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Combined Extended and Superposed Finite Element Method for Modeling of Cracks

Combined Extended and Superposed Finite Element Method for M...

The Sixth World Congress on Computational Mechanics in Conjunction with the Second Asian-Pacific Congress on Computational MechanicsⅠ

作者： Sang-Ho Lee Jeong-Hoon Song Young-Cheol Yoon Goangseup Zi Ted Belytschko School of Civil and Environmental Engineering Yonsei University 134 Sinchon-dong Seodaemun-gu Seoul 120-749 Korea Department of Mechanical Engineering Northwestern University 2145 Sheridan Road Evanston IL 60208-3111 U.S.A. Department of Civil & Environmental Engineering Korea University Anam-dong 5-ga seongbukgu 136-701

A hybrid method, a combination of the extended finite element method (XFEM) [1] and the mesh superposition method (s-version FEM, or SFEM) [2], for modeling of stationary and growing cracks is presented. It is called the combined extended and superposed finite element method (XS- FEM). The near-tip field is modeled by superimposed quarter point singular elements on an overlaid patch and the rest of the discontinuity is implicitly described by a step function partition of unity in the same manner of XFEM. The two displacement fields are matched through a transition region. The proposed method simplifies the treatment of the moving near-tip fields [3]. Furthermore, a local partition of unity does not lose the reproducing property when the enriched elements are blended with standard finite elements, and the interpolation spaces are well defined when the near-tip field matches with enriched displacement field because the near-tip field totally participates in the complete approximation. It also avoids linear dependency. The quadrature of the weak form where the integrand is discontinuous due to arbitrary overlap of mesh becomes awkward in SFEM but the proposed method can effectively deal with it by a double mapping procedure. The crack growth is treated by the translation and rotation of the overlaid mesh and the update of the enriched nodes on the basic mesh. Numerical experiments for linear elastic fracture mechanics problems and cohesive cracks are provided to demonstrate the effectiveness and robustness of the proposed method.

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