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Research Papers

A Novel Small-Specimen Planar Biaxial Testing System With Full In-Plane Deformation Control

[+] Author and Article Information
Samuel Potter

Department of Mechanical Engineering,
Willerson Center for Cardiovascular
Modeling and Simulation,
Institute for Computational Engineering
and Sciences,
The University of Texas at Austin,
240 East 24th Street,
Austin, TX 78712

Jordan Graves

Department of Biomedical Engineering,
Willerson Center for Cardiovascular
Modeling and Simulation,
Institute for Computational Engineering
and Sciences,
The University of Texas at Austin,
240 East 24th Street,
Austin, TX 78712

Borys Drach

Department of Mechanical and
Aerospace Engineering,
New Mexico State University,
Las Cruces, NM 88003

Thomas Leahy

Department of Biomedical Engineering,
Willerson Center for Cardiovascular
Modeling and Simulation,
Institute for Computational Engineering and Sciences,
The University of Texas at Austin,
240 East 24th Street,
Austin, TX 78712

Chris Hammel

Department of Mechanical Engineering,
Willerson Center for Cardiovascular
Modeling and Simulation,
Institute for Computational Engineering and Sciences,
The University of Texas at Austin,
240 East 24th Street,
Austin, TX 78712

Yuan Feng

Center for Molecular Imaging and Nuclear Medicine,
School of Radiological and Interdisciplinary
Sciences (RAD-X),
Soochow University,
Collaborative Innovation Center of Radiation
Medicine of Jiangsu Higher Education Institutions,
Suzhou 215123, China

Aaron Baker

Department of Biomedical Engineering,
Willerson Center for Cardiovascular
Modeling and Simulation,
The University of Texas at Austin,
107 W Dean Keeton Street, Stop C0800,
Austin, TX 78712

Michael S. Sacks

Department of Biomedical Engineering,
Willerson Center for Cardiovascular Modeling and
Simulation,
Institute for Computational Engineering and Sciences,
The University of Texas at Austin,
240 East 24th Street,
Austin, TX 78712

1Corresponding author.

Manuscript received June 1, 2017; final manuscript received December 11, 2017; published online February 13, 2018. Assoc. Editor: Thao (Vicky) Nguyen.

J Biomech Eng 140(5), 051001 (Feb 13, 2018) (18 pages) Paper No: BIO-17-1237; doi: 10.1115/1.4038779 History: Received June 01, 2017; Revised December 11, 2017

Simulations of soft tissues require accurate and robust constitutive models, whose form is derived from carefully designed experimental studies. For such investigations of membranes or thin specimens, planar biaxial systems have been used extensively. Yet, all such systems remain limited in their ability to: (1) fully prescribe in-plane deformation gradient tensor F2D, (2) ensure homogeneity of the applied deformation, and (3) be able to accommodate sufficiently small specimens to ensure a reasonable degree of material homogeneity. To address these issues, we have developed a novel planar biaxial testing device that overcomes these difficulties and is capable of full control of the in-plane deformation gradient tensor F2D and of testing specimens as small as ∼4 mm × ∼4 mm. Individual actuation of the specimen attachment points, combined with a robust real-time feedback control, enabled the device to enforce any arbitrary F2D with a high degree of accuracy and homogeneity. Results from extensive device validation trials and example tissues illustrated the ability of the device to perform as designed and gather data needed for developing and validating constitutive models. Examples included the murine aortic tissues, allowing for investigators to take advantage of the genetic manipulation of murine disease models. These capabilities highlight the potential of the device to serve as a platform for informing and verifying the results of inverse models and for conducting robust, controlled investigation into the biomechanics of very local behaviors of soft tissues and membrane biomaterials.

Copyright © 2018 by ASME
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Figures

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Fig. 1

Common modes of planar biaxial deformation that the device is designed to prescribe and control

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Fig. 2

(a) Top view of the device showing the specimen test area and (b) close up view of specimen mounted on actuation arms

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Fig. 3

Test system schematic showing the major hardware and software components of the device and the data interconnections between them

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Fig. 4

(a) The components and major dimensions of the actuation system in the unloaded configuration. Also shown in (b) is how the system deforms under a generalized loading state.

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Fig. 5

A schematic of control algorithm process flow during run-time

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Fig. 6

Details of the system components included in the simulation of the device performance: (a) actuation system components and (b) specimen spring damper model

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Fig. 7

FE simulation results for the Von Mises stress index over the entire specimen, with the each pin displaced 0.5 mm either along the x1 or the x2, depending on its side. Results clearly show a high degree of stress field homogeneity, with the stress concentrations induced by the pin attachments producing only local effects.

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Fig. 8

(a) FE results for simple shear for each component of S and (b) resulting plots of the components of S versus x1, using the elements shown in the inset in (a)

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Fig. 9

Plots of actual versus prescribed deformation gradient component for a general planar biaxial deformation

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Fig. 10

Plots of deformation gradient tensor components at maximum deformation interpolated throughout the measurement region for a general planar biaxial deformation, showing good uniformity in responses

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Fig. 11

The measured positions of the 3 × 3 marker array in the deformed state versus after a representative experimental F was applied to each measured position of the array in reference state for a bovine pericardium specimen. The close agreement in final positions indicates that the strain field as controlled by the 2 × 2 array was relatively homogeneous over the entire region.

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Fig. 12

(a) Location of specimen subregions in aortic valve leaflet, showing an example of marked subregion of specimen and (b) resulting mechanical responses of the subregions

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Fig. 13

Response of the basilar region of the aortic valve leaflet to a simple shear deformation

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Fig. 14

Mechanical response of pericardial specimen to extension deformation

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Fig. 15

(a) Location of specimen in murine aorta and (b) shear stress versus shear deformation response

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Fig. 16

(a) A schematic of the bell-crank mechanism used in the device outlining geometric relationships used to design a one to one relationship between input and output displacement and (b) close up of the needle holder, showing the needle and specimen

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Fig. 17

(a) Discontinuous versus continuous stabilizing control laws and (b) sample tracking error plot generated by holding the value of κ constant while varying vs and L

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Fig. 18

(a) Actuation components of the device involved in determining the force vectors. Inset A: Numbering scheme for force vectors. (b) Geometric quantities involved in determining force vectors attached to the bell-crank attachments. (c) Geometric quantities involved in determining center force vectors.

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Fig. 19

(a) Force vectors in the deformed configuration and (b) resulting normal and shear traction distributions in the reference configuration

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