A universal optimum quarter point element

Abstract Finding the optimum quarter point element (QPE) in numerical fracture mechanics is complicated by the variability of the singularity-dominated zone existing in the vicinity of a cracktip from one crack configuration to another. This forces the universal optimum to be defined in a weak sense. Apart from their characteristics as “sentinel”-elements, proper sizing for singular transition elements is proposed. Numerical assessments indicate that certain geometrical shape regularity is required for the QPE, and that with the use of transition elements, the universal optimum QPE size lies in the range of 15–25% of the crack length for a 5% error bound. Supported by numerical experiments conducted and the use of proper transition elements' sizes proposed, this result can reasonably be conjectured to general crack configurations. In fact in a crack propagation model without adaptivity technique, the universal optimum strategy should give the “best” results possible. In a crack propagation model where topological changes discretely occur, the universal optimum in the strong sense may only be attainable when both remeshing and adaptivity techniques are blended. For an accurate determination of stress intensity factors (SIFs), it is recommended to conduct a few convergence studies about the universal optimum size to obtain the lower bound error. For a crack propagation model that uses stresses and/or energy-based failure criteria, it is suggested that the second term of the Williams' series expansion be included to improve accuracy.