Consistent element-free Galerkin method for three-dimensional crack propagation based on a phase-field model

Abstract Element-free Galerkin (EFG) method for three-dimensional phase-field model of cracks is described. Quadratic moving least-squares (MLS) approximation is constructed for both the phase field and the displacement. The quadratically consistent 4-point (QC4) integration scheme using background tetrahedral elements (cells) is employed to efficiently compute the domain integrals in weak forms. As cracks propagate, adaptive refinement of the approximation nodes around crack fronts is implemented with the use of background integration cells. The refinement is triggered by the maximum residual strain energy history. New approximation nodes are inserted at the midpoints of the element edges. Several benchmark examples are investigated. Numerical results show that three-dimensional crack propagation is successfully modeled by the proposed method and correct crack paths and load-displacement responses are obtained. Due to the implemented h-adaptivity, lots of approximation nodes are saved and the computational scale is significantly reduced. Improved accuracy of the proposed method in stress distribution and crack width is also demonstrated.