Abstract
The problem of an anti-plane crack opened by a time varying concentrated load at the origin, and propagating self-similarly in an elastic body was treated. The analysis is based on Chaplygin's transformation and the solution is effected by using the conformal mapping technique. The problem was reduced to a mixed boundary value problem for an analytic function in the half-plane, which is solvable by the Keldysh-Sedov formula.
Résumé
On traite du problème de l'ouverture, puis de la propagation, d'une fissure antiplanaire dans un corps élastique, sous l'effet d'une charge concentrée à son origine, et caractérisée par des variations dans le temps. L'analyse est basée sur une transformation de Chaplygin, solutionnée en recourant à une technique de représentation conforme. Le problème a été réduit à un problème mixte de valeurs aux limites d'une fonction analytique dans le demi-plan, laquelle peut être résolue par une fonction de Keldish-Sedov.
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Theocaris, P.S., Georgiadis, H.G. Transient propagation of anti-plane cracks opened by time varying loads. Int J Fract 28, 223–230 (1985). https://doi.org/10.1007/BF00035217
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DOI: https://doi.org/10.1007/BF00035217