The stress-corrected asymptote solves the problem of a semi-infinite fluid-driven fracture propagating through multiple stress layers in a permeable elastic medium. Such a problem represents the tip region of a planar hydraulic fracture.
This module implements three approaches to incorporate the effect of stress layers into the tip asymptote: integral formulation, toughness corrected asymptote, and an ODE approximation. The integral formulation approach involves solving the non-singular integral formulation for the problem. The second, toughness-corrected asymptote, utilizes the universal asymptotic solution and the concept of an effective toughness, which is calculated using the toughness-dominated asymptote and stress intensity factor correction due to stress layers. The ODE approach is based on the ordinary differential equation approximation of the non-singular integral formulation.
The schematics for fracture width and distance to the fracture front computation is shown below. For a detailed description of the mathematical background see References section.
