the cracked brazilian disc (cbd) specimen is widely used in order to determine mode-i/ii and mixed-mode fracture toughness of a rock medium. in this study, the stress intensity factor (sif) on the crack-tip in this specimen is calculated for various geometrical crack conditions using the extended-finite element method (x-fem). this method is based upon the finite element method (fem). in this m...

Recently, a new strategy was proposed to solve stochastic partial differential equations on random domains. It is based on the extension to the stochastic framework of the eXtended Finite Element Method (X-FEM). This method leads by a “direct” calculus to an explicit solution in terms of the variables describing the randomness on the geometry. It relies on two major points: the implicit represe...

Dendritic solidification of pure materials from an undercooled melt is studied using the extended finite element method/level set method for modelling the thermal problem and a volume-averaged stabilized finite element formulation for modelling fluid flow. The extended finite element method using evolving enrichment functions allows accurate modelling of the discontinuous thermal conditions at ...

Extended finite element method (XFEM) is the most effective numerical method to solve discrete mechanical problem. Crack growth problem of two-dimension finite length rectangle panel is researched based on Abaqus XFEM frame. Stress intensity factor is obtained respectively by theoretical calculation and XFEM simulation, which proves reliability of XFEM and the software.

Goal oriented error estimation and adaptive procedures are essential for the accurate and efficient evaluation of numerical simulations that involve complex domains. By locally improving the approximation quality we can solve expensive problems which could result intractable otherwise. Here, we present an error estimation technique for enriched finite element approximations that is based on an ...

In this note we propose a finite element method for incompressible (or compressible) elasticity problems with discontinuous modulus of elasticity (or, if compressible, Poisson’s ratio). The problem is written on mixed form using P 1–continuous displacements and the space of piecewise P 0 pressures, leading to the possibility of eliminating the pressure beforehand in the compressible case. In th...

A general review of the extended finite element method and its application to the simulation of first-order phase transitions is provided. Detailed numerical investigations are then performed by focusing on the one-dimensional case and studying: (i) spatial and temporal discretisations, (ii) different numerical techniques for the interface-condition enforcement, and (iii) different treatments f...