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Validation of Riera Loading in LS-DYNA Models of Missile Impact
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John A. Vera, Ph.D.
Presented by:
Gordon S. Bjorkman Jr., Ph.D.
Background• The VTT and IRSN have used computer codes to predict
the effects of impact on concrete structures (Saarenheimo et al. (2007), Tarallo et al. (2007)).
• These efforts make use of Riera loading to simulate actual missile impact In the VTT tests modeled two
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actual missile impact. In the VTT tests modeled, two types of missiles were used: "dry", or hollow cylinder, and "wet", cylinder filled with water.
• While modeling results have shown good agreement with test data, there are conflicting conclusions regarding Riera loading for "wet" missile conditions.
• Contrary to results presented by VTT, IRSN authors concluded that Riera loading was inadequate for a “wet” missile case.
Introduction• VTT has carried out tests of missile impact against concrete walls. The tests referred to here consisted of impacts to a 2 m by 2.3 m (6.5 ft by 7.5 ft), 150 mm (5.9 inches) thick reinforced concrete wall.
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Firgure: Lastunen, A., Hakola, I., Järvinen, E., Hyvärinen, J. and Calonius, K., “Impact Test Facility,” Proc. SMiRT 2007.
Introduction
• Both VTT and ISRN have used results from these tests to benchmark computational models of the experiments.
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Lastunen, A., Hakola, I., Järvinen, E., Hyvärinen, J. and Calonius, K., “Impact Test Facility,” Proc. SMiRT 2007.
Introduction
• Both these studies have used Riera loading for these models.
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P(t) = Pb[x(t)] + μ[x(t)] * V2(t)
Pb[x(t)] = Crushing load of impactor as function of distance from surface as function of time.μ[x(t)] * V2(t) = Mass per unit length as function of distance from surface as function of time, times velocity as function of time, squared.
Introduction• In the VTT tests modeled, two types of missiles
were used: "dry", or hollow cylinder, and "wet", cylinder filled with water.
• Contrary to results presented by VTT, IRSN authors
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concluded that Riera loading was inadequate for a “wet” missile case.
• The current study simulated experiments 642 and 644 using LS-DYNA and Riera loads as derived by various authors.
• Results from all studies were compared to infer the suitability of Riera loading for impact simulations.
LS-DYNA Models• Concrete is modeled with 60,000 eight-node solid elements. Element edge length is 25 mm.
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• Truss elements are used for the rebar (14,000).
• Load is applied as pressure at center of wall.
• Boundary conditions are taken as simply supported.
Material Models
• Concrete was modeled with LS-DYNA’s MAT_159 concrete material model and with the more complex Winfrith concrete material model (MAT_084).
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• Rebar (steel) was modeled with a plastic-kinematic model with rate effects (MAT_003).
• Material model parameters were taken from Saarenheimo, A., et al., “Numerical studies on impact loaded reinforced concrete walls,” Transactions SMIRT 2007.
Loading• Riera Load graphs derived are similar to previous
works.
2000
2400
Saarenheimo, Dry
S h i W t
1000
1200
Dry Load, Uniform
Wet Load, Uniform
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0
400
800
1200
1600
0 2 4 6 8 10 12
Saarenheimo, Wet
Saarenheimo,Simplified Wet
Rie
ra L
oa
d (
kN
)
Time (ms)
After Saarenheimo, A., et al., “Numerical studies on impact loaded reinforced concrete walls,” Transactions SMIRT 2007.
0
200
400
600
800
0 2 4 6 8 10 12 14 16 18
,
Rie
ra L
oa
d (
kN
)
Time (ms)
Loading• Riera Load graphs derived are similar to previous
works.
