Numerical investigation on corner singularities in cracked plates using the G-theta method with an adapted θ field

•G-theta method with appropriated virtual crack extension (θ field).•Energy release rate along a crack edge non-orthogonal to the free surface.•Investigation of the corner singularities in cracked plates.•Dependence of vertex singularity to plate thickness.

G-theta method with appropriate virtual crack extension (θ field) is proposed for the accurate evaluation of energy release rate along a crack edge which is non-orthogonal to the free surface. This method is implemented in the framework of finite element procedure as well as extended finite element one. This numerical procedure is then applied to investigate the corner singularities in cracked plates. The superposition of numerical solution to asymptotic solution within the boundary layer of crack front allows showing the dependence of vertex singularity to plate thickness.