Determination of coefficients of the crack tip asymptotic field by fractal hybrid finite elements

This paper applies the fractal finite element method (FFEM) together with 9-node Lagrangian hybrid elements to the calculation of linear elastic crack tip fields. An explicit stabilization scheme is employed to suppress the spurious kinematic modes of the sub-integrated Lagrangian element. An extensive convergence study has been conducted to examine the effects of the similarity ratio, reduced integration and the type of elements on the accuracy and stability of the numerical solutions. It is concluded that (i) a similarity ratio close to unity should be used to construct the fractal mesh, (ii) sub-integrated Lagrangian elements with occasionally unstable behaviour should not be used, and (iii) the good accuracy (with differences less than 0.5% with existing available solutions) and stability over a wide range of numerical tests support the use of fractal hybrid finite elements for determining crack tip asymptotic fields.