Crack Path Prediction in Anisotropic Brittle Materials
Dr. V. Hakim and Dr. A. Karma of Ecole Normale Superieure, Paris, France, worked out a crack path prediction formula by utilizing a generalized energy-momentum tensor whose integral along an arbitrary closed path around crack tip yields all forces acting on the crack, including Eshelby's configurational forces, cohesive forces, and dissipative forces.
Crack Path Prediction in Anisotropic Brittle Materials,
By Vincent Hakim and Alain Karma, Physical Review Letters, 95, 235501, (2005)
They adopted a so-called phase-field approach (Ginzburg-Landau), and the generalized energy-momentun tensor is formulated in a four-dimensional vector field. In a numerical computation, they showed that they can prescisely predict the crack path in an anisotropic brittle material.