An improvement of a new technique for modelling cracks in the ÿnite element framework is presented. A standard displacement-based approximation is enriched near a crack by incorporating both discontinuous ÿelds and the near tip asymptotic ÿelds through a partition of unity method. A methodology that constructs the enriched approximation from the interaction of the crack geometry with the mesh is developed. This technique allows the entire crack to be represented independently of the mesh, and so remeshing is not necessary to model crack growth. Numerical experiments are provided to demonstrate the utility and robustness of the proposed technique.
An improvement of a new technique for modelling cracks in the ÿnite element framework is presented. A standard displacement-based approximation is enriched near a crack by incorporating both discontinuous ÿelds and the near tip asymptotic ÿelds through a partition of unity method. A methodology that constructs the enriched approximation from the interaction of the crack geometry with the mesh is developed. This technique allows the entire crack to be represented independently of the mesh, and so remeshing is not necessary to model crack growth. Numerical experiments are provided to demonstrate the utility and robustness of the proposed technique.
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
SUMMARYA key challenge while employing non-interpolatory basis functions in finite-element methods is the robust imposition of Dirichlet boundary conditions. The current work studies the weak enforcement of such conditions for B-spline basis functions, with application to both second-and fourth-order problems. This is achieved using concepts borrowed from Nitsche's method, which is a stabilized method for imposing constraints on surfaces. Conditions for the stability of the system of equations are derived for each class of problem. Stability parameters in the Nitsche weak form are then evaluated by solving a local generalized eigenvalue problem at the Dirichlet boundary. The approach is designed to work equally well when the grid used to build the splines conforms to the physical boundary of interest as well as to the more general case when it does not. Through several numerical examples, the approach is shown to yield optimal rates of convergence.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.