On crack propagation shapes in elastic bodies

Abstract

We consider a two dimensional elastic isotropic body with a curvilinear crack. The formula for the derivative of the energy functional with respect to the crack length is discussed. It is proved that this derivative is independent of the crack path provided that we consider quite smooth crack propagation shapes. An estimate for the derivative of the energy functional being uniform with respect to the crack propagation shape is derived.

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Correspondence to Martin Brokate.

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Brokate, M., Khludnev, A. On crack propagation shapes in elastic bodies . Z. angew. Math. Phys. 55, 318–329 (2004). https://doi.org/10.1007/s00033-003-3026-3

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Mathematics Subject Classification (2000):

  • 35J55
  • 74B05
  • 74R99

Keywords.

  • Griffith kriterion
  • crack propagation
  • shape dependence
  • linear elasticity
  • fracture mechanics