1000
1200
Dry Load, Uniform
Wet Load, Uniform 1000
1200
1400
Tarallo, Dry
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0
200
400
600
800
0 2 4 6 8 10 12 14 16 18
,
Rie
ra L
oa
d (
kN
)
Time (ms)
0
200
400
600
800
1000
0 1 2 3 4 5 6 7 8 9 10 11 12
Tarallo, Wet
Rie
ra L
oa
d (
kN
)
Time (ms)
After Tarallo, F., et al., “Interpretation of soft impact medium velocity tests on concrete slabs”. Transactions SMIRT 2007
Results• Assuming evenly
distributed mass for a cylindrical missile, we find overestimation of
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0
0.00 0.01 0.02 0.03 0.04
Dry Test
Uniform Mass Load, Winfrith
Uniform Mass Load, MAT_159
Dis
pla
ce
me
nt
(mm
)
Time (s)
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response for the dry case and the opposite for the wet case.
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0
0.00 0.01 0.02 0.03 0.04
Time (s)
Dis
pla
cem
ent
(mm
)
Wet Test
Uniform Mass Load, Winfrith
Uniform Mass Load, MAT_159
• Plots show displacement in location closest to centermost displacement gage in tests.
Results
• Tarallo et al. found a similar underestimation of response for the wet case. However…
0.00 0.01 0.02 0.03 0.04 0 0.01 0.02 0.03 0.04
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-80
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0
Time (s)
Dis
pla
cem
ent
(mm
)
Wet Test
Uniform Mass Load, Winfrith
Uniform Mass Load, MAT_159
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0
0 0.01 0.02 0.03 0.04
Wet Test
Tarallo Results
Dis
pla
ce
me
nt
(mm
)
Time (s)
Results• …using the Tarallo loads on our model
produced incongruent results: the wet case matched up well, while the dry case severely overestimated the response.
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y p
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0
0 0.01 0.02 0.03 0.04
Dry Test
Tarallo Load, Winfrith
Tarallo Load, MAT159
Tarallo ResultsD
isp
lac
em
en
t (m
m)
Time (s)-80
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0
0 0.01 0.02 0.03 0.04
Wet TestTarallo ResultsTarallo Load, WinfrithTarallo Load, MAT159
Dis
pla
ce
me
nt
(mm
)
Time (s)
Results• Using the Saarenheimo loads on our model produced
more consistent results, but using different material models showed noticeable difference, especially for the wet case.
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0
0 0.01 0.02 0.03 0.04
Dry TestSaarenheimo, WinfrithSaarenheimo, MAT159Saarenheimo Results
Dis
pla
ce
me
nt
(mm
)
Time (s)-100
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0
0 0.01 0.02 0.03 0.04
Wet TestSaarenheimo, WinfrithSaarenheimo, MAT_159Saarenheimo Results
Dis
pla
ce
me
nt
(mm
)
Time (s)
Riera Load Refinement – Dry case• The (extremely simplified) initial assumption for our initial Riera load was that all mass was evenly distributed.
• As we saw, this initial case produced overestimated response in the dry case and underestimated response in
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response in the dry case and underestimated response in the wet case.
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0
0.00 0.01 0.02 0.03 0.04
Dry Test
Uniform Mass Load, Winfrith
Uniform Mass Load, MAT_159
Dis
pla
ce
me
nt
(mm
)
Time (s)-80
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0
0.00 0.01 0.02 0.03 0.04
Time (s)
Dis
pla
cem
ent
(mm
)
Wet Test
Uniform Mass Load, Winfrith
Uniform Mass Load, MAT_159
Riera Load Refinement – Dry case• A refinement was made to account for the missile features. The thicker, heavier steel part at the back of the missile acts like an extra weight, or force.
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Picture from: Lastunen, A., Hakola, I., Järvinen, E., Hyvärinen, J. and Calonius, K., “Impact Test Facility” Transactions SMiRT 2007.
Riera Load Refinement – Dry case• The second approach considered the mass of the steel as a force generated from an impulse. This additional force was assumed to be proportional by mass to the initial effect of the aluminum impact.
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Psteel = [Msteel / Maluminum ] * μaluminum * [Vo]2
Riera Load Refinement – Wet case
Psteel = [Msteel / Maluminum ] * μaluminum * [Vo]2
• For the wet case, the same approach was taken for considering the steel portion.
