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Application of SPH
to solid mechanics
problems
Tom De Vuyst
Rade Vignjevic
James Campbell
Nenad Djordjevic
Kevin Hughes
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Brunel University London
Overview
• Introduction/Motivation
• In-house SPH code overview
• Fluid-structure interaction
• Solid mechanics - examples
• Solid mechanics - current work
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Introduction/Motivation
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Brunel University London
Introduction/Motivation
• Failure of materials and structures due to transient loading (e.g. impact, crash)
• Simulation tools are not always able to accurately predict behaviour
• SPH has attractive features:
• Large deformations
• Lagrangian
• Treatment of fracture
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In-house SPH code
overview
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Brunel University London
In-house SPH code overview
Eulerian and Total Lagrangian kernel formulations
Constitutive models (elastic, elasto-plastic, composites)
Equations of state (Tait, Mie-gruneisen)
Boundary conditions (prescribed displacement, velocity, acceleration)
Body force
Multiple materials
Contact
Subcycling
Coupled to LLNL-Dyna3D FEM solver
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Starting Point
Hypervelocity Impact (1997)
Experiment Image from Libersky et al (1993) J Comp Phys 109, 67-75
17 July 2019
Presentation Title 7
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Fluid-structure
interaction
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Brunel University London
Fluid-structure interaction
Interested in structural response
Sloshing ESA
Explosive forming
Ditching helicopter/aircraft
Extreme wave Buoy/wave impact
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Brunel University London
Analysis of Extreme Loading
Applications:
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Brunel University London
Sloshing
A cylindrical tank (with a hemi-spherical base):
• Partially filled
• Subjected to Constant frequency base excitation.
The measured parameters are:
• Sloshing force (the reaction force at the attachment of the tank support structure to the shaker table),
• Interface force between the tank and the support structure,
• Fluid motion
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Sloshing
0.2m fill Constant sweep frequency
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Brunel University London
Sloshing
Fill Ratio 1 - 0.2m, 1.7335HzWave height, m VS Time, s
Time, s
1.7335Hz, Amplitude 0.02m
Wav
e H
eigh
t ,m
Artificial Viscosity – 1.00
Maximum Wave height ~ 0.4006m at time 1.58231s
A, ~2.4s B, ~3.2s C, ~6.5s
Region Water motion
0A Sloshing
AB Transition from Sloshing to Swirling
BC Initial Swirling
CD Steady/stabilised Swirling
D0
0.2m fill
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Brunel University London
• Explosive forming
• Main components involved:
• Explosive Charge
• Energy Transfer Medium
• Forming Die + Clamping
• Workpiece
Explosive forming 17 July 2019
Explosive Forming – Numisheet 2016 T De Vuyst 14
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Brunel University London
Explosive forming
single explosive multi explosive 3
17 July 2019
Explosive Forming – Numisheet 2016 T De Vuyst 15
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Brunel University London
Low angle water impact
Part of FP7 SMAES project, using guided
water impact facility (INSEAN) developed
to allow high-velocity, low angle water
impact experiments.
> 47 tests on flat & curved thick plates
> 17 tests on metallic and composite deformable
plates
> 2 tests on stiffened panel component
Extreme Fluid-Structure Interaction 16
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Low angle water impact
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Structural component
(underwater view)
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Low angle water impact
Velocity Strain gauges
4º pitch
10º pitch
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0
20
40
60
80
100
120
140
160
0 0.01 0.02 0.03 0.04 0.05 0.06To
tal
z f
orc
e (
kN
)Time (s)
Cavitation
Reference model
Aeration (10%)
Cavitation
Aerated water
Low angle water impact
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Solid mechanics
examples
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Fragmentation
Explosively driven
17 July 2019
Presentation Title 21
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Bird Strike 17 July 2019
Presentation Title 22
Vignjevic et al. (2013) International Journal of
Impact Engineering, 60, 44-57
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Brunel University London
Ice Impact
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Brunel University London
Ballistic/Hypervelocity Impact
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Machining
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Solid mechanics
current work
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Brunel University London
The work presented forms part of H2020 project EXTREME (grant agreement No 636549)
on dynamic loading of composite structures
www.extreme-h2020.eu
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Brunel University London
Solid mechanics
current work
Dynamic loading of composite materials
• Strain softening
• Interaction area damage
• FE-SPH coupling and adaptivity
Applications
• Birdstrike and debris impact on flat panel
• Birdstrike fan, engine cowl, leading edge
• Debris impact on stiffened panel
• Blade-off
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Solid mechanics
current work
• During FEM simulations of impact on CFRP excessive element
deletion can be a problem
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Brunel University London
Solid mechanics
current work
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Non-local properties – strain softening
SPH as Non-local Regularisation Method
FEM SPH
17 July 2019
Presentation Title 31
Vignjevic et. al. (2014) Comput.
Methods Appl. Mech. Engrg. 277, 281–304
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Interaction Area Damage
Swegle Interaction Area*
Force on particle i
can be rewritten as:
with:
* J.W. Swegle, Conservation of momentum and tensile instability in particle methods., USA: Sandia National Laboratories, 2000. SAND2000-1223
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Interaction Area Damage
Standard approach (Kachanov, Lemaitre) in damage mechanics:
• A damage variable, represents an effective surface density due to presence of
microscopic cracks or voids within the material
• Leads to concept of an effective stress
* Kachanov LM. Time of the rupture process under creep conditions. Izv. Akad. Nauk., S.S.R., Otd Tech Nauk 1958;8(8):26-31
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Brunel University London
Interaction Area Damage
• Impact on brittle material modelled with isotropic elastic with failure stress;
17 July 2019
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Interaction Area Damage 17 July 2019
Modelling failure in solids using inter-particle interactions in SPH 35
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Coupling Algorithms
• Belytschko
• Huerta and Fernandez-Mendez
Domain discretised with a set of particles and a set of FE, where particles are not exactly located at the FE nodes ;
Blended shape function methods with higher order reproducibility;
Particle shape functions are modified to improve the quality of the approximation taking into account the interpolation functions and positions of active FE nodes and the particles;
FE shape functions for the non active elements are switched off;
Interpolation space within element replaced by contributions from neighbouring particles and red nodes only;
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