Employment of Eulerian, Lagrangian, and arbitrary Lagrangian-Eulerian description for crack opening problem

Numerical study of crack opening in the solid material of rock formation is presented in this article. Initially introduced straight-line crack is widened by increasing internal pressure. The crack shape evolution resembles hydraulic fracturing and is considered as a transient process. Commercial code LS-DYNA was employed to obtain solutions by three types of descriptions, they are compared to the solution obtained in Eulerian description by a program based on the finite-volume method and written in Python language. The main features of the self-developed code are a direct relation between velocities and strains, and a deriving of the aperture through density distribution.