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research-article

Isotropic Failure Criteria are not Appropriate for Anisotropic Fibrous Biological Tissues

[+] Author and Article Information
Christopher E. Korenczuk

Department of Biomedical Engineering University of Minnesota Minneapolis, MN 55455
koren046@umn.edu

Lauren E. Votava

Department of Biomedical Engineering University of Minnesota Minneapolis, MN 55455
vota0017@umn.edu

Rohit Y. Dhume

Department of Mechanical Engineering University of Minnesota Minneapolis, MN 55455
dhume001@umn.edu

Shannen B. Kizilski

Department of Mechanical Engineering University of Minnesota Minneapolis, MN 55455
kizil015@umn.edu

George E. Brown

Department of Computer Science and Engineering University of Minnesota Minneapolis, MN 55455
brow2327@umn.edu

Rahul Narain

Department of Computer Science and Engineering University of Minnesota Minneapolis, MN 55455
narain@umn.edu

Victor H. Barocas

Department of Biomedical Engineering University of Minnesota Minneapolis, MN 55455
baroc001@umn.edu

1Corresponding author.

ASME doi:10.1115/1.4036316 History: Received December 15, 2016; Revised March 09, 2017

Abstract

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. 2D 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.

Copyright (c) 2017 by ASME
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