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**Stabilized global-local X-FEM for 3D non-planar frictional crack using relevant meshes.**
*(English)*
Zbl 1242.74121

Summary: A stabilized global-local quasi-static contact algorithm for 3D non-planar frictional crack is presented in the X-FEM/level set framework. A three-field weak formulation is considered and allows an independent discretization of the bulk and the crack interface. Then, a fine discretization of the interface can be defined according to the possible complex contact state along the crack faces independently from the mesh in the bulk. Furthermore, an efficient stabilized non-linear LATIN solver dedicated to contact and friction is proposed. It allows solving in a unified framework frictionless and frictional contact at the crack interface with a symmetric formulation, no iterations on the local stage (unilateral contact law with/without friction), no calculation of any global tangent operator, and improved convergence rate. 2D and 3D patch tests are presented to illustrate the relevance of the proposed model and an actual 3D frictional crack problem under cyclic fretting loading is modeled.

### MSC:

74S05 | Finite element methods applied to problems in solid mechanics |

74R10 | Brittle fracture |

74M10 | Friction in solid mechanics |

### Keywords:

three-field weak formulation; frictional contact algorithm; X-FEM; LBB condition; stabilization
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\textit{A. Gravouil} et al., Int. J. Numer. Methods Eng. 88, No. 13, 1449--1475 (2011; Zbl 1242.74121)

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