An extended finite element method (X-FEM) for three-dimensional crack modelling is described. A discontinuous function and the two-dimensional asymptotic crack-tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity. This enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces. Computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed. Stress intensity factors (SIFs) for planar three-dimensional cracks are presented, which are found to be in good agreement with benchmark solutions. Copyright © 2000 John Wiley & Sons, Ltd.

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Extended finite element method for three-dimensional crack modelling

Brittle failure of components weakened by cracks or sharp and blunt V-notches is a topic of active and continuous research. It is attractive for all researchers who face the problem of fracture of materials under different loading conditions and deals with a large number of applications in different engineering fields, not only with the mechanical one. This topic is significant in all the cases where intrinsic defects of the material or geometrical discontinuities give rise to localized stress concentration which, in brittle materials, may generate a crack leading to catastrophic failure or to a shortening of the assessed structural life. Whereas cracks are viewed as unpleasant entities in most engineering materials, U- and V-notches of different acuities are sometimes deliberately introduced in design and manufacturing of structural components. Dealing with brittle failure of notched components and summarizing some recent experimental results reported in the literature, the main aim of the present contribution is to present a review of some local approaches applicable near stress raisers both sharp and blunt. The reviewed criteria allowed the present authors to develop a new approach based on the volume strain energy density (SED), which has been recently applied to assess the brittle failure of a large number of materials. The main features of the SED approach are outlined in the paper and its peculiarities and advantages accurately underlined. Some examples of applications are reported, as well. The present review is based on the authors’ experience over more than 15 years and the contents of their personal library. It is not a dispassionate literature survey.

Recent developments in brittle and quasi-brittle failure assessment of engineering materials by means of local approaches

J.P. Benthem

Papers

State of stress at the vertex of a quarter-infinite crack in a half-space

The quarter-infinite crack in a half space; Alternative and additional solutions