Equation of the Crack Front with Allowance for the Metric Properties of the Material

The geometric representation of the crack front propagation is examined in a Finsler space in the context of the discontinuity theory. The structure of the medium is taken into account via the connectivity coefficients of the Finsler space and its metric. It is demonstrated that this approach leads to the construction of fiber spaces and allows the gauge invariance to be introduced correctly and noncontradictorily into the fracture theory. The Lie derivative is used to proceed from discontinuities to differentials. The equation of the front crack surface is retrieved.