263 research outputs found
Stability of incompressible formulations enriched with X-FEM
The treatment of (near-)incompressibility is a major concern for applications involving rubber-like materials, or when important plastic ows occurs as in forming processes. The use of mixed nite element methods is known to prevent the locking of the nite element approximation in the incompressible limit. However, it also introduces a critical condition for the stability of the formulation, called the infsup or LBB condition. Recently, the nite element method has evolved with the introduction of the partition of unity. The eXtended Finite Element Method (XFEM) uses the partition of unity to remove the need to mesh physical surfaces or to remesh them as they evolve. The enrichment of the displacement eld makes it possible to treat surfaces of discontinuity inside nite elements. In this paper, some strategies are proposed for the enrichment of mixed nite element approximations in the incompressible setting. The case of holes, material interfaces and cracks are considered. Numerical examples show that for well chosen enrichment strategies, the nite element convergence rate is preserved and the inf-sup condition is passed
Multiscale Partition of Unity
We introduce a new Partition of Unity Method for the numerical homogenization
of elliptic partial differential equations with arbitrarily rough coefficients.
We do not restrict to a particular ansatz space or the existence of a finite
element mesh. The method modifies a given partition of unity such that optimal
convergence is achieved independent of oscillation or discontinuities of the
diffusion coefficient. The modification is based on an orthogonal decomposition
of the solution space while preserving the partition of unity property. This
precomputation involves the solution of independent problems on local
subdomains of selectable size. We deduce quantitative error estimates for the
method that account for the chosen amount of localization. Numerical
experiments illustrate the high approximation properties even for 'cheap'
parameter choices.Comment: Proceedings for Seventh International Workshop on Meshfree Methods
for Partial Differential Equations, 18 pages, 3 figure
Méthode X-SFEM pour le calcul de structure à géométrie aléatoire : application au calcul d'un joint de soudure
In structural analysis, stochastic finite element methods offer a robust tool to deal with randomness on material properties or loadings. Unfortunately, there is still no available efficient strategy to deal with uncertainties on the geometry. Here, we bring an answer to this problem by proposing a new method based on an extension to the stochastic framework of the eXtended Finite Element Method (X-FEM). This method lies on the use of the level set technique for the implicit description of the random geometry and the use of Galerkin approximation at deterministic and stochastic levels. Here, this method is applied to the analysis of a random welded joint
Mitochondrial quality control and neurological disease: an emerging connection
The human brain is a highly complex organ with remarkable energy demands. Although it
represents only 2% of the total body weight, it accounts for 20% of all oxygen
consumption, reflecting its high rate of metabolic activity. Mitochondria have a crucial
role in the supply of energy to the brain. Consequently, their deterioration can have
important detrimental consequences on the function and plasticity of neurons, and is
thought to have a pivotal role in ageing and in the pathogenesis of several neurological
disorders. Owing to their inherent physiological functions, mitochondria are subjected to
particularly high levels of stress and have evolved specific molecular quality-control
mechanisms to maintain the mitochondrial components. Here, we review some of the most
recent advances in the understanding of mitochondrial stress-control pathways, with a
particular focus on how defects in such pathways might contribute to neurodegenerative
disease
A three-scale domain decomposition method for the 3D analysis of debonding in laminates
The prediction of the quasi-static response of industrial laminate structures
requires to use fine descriptions of the material, especially when debonding is
involved. Even when modeled at the mesoscale, the computation of these
structures results in very large numerical problems. In this paper, the exact
mesoscale solution is sought using parallel iterative solvers. The LaTIn-based
mixed domain decomposition method makes it very easy to handle the complex
description of the structure; moreover the provided multiscale features enable
us to deal with numerical difficulties at their natural scale; we present the
various enhancements we developed to ensure the scalability of the method. An
extension of the method designed to handle instabilities is also presented
The role of rock joint frictional strength in the containment of fracture propagation
The fracturing phenomenon within the reservoir environment is a complex process that is controlled by several factors and may occur either naturally or by artificial drivers. Even when deliberately induced, the fracturing behaviour is greatly influenced by the subsurface architecture and existing features. The presence of discontinuities such as joints, artificial and naturally occurring faults and interfaces between rock layers and microfractures plays an important role in the fracturing process and has been known to significantly alter the course of fracture growth. In this paper, an important property (joint friction) that governs the shear behaviour of discontinuities is considered. The applied numerical procedure entails the implementation of the discrete element method to enable a more dynamic monitoring of the fracturing process, where the joint frictional property is considered in isolation. Whereas fracture propagation is constrained by joints of low frictional resistance, in non-frictional joints, the unrestricted sliding of the joint plane increases the tendency for reinitiation and proliferation of fractures at other locations. The ability of a frictional joint to suppress fracture growth decreases as the frictional resistance increases; however, this phenomenon exacerbates the influence of other factors including in situ stresses and overburden conditions. The effect of the joint frictional property is not limited to the strength of rock formations; it also impacts on fracturing processes, which could be particularly evident in jointed rock masses or formations with prominent faults and/or discontinuities
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