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Arbitrary Discontinuities (arbitrary + discontinuity)

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Engineering	100%

Selected Abstracts

Arbitrary discontinuities in space,time finite elements by level sets and X-FEM

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004
Jack Chessa
Abstract An enriched finite element method with arbitrary discontinuities in space,time is presented. The discontinuities are treated by the extended finite element method (X-FEM), which uses a local partition of unity enrichment to introduce discontinuities along a moving hyper-surface which is described by level sets. A space,time weak form for conservation laws is developed where the Rankine,Hugoniot jump conditions are natural conditions of the weak form. The method is illustrated in the solution of first order hyperbolic equations and applied to linear first order wave and non-linear Burgers' equations. By capturing the discontinuity in time as well as space, results are improved over capturing the discontinuity in space alone and the method is remarkably accurate. Implications to standard semi-discretization X-FEM formulations are also discussed. Copyright © 2004 John Wiley & Sons, Ltd. [source]

A discrete model for the dynamic propagation of shear bands in a fluid-saturated medium

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2007
Julien Réthoré
Abstract The first part of this manuscript discusses a finite element method that captures arbitrary discontinuities in a two-phase medium by exploiting the partition-of-unity property of finite element shape functions. The fluid flow away from the discontinuity is modelled in a standard fashion using Darcy's relation, and at the discontinuity a discrete analogy of Darcy's relation is used. Subsequently, dynamic shear banding is studied numerically for a biaxial, plane-strain specimen. A Tresca-like as well as a Coulomb criterion is used as nucleation criterion. Decohesion is controlled by a mode-II fracture energy, while for the Coulomb criterion, frictional forces are transmitted across the interface in addition to the cohesive shear tractions. The effect of the different interface relations on the onset of cavitation is studied. Finally, a limited quantitative study is made on the importance of including a so-called dynamic seepage term in Darcy's relation when considering dynamic shear banding. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Towards the algorithmic treatment of 3D strong discontinuities

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2007
J. Mergheim
Abstract A geometrically non-linear finite element framework for the modelling of propagating discontinuities in three-dimensional continua is presented. By doubling the degrees of freedom in the discontinuous elements, the algorithm allows for arbitrary discontinuities which are not restricted to inter-element boundaries. The deformation field is interpolated independently on both sides of the discontinuity. In contrast to the X-FEM, the suggested approach thus relies exclusively on displacement degrees of freedom. On the discontinuity surface, the jump in the deformation is related to the cohesive tractions to account for smooth crack opening. Computational difficulties characteristic of three-dimensional crack propagation are addressed. The performance of the method is elaborated by means of a homogeneous three-dimensional tension problem and by means of the classical peel test. Copyright © 2006 John Wiley & Sons, Ltd. [source]

A note on enrichment functions for modelling crack nucleation

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2003
J. Bellec
Abstract For particular discretizations and crack configurations, the enhanced approximations of the eXtended finite-element method (X-FEM) cannot accurately represent the discontinuities in the near-tip displacement fields. In this note, we focus on the particular case where the extent of the crack approaches the support size of the nodal shape functions. Under these circumstances, the asymptotic ,branch' functions for each tip may extend beyond the length of the crack, resulting in a non-conforming approximation. We explain the limitations of the standard approximation for arbitrary discontinuities, and propose a set of adjustments to remedy the deficiencies. We also provide numerical results that demonstrate the advantages of the modified approximation. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Strong and weak arbitrary discontinuities in spectral finite elements

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 8 2005
A. Legay
Abstract Methods for constructing arbitrary discontinuities within spectral finite elements are described and studied. We use the concept of the eXtended Finite Element Method (XFEM), which introduces the discontinuity through a local partition of unity, so there is no requirement for the mesh to be aligned with the discontinuities. A key aspect of the implementation of this method is the treatment of the blending elements adjacent to the local partition of unity. We found that a partition constructed from spectral functions one order lower than the continuous approximation is optimal and no special treatment is needed for higher order elements. For the quadrature of the Galerkin weak form, since the integrand is discontinuous, we use a strategy of subdividing the discontinuous elements into 6- and 10-node triangles; the order of the element depends on the order of the spectral method for curved discontinuities. Several numerical examples are solved to examine the accuracy of the methods. For straight discontinuities, we achieved the optimal convergence rate of the spectral element. For the curved discontinuity, the convergence rate in the energy norm error is suboptimal. We attribute the suboptimality to the approximations in the quadrature scheme. We also found that modification of the adjacent elements is only needed for lower order spectral elements. Copyright © 2005 John Wiley & Sons, Ltd. [source]