Abstract
All soft tissues are modeled as either one-dimensionalstrings, two-dimensionalmembranes, or three-dimensionalsolids. Attention is restricted to tissues in which one of the principal stress components is large and positive in comparison with the other negligible components. Results indicate the following:
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(1)
If a deformed string isconstrained to lie on a surface and is free of tangential pressure, the tension is carried by rays which are geodesics of the surface. If a string or membrane isfree to deform in space without normal pressure, the tension rays are straight lines. If a membrane deforms without tangential surface loads, the tension rays are always geodesics on the deformed surface. If a solid deforms without body forces, the tension rays are straight lines.
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(2)
The stress in a string is a constant if the string is free of tangential pressure and has constant cross-sectional area. The stress in flat tension fields free of tangential surface loads decays inversely with distance along a tension ray from the edge of regression. The stress in a spherically symmetric tension field free of body forces decays inversely with the square of the distance from the center of the sphere.
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(3)
Stress singularities can occur in soft tissues, such as at the corners of a closed rectangular hole in a flat membrane strip.
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(4)
The tension rays in the torsion of soft annular membranes are more steeply inclined from the radial direction than the tension rays for hard metals equally displaced.
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This research was financially supported by Public Health Service Research Career Development Award 5KO4 GM70733-03 from the Institute of General Medical Sciences.
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Danielson, D.A. Tension field theories for soft tissues. Bltn Mathcal Biology 40, 161–182 (1978). https://doi.org/10.1007/BF02461433
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DOI: https://doi.org/10.1007/BF02461433