Department of Mechanical Engineering, University of Zaragoza, Spain.
Department of Management and Manufacturing Engineering, Faculty of Engineering and Architecture, University of Zaragoza, Spain; Applied Mechanics and Bioengineering, Aragón Institute of Engineering Research (I3A), University of Zaragoza, Spain.
J Mech Behav Biomed Mater. 2021 Jan;113:104070. doi: 10.1016/j.jmbbm.2020.104070. Epub 2020 Sep 12.
To test the capability of the multilayer model, we used previously published layer-specific experimental data relating to the axial pre-stretch, the opening angle, the fiber distribution obtained by polarized light microscopy measurements, and the uniaxial and biaxial response of the porcine descending and abdominal aorta. We fitted the mechanical behavior of each arterial layer using Gasser, Holzapfel and Ogden strain energy function using the dispersion parameter κ as phenomenological parameter obtained during the fitting procedure or computed from the experimental fiber distribution. A multilayer finite element model of the whole aorta with the dimensions of the circumferential and longitudinal strips were then built using layer-specific material parameters previously fitted. This model was used to capture the whole aorta response under uniaxial and biaxial stress states and to reproduce the response of the whole aorta to internal pressure. Our results show that a model based on a multilayer structure without residual stresses is unable to render the uniaxial and biaxial mechanical response of the aorta (R=0.6954 and R=0.8582 for descending thoracic aorta (DTA) and infrarenal abdominal aorta (IAA), respectively). Only an appropriate multilayer model that includes layer-specific residual stresses can reproduce the response of the whole aorta (R=0.9787 and R=0.9636 for DTA and IAA respectively). In addition, a multilayer model without residual stresses produces the same stress distribution as a monolayer model without residual stresses where the maximal value of circumferential and longitudinal stresses appears at the inner radius of the intima. Finally, if layer-specific residual stresses are not available, there is less error the stress distribution using a monolayer model with residual stresses that a multilayer model without residual stresses.
为了测试多层模型的能力，我们使用了先前发表的与轴向预拉伸、开口角、偏光显微镜测量得到的纤维分布以及猪降胸主动脉和腹主动脉的单轴和双轴响应有关的特定层实验数据。我们使用 Gasser、 Holzapfel 和 Ogden 应变能函数拟合每个动脉层的力学行为，使用在拟合过程中获得的分散参数 κ 或从实验纤维分布计算的 κ 作为唯象参数。然后，使用以前拟合的特定层材料参数构建了整个主动脉的具有圆周和纵向条带尺寸的多层有限元模型。该模型用于捕获单轴和双轴应力状态下整个主动脉的响应，并再现整个主动脉对内压的响应。我们的结果表明，没有残余应力的基于多层结构的模型无法呈现主动脉的单轴和双轴力学响应（降胸主动脉（DTA）和肾下腹主动脉（IAA）的 R=0.6954 和 R=0.8582）。只有包括特定层残余应力的适当多层模型才能再现整个主动脉的响应（DTA 和 IAA 的 R=0.9787 和 R=0.9636）。此外，没有残余应力的多层模型产生与没有残余应力的单层模型相同的应力分布，其中圆周和纵向应力的最大值出现在内膜的内半径处。最后，如果没有特定层的残余应力，使用具有残余应力的单层模型比使用没有残余应力的多层模型，应力分布的误差更小。
