A self-contained element for modeling crack propagation in beams

Abstract

The Cohesive Zone Model (CZM) has been used to model the propagation of cracks through beams and slabs, which is of practical application in a variety of fields. CZMs have been successfully incorporated into Finite Element (FE) models however, this involves significant pre-processing effort to develop a sufficiently fine mesh around cohesive elements, which also increases the required computational effort. To overcome this limitation, a self-contained’crack element,’ consisting of cohesive elements surrounded by pre-meshed bilinear bulk elements, was developed. A linear interpolation scheme to connect this crack element to adjoining beam elements, as well as a solution procedure using static condensation to solve crack propagation in beams was developed and implemented. Bilinear and non-linear CZMs were implemented to model the behavior of the cohesive elements. Under simple Mode I tension and flexure problems, the results were in-line with the expected behavior. It was found that the crack element was convergent with increasing mesh resolution, and needed to be only as long as its thickness, with the remainder of the beam being modeled by beam elements with just a handful of DOFs, reducing the size of the problem substantially. The element was also used to verify a theoretical model for the variation of modulus of rupture of a beam with its thickness, as well as a mixed-mode problem. In both those cases, the crack element showed good results.