A two-dimensional damaged finite element for fracture applications

A novel finite element was developed for fatigue and fracture applications. The new element is two-dimensional with an embedded edge crack. The crack is not physically modeled within the element, but instead, its influence on the local flexibility of the structure is accounted for by the reduction of the element stiffness as a function of the crack length. The components of the stiffness matrix for the cracked element are determined from the Castigliano’s first principle. The element was implemented in the commercial finite element code ABAQUS as a user element (UEL) subroutine. Models using the UEL are shown to produce accurate results when compared with results from traditional models using physical modeling of the crack. The newly developed element is useful for studies focused on the global response of a structure, and does not allow evaluation of the local stress singularity near the crack tip. An advantage of the developed UEL is that the singularity at the crack tip does not need to be captured accurately with a significant number of elements.