An eXtended Stochastic Finite Element Method has been recently proposed for the numerical solution of partial di erential equations de ned on random domains. This method is based on a mariage between the eXtended Finite Element Method and spectral stochastic methods. In this paper, we propose an extension of this method for the numerical simulation of random multi-phased materials. The random g...

The extended finite element method (XFEM) provides a natural way to incorporate strong and weak discontinuities into discretizations. It alleviates the need to mesh discontinuities, allowing simulation meshes to be nearly independent of discontinuity geometry. Currently, both quasistatic deformation and dynamic earthquake rupture simulations under standard FEM are limited to simplified fault ne...

In this paper a new technique aimed to obtain accurate estimates of the error in energy norm using a moving least squares (MLS) recovery-based procedure is presented. We explore the capabilities of a recovery technique based on an enhanced MLS fitting, which directly provides continuous interpolated fields, to obtain estimates of the error in energy norm as an alternative to the superconvergent...

This paper develops the extended finite element method (XFEM) to evolve patterns of multiple cracks, in a brittle thin film bonded to an elastic substrate, with a relatively coarse mesh, and without remeshing during evolution. A shear lag model describes the deformation in three dimensions with approximate field equations in two-dimensions. The film is susceptible to subcritical cracking, obeyi...

The development of the computational techniques used in the analyzes of the dynamic fracture and their implementation in numerical codes takes a growing importance in last years. This interest derives from the necessity to predict the localisation of the initiations of cracks, when and in which direction this crack will propagate throw the material under dynamic loads. Several numerical approac...

This paper presents and studies a residual a posteriori error estimator for Laplace’s equation in two space dimensions approximated by the eXtended Finite Element Method (XFEM). The XFEM allows to perform finite element computations on multi-cracked domains by using meshes of the non-cracked domain. The main idea consists of adding supplementary basis functions of Heaviside type and singular fu...

using computation software to simulate fracture behaviors of structures can shorten the time to estimate safety of engineering structures and reduce a lot of cost of experiment. However three dimensional numerical simulation for fracture process is a challenging issue, because the convergence and accuracy are not easily obtained and high computational cost is generated. In this paper, three new...

The bones of elderly people with osteoporosis are susceptible to either traumatic fracture as a result of external impact, such as what happens during a fall, or even spontaneous fracture without trauma as a result of muscle contraction [1, 2]. Understanding the fracture behavior of bone tissue will help researchers find proper treatments to strengthen the bone in order to prevent such fracture...

Interfacial energy plays an important role in equilibrium morphologies of nanosized microstructures of solid materials due to the high interface-to-volume ratio, and can no longer be neglected as it does in conventional mechanics analysis. The present work develops an effective numerical approach by means of a hybrid smoothed extended finite element/level set method to model nanoscale inhomogen...

Currently, there are many approaches in computer graphics (CG) that deal with topological changes; some of these are non-interactive animations, unstable or not precise enough to medical applications. It has been found that the Extended Finite Element Method (XFEM) is stable, accurate, with excellent performance and suitable for virtual surgery in real time; nevertheless, to maintain the provid...