Abstract
Some formulas connecting the direction and the curvature of smooth cracks in two-dimensional elastic body with the coefficients of eigenfunction expansion of the displacements are derived. The direction of the crack at the crack tip is given by using the coefficients of the lowest terms of this expansion. The crack curvature is given by the coefficients of the terms including higher order terms. The paper first describes the process to derive these formulas and then proposes a simple way to calculate these coefficients by using displacements near the crack tip. Some simple examples are shown to examine the validity of these formulas.
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Miyoshi, T. Direction and curvature of the cracks in two-dimensional elastic body. Japan J. Indust. Appl. Math. 17, 295 (2000). https://doi.org/10.1007/BF03167349
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DOI: https://doi.org/10.1007/BF03167349