International Journal for Numerical Methods in Engineering · 2002 · 647 citations · 30 references
EngineeringComputational EngineeringMechanical EngineeringComputational MechanicsFinite Element AnalysisFinite Element MethodsFracture GeometryFracture MechanicsFracture PropagationSolid Mechanics ApplicationsStructural Finite Element AnalysisComputational Fracture MechanicsCrack GrowthCrack Growth AnalysisCrack Growth ModelingFracture ModelingFracture Propagation AnalysisHeaviside Step FunctionSigned Distance Functions
The study presents a mesh‑independent methodology for solving three‑dimensional crack problems. The approach employs the extended finite element method, introducing a Heaviside step function and branch functions with asymptotic near‑tip fields, while representing the crack geometry through two signed distance functions defined at nodes, thereby eliminating the need for explicit crack representation and allowing extension to inelastic fracture. Illustrative examples of three‑dimensional elastostatic problems demonstrate that the method’s results agree with analytic and benchmark solutions. © 2002 John Wiley & Sons, Ltd.
Abstract A methodology for solving three‐dimensional crack problems with geometries that are independent of the mesh is described. The method is based on the extended finite element method, in which the crack discontinuity is introduced as a Heaviside step function via a partition of unity. In addition, branch functions are introduced for all elements containing the crack front. The branch functions include asymptotic near‐tip fields that improve the accuracy of the method. The crack geometry is described by two signed distance functions, which in turn can be defined by nodal values. Consequently, no explicit representation of the crack is needed. Examples for three‐dimensional elastostatic problems are given and compared to analytic and benchmark solutions. The method is readily extendable to inelastic fracture problems. Copyright © 2002 John Wiley & Sons, Ltd.
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