An extended finite element method for modeling crack growth with frictional contact

Abstract

A new technique for the ®nite element modeling of crack growth with frictional contact on the crack faces is presented. The eX tended Finite Element Method (X FEM) is used to discretize the equations, allowing for the modeling of cracks whose geometry are independent of the ®nite element mesh. This method greatly facilitates the simulation of a growing crack, as no remeshing of the domain is required. The conditions which describe frictional contact are formulated as a non smooth constitutive law on the interface formed by the crack faces, and the iterative scheme implemented in the LATIN method [Nonlinear Computational Structural Me chanics, Springer, New York, 1998] is applied to resolve the nonlinear boundary value problem. The essential features of the iterative strategy and the X FEM are reviewed, and the modi®cations necessary to integrate the constitutive law on the interface are presented. Several benchmark problems are solved to illustrate the robustness of the method and to examine convergence. The method is then applied to simulate crack growth when there is frictional contact on the crack faces, and the results are compared to both analytical and experimental results. Ó l evier cience All right re erved

Strength prediction of single- and double-lap joints by standard and extended finite element modelling

“…The employment of plastic enrichments in XFEM modelling is accredited to Elguedj et al [32], which used a new enriched basis function to capture the singular fields in elasto-plastic fracture mechanics. Modelling of contact by the XFEM was firstly introduced by Dolbow et al [33] and afterwards adapted to frictional contact by Khoei and Nikbakht [34]. Fagerströ m and Larsson [35] implemented geometrically non-linearities within XFEM.…”

Evaluación de la rigidez a flexión de puentes de viga y losa en concreto presforzado a partir de pruebas de carga. Caso de estudio: Puente La Parroquia vía La Renta - San Vicente de Chucurí

“…Si el problema es abordado usando el XFEM, la malla no se adapta a la geometría de la grieta y es necesario integrar funciones no continuas o singulares. Esta integración numérica ha sido objeto de distintos trabajos [13,[20][21][22][23][24][25][26].…”

“…La integración de dichos elementos debe ser abordada con cierto cuidado, debido a la presencia de funciones que presentan discontinuidades y singularidades. Las reglas de integración que se pueden emplear han sido consideradas en diversos trabajos [13,[20][21][22][23][24][25][26], que generalmente, se basan en la subdivisión del elemento en subelementos conformes con la geometría de la grieta; normalmente triángulos o cuadriláteros para dos dimensiones y en tetraedros o hexaedros para tres dimensiones, con las caras de los nuevos subelementos orientadas con la grieta.…”

Stability of incompressible formulations enriched with X-FEM

“…The resolution of compressible fracture mechanics problems has been extensively studied in the context of the X-FEM for both 2D [39,18,40,32,24] and 3D fracture mechanics [21,22]. The most common enrichment strategy consists in using the asymptotic displacement field as an enrichment for the displacement finite element approximation.…”

“…Proper enrichment of the finite element basis makes it possible to model crack, material inclusions and holes with non-conforming meshes. The X-FEM method has been used for the simulation of a wide variety of problems such as fracture mechanics problems (2D [18][19][20], 3D [21][22][23], plates [24,25], cohesive zone modeling [26,27], dynamic fracture [28], nonlinear fracture mechanics [29][30][31]), holes [32,33], but also material inclusions [33,34] or multiple phase flows [35]. Here, we focus on the application of this method to mixed formulations for the treatment of holes, material inclusions and cracks in the incompressible limit.…”