The nite element method is now well established as a robust and reliable numerical technique in many areas of solid mechanics. There are however problems where the use of the nite element method is cumbersome like the modeling of moving discon-tinuities due to the need to update the mesh to match the geometry of the discontinuity. Even for stationary cracks, in three-dimensional solids, contsru...

A numerical technique for planar three-dimensional fatigue crack growth simulations is proposed. The new technique couples the extended finite element method (X-FEM) to the fast marching method (FMM). In the X-FEM, 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 p...

This research pertains to the three-dimensional (3D) finite element analysis (FEA) of the stress intensity factors (SIFs) along the crack front in a spherical pressure vessel coated with functionally graded material (FGM). The vessel is subjected to internal pressure and thermal gradient. The exponential function is adopted for property of FGMs. SIFs are obtained for a wide variety of crack sha...

A methodology for solving three-dimensional crack problems with geometries that are independent of the mesh is described. The method is based on the extended 5nite element method, in which the crack discontinuity is introduced as a Heaviside step function via a partition of unity. In addition, branch functions are introduced for all elements containing the crack front. The branch functions incl...

We study the scaling of three-dimensional crack roughness using large-scale beam lattice systems. Our results for prenotched samples indicate that the crack surface is statistically isotropic, with the implication that experimental findings of anisotropy of fracture surface roughness in directions parallel and perpendicular to crack propagation is not due to the scalar or vectorial elasticity o...

Several automated border detection approaches for three-dimensional echocardiography have been developed in recent years, allowing quantification of a range of clinically important parameters. In this review, the background and principles of these approaches and the different classes of methods are described from a practical perspective, as well as the research trends to achieve a robust method.