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A fixed grid finite element algorithm, previously developed for the moving boundary simulation in non-linear diffusion problems, is adapted to the problem of planar equilibrium crack evolution. The equivalence in the moving boundary conditions between the two problems is initially established. The use of the fixed grid algorithm eliminates the solution interpolation step and makes the simulation numerically efficient and stable, in comparison to previously reported models which utilize migrating mesh techniques. The accuracy and the enhanced applicability of the developed algorithm are demonstrated by the penny-shaped and multi-layered model results.
hydraulic fracture, fracture propagation, equilibrium crack, fixed grid, finite element model, planar crack
Assistant Professor, Department of Mechanical Engineering, Sogang University, Seoul,