Mixed finite element method for end-notched flexure test

To permit more efficient use of the experimental data in the end notched flexure (ENF) test, a mixed finite element method is used to model the macromechanical situation with a small numer of four-noded quadrilateral elements. This small number of elements is made possible by the development of two types of specialty finite elements (constant shear-strain bending element and delamination bending element) within the Hu-Washizu variational principle. With these elements it is possible to satisfy exactly the kinematic boundary conditions of the ENF test—especially at the point of zero slope. Assuming linear elastic fracture mechanics, the critical interlaminar fracture toughness (\IG\N\dI\dI\I\dc\N) is found at one critical load by calculating the difference between the strain energy at the initial crack length and that for an incremental increase in crack length. For a 32-ply, unidirectional, linear transversely isotropic laminate of varying thickness, the values for \IG\N\dI\dI\Idc\N calculated by this finite element model compared well with the results obtained from a previously developed mixed experimental and structural model.