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steel steel aluminum aluminum o
• The water mass is taken into account as an addition on the linear density term corresponding to the deformable aluminum (uniformly distributed along the missile length).
Riera Load Refinement• The refined Riera loads are only slightly different in shape from the originals.
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Dry Load, Uniform
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0
200
400
600
800
1000
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018
Dry Load, Modified
Wet Load, Uniform
Wet Load, Modified
Rie
ra L
oa
d (
kN
)
Time (s)
Results
• Results show marked improvement in displacement response over initial Riera loads.
0.00 0.01 0.02 0.03 0.040.00 0.01 0.02 0.03 0.04
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0
Time (s)
Dis
pla
cem
ent
(mm
)
Wet Test
Uniform Mass Load, Winfrith
Uniform Mass Load, MAT_159
Modified Load, Winfrith
Modified Load, MAT_159
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0 Dry TestUniform Mass Load, WinfrithUniform Mass Load, MAT_159Modified Load, WinfrithModified Load, MAT_159
Dis
pla
ce
me
nt
(mm
)
Time (s)
Results• Rebar strains are comparable to test data
(calculated from nodal displacements in locations close to gages in actual tests).
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0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0 0.01 0.02 0.03 0.04
Dry Test
Upper Bound
Lower Bound
Average
Re
ba
r S
tra
in (
mm
/mm
)
Time (s)
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0 0.01 0.02 0.03 0.04
Wet Test
Upper Bound
Lower Bound
AverageRe
ba
r S
tra
in (
mm
/mm
)
Time (s)
Impactor Models• As additional information, analyses with actual impactors were performed.
• Since no actual information on weight distribution or t i l ti il bl ti h d t
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material properties was available, assumptions had to be made regarding these parameters.
• Water in the wet missile was modeled as elastic material with fluid option, with element erosion.
• Element erosion values used ranged from 50% to 95%.
Impactor Models• Impactors are modeled with four-node shell elements.
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• Water is modeled with 53,000 eight-node solid elements.
• Average element edge length for concrete/rebar is 25 mm, for shells and water 10 mm.
Results• For the dry case, it was observed that the response varied with
the mass ratio of steel and aluminum. More assumed weight for steel lessened the response.
• The response also depended on the assumed aluminum yield value.
0 00 0 01 0 02 0 03 0 04
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0
0.00 0.01 0.02 0.03 0.04
Time (s)
Dis
pla
ce
me
nt
(mm
)
Dry TestOriginal Ratio = 0.67Ratio = 0.50Ratio = 0.80Ratio = 0.80, Al yield = 120 MPa
Results• For the wet case, the response matched very well with the test.
This is due to water accounting for more than half the mass of the missile. The only parameter which affected the calculated response was the erosion factor for water elements, which converged from 75% to 95% strain.
0 0 01 0 02 0 03 0 04
25
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0 0.01 0.02 0.03 0.04
Wet TestErosion: 95% StrainErosion: 90% StrainErosion: 75% StrainErosion: 50% Strain
Dis
pla
ce
me
nt
(mm
)
Time (s)
Conclusions• It has been demonstrated that Riera loading can produce good results when applied in a finite element analysis.
• Somewhat differing results when considering differentsources for Riera loads show the sensitivity of the
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sources for Riera loads show the sensitivity of theproblem to the derivation of the loads.
• In order to achieve the most accurate results,adjustments should be made in the loads for the effectsof nondeformable parts of the impactors. This can be achallenge for predictive analysis.
• It must be noted that the Riera method will not giveaccurate results for cases where perforation orpenetration occur.
Acknowledgements
• The author would like to thank Abdul Sheikh, Dr. SyedAli, Jason Piotter, Bhasker Tripathi from the U.S. NRCfor their input and assistance in the preparation of thiswork
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work.
Special thanks to Dr. Gordon Bjorkman for presenting at SMiRT.
