A Review of Extended/Generalized Finite Element Methods for Material Modelling Ted Belytschko Department of Mechanical Engineering Northwestern University, 2145 Sheridan Road Evanston, IL 60208, U.S.A. E-mail: [email protected] Robert Gracie Department of Mechanical Engineering Northwestern University, 2145 Sheridan Road Evanston, IL 60208, U.S.A. E-mail: [email protected] Giulio Ventura Department of Structural Engineering and Geotechnics Politecnico di Torino, 10129 Torino, Italy Visiting scholar, Department of Mechanical Engineering Northwestern University E-mail: [email protected] Abstract. The extended and generalized finite element methods are reviewed with an emphasis on their applications to problems in material science: (1) fracture (2) dislocations (3) grain boundaries and (4) phases interfaces. These methods facilitate the modeling of complicated geometries and the evolution of such geometries, particularly when combined with level set methods, as for example in the simulation growing cracks or moving phase interfaces. The state of the art for these problems is described along with the history of developments. Keywords : Review, Extended Finite Element Method, Generalized Finite Element Method, fracture, dislocations, grain boundaries, phase interfaces
A Review of Extended/Generalized Finite Element Methods for Material Modelling
Jun 04, 2023
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