03_fracture.pdf

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03_fracture

EFG and XFEM Cohesive Fracture Analysis Methods in LS-DYNA Yong Guo*, Cheng-Tang Wu Livermore Software Technology Corporation LS-DYNA Seminar Stuttgart, Germany November 24, 2010 LS-DYNA Seminar 2 1. Overview on Failure/Crack Simulations 2. EFG and XFEM Cohesive Fracture Methods 3. Numerical Examples 4. Conclusions Outline LS-DYNA Seminar 3 1. Overview on Failure/Crack Simulations  Tie-break Interface Force/stress-based failure + spring element, rigid rods, or other constraints Suitable for delamination, debonding, known weak areas  Element Erosion Stress/strain-based failure + contact force Loss of conservation, strong mesh dependence and inadequate accuracy  Cohesive Interface Element Cohesive zone model + interface element + contact force Crack along interfaces: Mesh dependence  EFG Cohesive zone model + moving least-square + EFG visibility  XFEM Cohesive zone model + level sets + extended finite element LS-DYNA Seminar 4 2. EFG and XFEM Cohesive Failure Methods EFG and XFEM Failure Analysis  Both are discrete approaches (strong discontinuity).  Crack initiation and propagation are governed by cohesive law (Energy release rate).  Crack propagates cell-by-cell in current implementation.  EFG is defined by visibility; XFEM is defined by Level Set.  Minimized mesh sensitivity and orientation effects in cracks.  Applied to quasibrittle materials and some ductile materials.  EFG for Solid with 4-noded integration cells.  XFEM for 2D plain strain and shells. LS-DYNA Seminar 5 2.1 EFG Cohesive Failure Method +?0 ??0 ( )ηX Meshfree Method: MLS + Visibility Criterion (Belytschko et al. 1996) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ),hW ,hWΦ Φ IJ T J J II T I I I I h XXXPXPXA XXXPXAXP uXXu ?= ?= = ∑ ∑ ? = 1 1 ( ) ( ) ( )( ) ( )( ) ( ) ( ) ( ) ( ) ( ) η ηΨΨ η ηΦ η η ηΨηΨηΦη ?J ?J J J J J FEM I I I ?J ?J JJJJI I FEM I ? ? ? ? ? ? ? ? ? ? ? ? ?+ ? ? ?+ ? ? ?= ? ? ? ? ? ? ? ? ? ? ++= ∑ ∑∑ ∑ ∑∑ + ? + ? ∈ ∈= ∈ ∈= X X X u X X uX x uXuXXx 0 0 0 0 2 1 2 1 2 1 2 1 M

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