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The plane deformation of a fine elliptical crack which is first squeezed shut by pressure and then sheared is calculated. It is found that the crack deforms as a straight rotating and elongating slit and that the tractions acting on the crack surface are uniform. The uniformity of the tractions often appears as an assumption in analyses of the mechanics of rock fracture or the mechanism of earthquakes. The pressure required to close an elliptical carck of width 2b and length 2a in an incompressible material of shear modulus G is found to be 2Gb:a; comparison of this value with data on rocks in compression indicates that the typical cracks in rocks are very fine, with aspect ratios (b:a) of the order 10U-3D.
Charles A. Berg (1965) studied this question.
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