Accurate determination of the coefficients of elastic crack tip asymptotic field by a hybrid crack element with p-adaptivity

A hybrid crack element (HCE) originally introduced by Tong, Pian and Lasry for evaluating the stress intensity factor (SIF) is improved to have p-adaptivity and is applied to calculate directly not only the SIF but also the coefficients of the higher order terms of the elastic crack tip asymptotic field. The latter are of great relevance to describing the fracture behaviour of elastic–plastic materials and to interpreting the size effect of quasi-brittle materials. The ambiguities in the variational background, parameter matching condition and integration order of HCE, as well as the arguments on its applicability to crack problems are cleared. Numerical results show that the computed coefficients of the higher order terms as well as the SIF converge rapidly with p-refinement of the HCE and the h-refinement of the remaining regular elements, and that they are stable when the HCE size to the crack length ratio is larger than 0.25. The HCE is efficient down to very short cracks. As expected, the accurate determination of the coefficients of higher order terms is more difficult than that of the SIF; it requires a higher order HCE together with a finer subdivision of the remainder of the body by regular elements.