Hybrid analytical and extended finite element method (HAX‐FEM): A new enrichment procedure for cracked solids

Abstract

To cite this version:Julien Réthoré, Stéphane Roux, François Hild. Hybrid analytical and extended finite element method (HAX-FEM): A new enrichment procedure for cracked solids. International Journal for Numerical Methods in Engineering, Wiley, 2010, 81, pp.269-285. 10 SUMMARYA new numerical method is proposed to estimate directly stress intensity factors at the tip of a crack in an elastic body. In the same spirit as for the extended finite element method, the approximation of the displacement field is enriched in the vicinity of the crack tip. Yet the method proposed herein differs by the way the enrichment is introduced. Instead of using partition of unity concepts, a two-description formulation is implemented. The first one uses standard finite elements while the second one, in the vicinity of the crack tip, resorts to a few purely analytical expressions. These two descriptions are then coupled by partitioning the energy with an overlapping zone. The performance of this new enrichment technique is illustrated and compared with existing techniques by means of two examples.

Direct estimation of generalized stress intensity factors using a three‐scale concurrent multigrid X‐FEM

“…In order to close the problem, one needs to impose the compatibility of displacement fields. In opposition with the method proposed in [31], the sub-domains are non-overlapping, their intersection reduces to an interface denoted Γ W . Thus the coupling is no longer ensured thanks to a partition of the energy technique (i.e.…”

“…Here the same interpolation as HAX-FEM [31] is used. In the sequel, a brief review of the main aspects is given.…”

“…First, an edge-cracked plate in remote tension (ECPT) is used to compare the efficiency of the method with that of [31]. Then a wedge splitting specimen (WS), case for which an in-depth study is provided by [14], shows that the method is also appropriate for the accurate estimation of higher order terms of the Williams' expansion.…”

“…For different values of the order of truncation n max of the williams' expansion, the normalized value of K I is plotted as a function of the size of the analytical patch r W on Figure 3(a) for the Arlequin matching (from [31]) and on Figure 3(b) for the integral matching proposed herein. A comparable level of accuracy is obtained and the dependence on the size of the patch observed for n max = 2 vanishes similarly when higher order terms are taken into account.…”

“…This last method provides more accurate SIF and also yields higher order coefficients precisely. Recently, a Hybrid Analytical and eXentended Finite Element Method (HAX-FEM) was proposed by Réthoré et al [31]. This convenient and accurate tool couples two different models: an analytical reduced order model based on a truncated Williams' expansion in the vicinity of the crack tip and a standard X-FEM model with the discontinuous function along the crack faces alone.…”