A New Method for Predicting the Opening Angle for Soft Tissues

[+] Author and Article Information
Timothy J. Van Dyke, Anne Hoger

Department of Mechanical & Aerospace Engineering, University of California, San Diego, 9500 Gilman Road, La Jolla, CA 92093

J Biomech Eng 124(4), 347-354 (Jul 30, 2002) (8 pages) doi:10.1115/1.1487881 History: Received November 01, 2000; Revised April 01, 2002; Online July 30, 2002
Copyright © 2002 by ASME
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Schematic of the opening angle experiment which is used for assessing the residual stress in biological organs with approximately cylindrical geometry. The figure shows the configuration before the radial cut is made (the closed configuration) and the configuration after the radial cut (the open configuration). As shown in the figure, the ring typically opens after the radial cut because of the residual stress present in the intact ring.
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Residual stress distributions in the closed configuration with d=1. Note that d equals the maximum circumferential stress. The two distributions used in the paper are shown. In Distribution A, the circumferential component of the Cauchy stress varies linearly with radial location. In both cases, the radial component of the residual stress is determined from the requirement that the closed configuration be in equilibrium.
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The opening angles predicted for residual stress Distribution A as a function of d. The MPE, PK, and RE methods all yield essentially the same opening angle as that calculated by the finite element model, even for large opening angles.
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The opening angle predicted for residual stress Distribution B as a function of d. The predictions of the PK and RE methods depart significantly from the opening angle calculated with the finite element model. The MPE method gives accurate values of the opening angle even for large d.
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The closed configuration of the ring with residual stress Distribution B and d=12, together with the associated open configuration obtained from the finite element model. Only the lower half of the ring is shown; the geometry and the stress distribution in the upper half of the ring can be inferred by symmetry. The arrows in the figure indicate the magnitude and direction of the principal Cauchy stresses. The magnitudes of the principal stresses in the radial direction are much smaller than magnitude of the principal stresses in the circumferential direction, so they cannot be seen in the figure. Clockwise arrows correspond to compression and counterclockwise arrows to tension. The opening angle is 106.8°
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The opening angle calculated by the finite element model and by the MPE method for residual stress Distribution B. Results are shown for rings of four different thicknesses and are displayed as a function of d scaled by (Ro−Ri)/Ro. Note that the MPE method yields accurate opening angles even for large values of d and relatively thick rings.




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