Korenczuk Christopher E, Votava Lauren E, Dhume Rohit Y, Kizilski Shannen B, Brown George E, Narain Rahul, Barocas Victor H
J Biomech Eng. 2017 Jul 1;139(7):0710081-07100810. doi: 10.1115/1.4036316.
The von Mises (VM) stress is a common stress measure for finite element models of tissue mechanics. The VM failure criterion, however, is inherently isotropic, and therefore may yield incorrect results for anisotropic tissues, and the relevance of the VM stress to anisotropic materials is not clear. We explored the application of a well-studied anisotropic failure criterion, the Tsai–Hill (TH) theory, to the mechanically anisotropic porcine aorta. Uniaxial dogbones were cut at different angles and stretched to failure. The tissue was anisotropic, with the circumferential failure stress nearly twice the axial (2.67 ± 0.67 MPa compared to 1.46 ± 0.59 MPa). The VM failure criterion did not capture the anisotropic tissue response, but the TH criterion fit the data well (R2 = 0.986). Shear lap samples were also tested to study the efficacy of each criterion in predicting tissue failure. Two-dimensional failure propagation simulations showed that the VM failure criterion did not capture the failure type, location, or propagation direction nearly as well as the TH criterion. Over the range of loading conditions and tissue geometries studied, we found that problematic results that arise when applying the VM failure criterion to an anisotropic tissue. In contrast, the TH failure criterion, though simplistic and clearly unable to capture all aspects of tissue failure, performed much better. Ultimately, isotropic failure criteria are not appropriate for anisotropic tissues, and the use of the VM stress as a metric of mechanical state should be reconsidered when dealing with anisotropic tissues.
冯·米塞斯（VM）应力是组织力学有限元模型中常用的应力度量。然而，VM失效准则本质上是各向同性的，因此对于各向异性组织可能会产生错误的结果，并且VM应力与各向异性材料的相关性尚不清楚。我们探讨了一种经过充分研究的各向异性失效准则——蔡-希尔（TH）理论在机械各向异性猪主动脉上的应用。将单轴哑铃形试样切成不同角度并拉伸至破坏。该组织是各向异性的，周向破坏应力几乎是轴向破坏应力的两倍（分别为2.67±0.67兆帕和1.46±0.59兆帕）。VM失效准则未能捕捉到各向异性组织的响应，但TH准则与数据拟合良好（R2 = 0.986）。还测试了剪切搭接试样，以研究每个准则在预测组织破坏方面的有效性。二维破坏传播模拟表明，VM失效准则在捕捉破坏类型、位置或传播方向方面远不如TH准则。在所研究的加载条件和组织几何形状范围内，我们发现将VM失效准则应用于各向异性组织时会产生有问题的结果。相比之下，TH失效准则虽然简单且显然无法捕捉组织破坏的所有方面，但表现要好得多。归根结底，各向同性失效准则不适用于各向异性组织，在处理各向异性组织时，应重新考虑将VM应力用作机械状态度量的做法。
