Meshfree Applications to Strain Localization and Fracture in Ductile Metals

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Meshfree Applications to Strain Localization and
Fracture in Ductile Metals

• Darren Luke
• University of New Mexico

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Outline

• Meshfree/Hybrid Particle Methods
• Advantages/Disadvantages
• Applications
• Fracture Simulation in Ductile Metals
• Approaches/Concepts
• Meshfree Applications

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Meshfree Methods

• Advantages
• Shape functions are mesh independent
• Ability to sustain large deformation
• Discretization time can be reduced significantly
• Remeshing is not required
• h and p-type adaptivity is straightforward
• Non-local support reduces mesh sensitivity
• Disadvantages
• Mainly demonstrated in academia
• Difficult to impose essential boundary
  conditions
• Increase in computational cost

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Hybrid Methods

• Advantages
• Similar advantages as meshfree methods
• Essential BCs are more easily satisfied
• Disadvantages
• Mainly demonstrated in academia
• Higher computational cost than FEM but can be
• lower than meshfree techniques

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Applications

• Large Deformation Solid Mechanics
• Strain Localization
• Impact, Penetration, and Fragmentation
• Blast Response
• Fluid Dynamics
• Forming, Stamping, and Extrusion
• Fracture

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Large Deformation
Land Slide Analysis
Pinching of a Cylinder
Rabczuk Wall
Compression of Box Beam
Li Hao (2000)
Li Hao (2000)
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Strain Localization
Shear Band Simulation
Adaptive Remeshing
Li Liu (2000)
Li Liu (2000)
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Penetration and Impact
Vase Impact on Rigid Surface
Simultaneous Impact of Four Projectiles
Hao Liu (2006)
Zhang et al. (2006)
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Blast and Penetration
Projectile Impact and Penetration
Surface Charge on a Concrete Slab
Rabczuk Wall
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Fluid Dynamics
Water Column Collapse
Rigid Body Entering Water
Idelsohn Onate (2006)
Idelsohn Onate (2006)
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Extrusion and Forming
Stretch Flange Forming
Extrusion Process
Alfaro et. al. (2006)
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Meshfree Fracture Applications

• Visibility Criterion
• Crack Growth Criterion
• Crack Advancement Method

Sandia National Laboratories
Fries et al. (2004)
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Ductile Crack Growth Criterions

• J-Integral or KIC
• Crack Tip Opening Angle/Displacement
• Micromechanical Constitutive Models
• Uncoupled Damage Models\Phenomenological Models

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Crack Advancement
Plate Containing 31 Holes
Li (2001)
Li et al. (2004)
Ductile Fracture using GTN
Li (2004)
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Combined Approach
Beam Failure - Lemaitre CDM
Rabczuk Belytschko (2006)
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Remarks

• Recent and ongoing research in meshfree
  applications to the ductile failure process
• Newly arriving formulations of hybrid or
  particle element methods advertise advantages of
  both FEM and meshfree
• Approaches for coupling particle methods with FEM
  has also been subject of recent investigation for
  reducing cost
• Micromechanical constitutive damage models have
  continued to advance in the past two decades
• Combination of a constitutive damage model with a
  particle based formulation has provided promising
  results
• Computational cost and essential boundary
  conditions are still significant issue

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Questions and Comments