Optimization of a stabilized X-FEM formulation for frictional cracks

• Published in: Finite elements in analysis and design Vol. 59; pp. 18 - 27
• Main Authors: Trollé, B., Gravouil, A., Baietto, M.-C., Nguyen-Tajan, T.M.L.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-10-2012; Elsevier
• Subjects: Cracks; Engineering Sciences; Exact sciences and technology; Finite element method; Fracture mechanics (crack, fatigue, damage...); Frictional contact algorithm; Fundamental areas of phenomenology (including applications); LBB condition; Mathematical analysis; Mathematical models; Mathematics; Mechanical contact (friction...); Mechanics; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis. Scientific computation; Optimization; Physics; Sciences and techniques of general use; Searching; Solid mechanics; Solvers; Structural and continuum mechanics; Three dimensional; Three field weak formulation; X-FEM; X-FEM; Three field weak formulation; Optimization; Frictional contact algorithm; LBB condition; Performance evaluation; Stabilization; Mechanical contact; Boundary condition; Modeling; Global local method; Finite element method; Finite geometry; Weak solution; Efficiency; Convergence rate; Non linear effect; Numerical convergence; Sliding friction; Crack; eXtended Finite Element Method
• ISSN: 0168-874X; 1872-6925
• DOI: 10.1016/j.finel.2012.04.010

An efficient stabilized nonlinear LATIN solver dedicated to frictional cracks in the X-FEM framework is proposed. The performance of such a solver has already been emphasized in detail in a previous paper of Gravouil et al. [Stabilized global–local X-FEM for 3D non-planar frictional crack using relevant meshes, Int. J. Numer. Methods Eng. 88 (2011)1449–1475] Here, an optimization of the search direction of the LATIN solver is proposed. Intrinsic a priori formulas are proposed independently on the friction coefficient, the finite element mesh, the geometry and the boundary conditions. About one hundred thousand of calculations have been carried out in order to show the existence of a unique set of parameters ensuring the optimal convergence rate. The number of iterations required to reach the given level of accuracy is plotted versus two numerical parameters introduced, the search direction k and the stabilization operator ξ. A considerable decrease in the number of iterations and thus in the computing time is obtained, an important condition to carry out with a maximum efficiency of 3D simulations.
► Optimal stabilized X-FEM nonlinear solver for 2D/3D frictional cracks. ► Optimization of the convergence rate according to both the search direction and the stabilization operator. ► Parametric study of the influence/non-influence of the boundary conditions, mesh size, material, friction coefficient, crack shape on these parameters. ► Robustness and control the convergence rate of the LATIN nonlinear solver is demonstrated.