Crack trajectory instability: Propagation in inhomogeneous medium

The problem of crack trajectory stabilization in composite material is investigated. The equation for a crack path is found from the variational principle. It is considered as a path along which the extreme amount of energy is generated during the destruction. This statement corresponds to the variational problem analogous to the Lagrange-d'Alembert principle of classic mechanics and to the Fermat principle in optic and acoustic. For a crack path in inhomogeneous medium, nonlinear differential equation is obtained. Stability of the crack propagation in the inhomogeneous medium is considered. In particular, a 2D crack propagating in a composite material is considered. The path of propagation is assumed to cross layers or fibres. For layered and piece-wise continuous composites, the resulting governing equation corresponds to different kind of Duffing's equation. The bifurcations of the trajectory and instability of crack path are investigated numerically. Conditions of crack trajectory stabilization are found. Properties of the materials that stabilized the crack trajectory are found.