Implementation of the phase-field method for brittle fracture and application to porous structures

Recently, the phase field approach has gained popularity as a versatile tool for simulating crack propagation. The purpose of this study is to employ the capabilities of the phase field method for crack growth modeling in complex structures such as porous media. The phase field method does not need predefined cracks and it can simulate curvilinear crack path. This goal is accomplished by replacing the sharp discontinuities with a scalar damage phase field parameter representing the diffuse crack topology. To simulate brittle fracture in this study, the equations of elastic displacement field and fracture phase field are first introduced. Afterwards, using the weak form of the equations, the staggered solution of the equations is performed. To implement the equations in the finite element method, the Abaqus software with User Element Subroutine (UEL) is used. Given that the bone structure is somehow a porous structure, a representative volume element of the bone is selected for phase field simulation. In order to verify the developed model, the tensile test of the single edge notched specimen has been simulated. Subsequently, crack propagation in a porous media with different porosities under tensile loading was simulated. The simulation results illustrate the capability of the phase field method in predicting crack growth in geometrically complex structures. In addition, the load-carrying capacity or the strength of the porous structure continuously decreases with increasing porosity and noteworthy is that such a strength is suddenly decreased around a critical porosity value.