Simulation of the mechanical behavior of soft tissues is critical for many physiological and medical device applications. Accurate mechanical test data is crucial for both obtaining the form and robust parameter determination of the constitutive model. For incompressible soft tissues that are either membranes or thin sections, planar biaxial mechanical testing configurations can provide much information about the anisotropic stress–strain behavior. However, the analysis of soft biological tissue planar biaxial mechanical test data can be complicated by in-plane shear, tissue heterogeneities, and inelastic changes in specimen geometry that commonly occur during testing. These inelastic effects, without appropriate corrections, alter the stress-traction mapping and violates equilibrium so that the stress tensor is incorrectly determined. To overcome these problems, we presented an analytical method to determine the Cauchy stress tensor from the experimentally derived tractions for tethered testing configurations. We accounted for the measured testing geometry and compensate for run-time inelastic effects by enforcing equilibrium using small rigid body rotations. To evaluate the effectiveness of our method, we simulated complete planar biaxial test configurations that incorporated actual device mechanisms, specimen geometry, and heterogeneous tissue fibrous structure using a finite element (FE) model. We determined that our method corrected the errors in the equilibrium of momentum and correctly estimated the Cauchy stress tensor. We also noted that since stress is applied primarily over a subregion bounded by the tethers, an adjustment to the effective specimen dimensions is required to correct the magnitude of the stresses. Simulations of various tether placements demonstrated that typical tether placements used in the current experimental setups will produce accurate stress tensor estimates. Overall, our method provides an improved and relatively straightforward method of calculating the resulting stresses for planar biaxial experiments for tethered configurations, which is especially useful for specimens that undergo large shear and exhibit substantial inelastic effects.
Skip Nav Destination
Article navigation
June 2015
Technical Briefs
A Generalized Method for the Analysis of Planar Biaxial Mechanical Data Using Tethered Testing Configurations
Will Zhang,
Will Zhang
Department of Biomedical Engineering,
Center for Cardiovascular Simulation,
Institute for Computational Engineering and Sciences,
Center for Cardiovascular Simulation,
Institute for Computational Engineering and Sciences,
The University of Texas at Austin
,Austin, TX 78712-1229
Search for other works by this author on:
Yuan Feng,
Yuan Feng
1
Department of Biomedical Engineering,
Center for Cardiovascular Simulation,
Institute for Computational Engineering and Sciences,
Center for Cardiovascular Simulation,
Institute for Computational Engineering and Sciences,
The University of Texas at Austin
,Austin, TX 78712-1229
1Present address: School of Mechanical and Electronic Engineering, Soochow University, SuZhou, Jiangsu 512000, China.
Search for other works by this author on:
Chung-Hao Lee,
Chung-Hao Lee
Department of Biomedical Engineering,
Center for Cardiovascular Simulation,
Institute for Computational Engineering and Sciences,
Center for Cardiovascular Simulation,
Institute for Computational Engineering and Sciences,
The University of Texas at Austin
,Austin, TX 78712-1229
Search for other works by this author on:
Kristen L. Billiar,
Kristen L. Billiar
Department of Biomedical Engineering,
Worcester Polytechnic Institute
,Worcester, MA 01609-2280
Search for other works by this author on:
Michael S. Sacks
Michael S. Sacks
2
W. A. “Tex” Moncrief, Jr. Simulation-Based
Engineering Science Chair I,
Professor of Biomedical Engineering,
Institute for Computational Engineering and Sciences,
Department of Biomedical Engineering,
Center for Cardiovascular Simulation,
e-mail: msacks@ices.utexas.edu
Engineering Science Chair I,
Professor of Biomedical Engineering,
Institute for Computational Engineering and Sciences,
Department of Biomedical Engineering,
Center for Cardiovascular Simulation,
The University of Texas at Austin
,Austin, TX 78712-1229
e-mail: msacks@ices.utexas.edu
2Corresponding author.
Search for other works by this author on:
Will Zhang
Department of Biomedical Engineering,
Center for Cardiovascular Simulation,
Institute for Computational Engineering and Sciences,
Center for Cardiovascular Simulation,
Institute for Computational Engineering and Sciences,
The University of Texas at Austin
,Austin, TX 78712-1229
Yuan Feng
Department of Biomedical Engineering,
Center for Cardiovascular Simulation,
Institute for Computational Engineering and Sciences,
Center for Cardiovascular Simulation,
Institute for Computational Engineering and Sciences,
The University of Texas at Austin
,Austin, TX 78712-1229
Chung-Hao Lee
Department of Biomedical Engineering,
Center for Cardiovascular Simulation,
Institute for Computational Engineering and Sciences,
Center for Cardiovascular Simulation,
Institute for Computational Engineering and Sciences,
The University of Texas at Austin
,Austin, TX 78712-1229
Kristen L. Billiar
Department of Biomedical Engineering,
Worcester Polytechnic Institute
,Worcester, MA 01609-2280
Michael S. Sacks
W. A. “Tex” Moncrief, Jr. Simulation-Based
Engineering Science Chair I,
Professor of Biomedical Engineering,
Institute for Computational Engineering and Sciences,
Department of Biomedical Engineering,
Center for Cardiovascular Simulation,
e-mail: msacks@ices.utexas.edu
Engineering Science Chair I,
Professor of Biomedical Engineering,
Institute for Computational Engineering and Sciences,
Department of Biomedical Engineering,
Center for Cardiovascular Simulation,
The University of Texas at Austin
,Austin, TX 78712-1229
e-mail: msacks@ices.utexas.edu
1Present address: School of Mechanical and Electronic Engineering, Soochow University, SuZhou, Jiangsu 512000, China.
2Corresponding author.
Manuscript received November 10, 2013; final manuscript received November 9, 2014; published online April 15, 2015. Assoc. Editor: Stephen M. Klisch.
J Biomech Eng. Jun 2015, 137(6): 064501 (13 pages)
Published Online: June 1, 2015
Article history
Received:
November 10, 2013
Revision Received:
November 9, 2014
Online:
April 15, 2015
Citation
Zhang, W., Feng, Y., Lee, C., Billiar, K. L., and Sacks, M. S. (June 1, 2015). "A Generalized Method for the Analysis of Planar Biaxial Mechanical Data Using Tethered Testing Configurations." ASME. J Biomech Eng. June 2015; 137(6): 064501. https://doi.org/10.1115/1.4029266
Download citation file:
Get Email Alerts
Cited By
Development of a Strain-Based Model to Predict Eviscerated Thoracic Response From Dynamic Individual Rib Tests
J Biomech Eng (October 2022)
Related Articles
Simple Shear Testing of Parallel-Fibered Planar Soft Tissues
J Biomech Eng (April,2001)
Effects of Boundary Conditions on the Estimation of the Planar Biaxial Mechanical Properties of Soft Tissues
J Biomech Eng (August,2005)
Computational Modeling of Ventricular Mechanics and Energetics
Appl. Mech. Rev (March,2005)
Biaxial Mechanical Response of Bioprosthetic Heart Valve Biomaterials to High In-plane Shear
J Biomech Eng (June,2003)
Related Proceedings Papers
Related Chapters
Conclusion
Ultrasonic Methods for Measurement of Small Motion and Deformation of Biological Tissues for Assessment of Viscoelasticity
Analysis of Components: Strain- and Deformation-Controlled Limits
Design & Analysis of ASME Boiler and Pressure Vessel Components in the Creep Range
Introduction to Stress and Deformation
Introduction to Plastics Engineering