3D Dynamic Crack under Cyclic Loading using XFEM: Numerical Treatment. Issue 1 (18th November 2019)

• Record Type: Journal Article
• Authors: Lyu, Tengfei; Löhnert, Stefan; Wriggers, Peter
• Other Names: Eberhardsteiner J. guestEditor.; Schöberl M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 19:Issue 1(2019)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2019-11-18
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201900147
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: The eXtended Finite Element Method (XFEM) is a special numerical method to handle arbitrary discontinuities in the displacement field independent of the finite element mesh. This is advantageous during crack initiation, growth and propagation processes. In the range of continuum damage mechanics, gradient‐enhanced damage models can be used to model damage and fracture without spurious mesh dependencies. Gradient‐enhanced damage models have been investigated extensively in the context of quasi‐brittle and elasto‐plastic materials. To avoid fracture and failure of materials, modelling the component under cyclic loading is significant for fatigue lifetime prediction. The focus of this contribution is set on algorithmic issues. The numerical treatment of 3d cracks under cyclic loading is investigated. The domain is discretized with ten‐node tetrahedral elements. Discrete cracks are captured using XFEM and updated by level set methods. In oder to take advantage of the explicit time discretization scheme, a modified differential equation for the gradient‐enhanced damage is presented and the central difference explicit time stepping method is employed to obtain 2 nd oder accuracy of the solved equations.