/s10439-006-9252-z )) and accounts for both circumferential and axial residual deformations of the individual layers of arteries-intima, media and adventitia. Each layer exhibits distinctive nonlinear and anisotropic mechanical behaviour originating from its unique microstructure; therefore, we use the most general form of strain-energy function (Holzapfel et al. 2015, J. R. Soc. Interface 12, 20150188. ( doi:10.1098/rsif.2015.0188 )) to derive residual stresses for each layer individually. Finally, the systematic experimental data (Niestrawska et al. 2016, J. R. Soc. Interface 13, 20160620. ( doi:10.1098/rsif.2016.0620 )) on both mechanical and structural properties of the different layers of the human abdominal aorta facilitate our discussion on (i) the importance of anisotropy in modelling residual stresses; (ii) the variability of residual stresses within the same class of tissue, the abdominal aorta; (iii) the limitations of conventional opening angle method to account for complex residual deformations; and (iv) the effect of residual stresses on the loaded configuration of the aorta mimicking in vivo conditions.
本文深入探讨了各向异性在分析动脉残余应力中的作用。残余变形是根据 Holzapfel 和 Ogden（Holzapfel 和 Ogden，2010，J. R. Soc. Interface，7，787-799. (doi:10.1098/rsif.2009.0357)）的模型进行的，该模型基于大量关于人体腹主动脉的实验数据（Holzapfel 等人，2007，Ann. Biomed. Eng.，35，530-545. (doi:10.1007/s10439-006-9252-z)），并考虑了动脉各层——内膜、中膜和外膜——的周向和轴向残余变形。各层都表现出独特的非线性和各向异性力学行为，这源于其独特的微观结构；因此，我们使用应变能函数的最一般形式（Holzapfel 等人，2015，J. R. Soc. Interface，12，20150188. (doi:10.1098/rsif.2015.0188)）来分别为各层推导残余应力。最后，关于人体腹主动脉不同层的机械和结构性能的系统实验数据（Niestrawska 等人，2016，J. R. Soc. Interface，13，20160620. (doi:10.1098/rsif.2016.0620)）有助于我们讨论（i）各向异性在模拟残余应力中的重要性；（ii）同一类组织——腹主动脉内残余应力的可变性；（iii）传统开口角法在考虑复杂残余变形方面的局限性；以及（iv）残余应力对模拟体内条件的主动脉加载构型的影响。
