Numerical simulation of cohesive crack growth and the normal contact in porous media using enriched element-free Galerkin method

This study addresses the numerical simulation of cohesive crack propagation and the problem of normal contact in porous media. Penalty method is used to inforce essential boundary conditions. The strong discontinuity in the deformation field is effectively modeled by exploiting the partition of unity property of element-free Galerkin shape functions and employing an external enrichment strategy. To account for the crack initiation and propagation behavior in mode I, which occurs under tensile stresses, as well as the compressive behavior at the edges of a closed crack in compression, the cohesive crack theory and the penalty method are incorporated into the existing computer program prepared for the simulation of porous media using the enriched element-free Galerkin method. The resulting algebraic system of equations are strongly non-linear. So, a suitable approach must be utilized to linearize and solve the equations. Newton-Raphson technique is utilized in this study for this purpose. The results obtained from solving the problems of tensile cracks and cracks under compression (i.e., the contact of two crack edges) indicate the capabilities of the numerical formulation and the prepared computer program. Expanding the prepared numerical model allows for the modeling of crack growth problems in porous media in the presence of fluids, as seen in processes like hydraulic fracturing.