Abstract
This chapter considers some basic problems in the mechanics soft tissues. Problems include stretching of bars and membranes, shear of a rectangular block, extension and inflation of a tube, extension and torsion of a cylinder, inflation of a spherical shell, and bending of a block. All problems are solved using nonlinear elasticity, with numerical results illustrating fundamental behavior.
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Notes
- 1.
A negative pressure (suction) would cause circumferential compression that may buckle the tube into an asymmetric shape. This possibility is not considered here.
- 2.
Only passive deformation is considered here; active contraction is explored in the next chapter.
- 3.
As mentioned previously, we use lowercase indices for tensor components even when their associated base vectors have indices of upper case. This is done for simplicity, it is hoped without confusion.
- 4.
The moment resultant applied at each end represents a couple, which has magnitude and direction independent of the reference point.
- 5.
In mechanics, a membrane is a very thin shell with negligible bending stiffness.
- 6.
Rotating rigid plates attached at Y = ±b can produce this deformation.
- 7.
Notice how nicely the base vectors work out.
- 8.
Beam and plate theories are discussed more fully in Chap. 8.
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Taber, L.A. (2020). Problems in Soft Tissue Biomechanics. In: Continuum Modeling in Mechanobiology. Springer, Cham. https://doi.org/10.1007/978-3-030-43209-6_4
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DOI: https://doi.org/10.1007/978-3-030-43209-6_4
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