Rocks: A Modeling Challenge

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(No Transcript)
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RocksA Modeling Challenge
Part 1 Introduction
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The modeling of material behavior is the biggest
shortcoming in code calculations, and the primary
reason for bad results..
Part 1 Introduction
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What I wont talk about, but are important
Part 1 Introduction

• Eulerian v. Lagangian codes
• Handling Mixtures in Eulerian codes
• Boundaries in Eulerian codes
• Grid distortion in Lagrangian
• N-body codes Limited material behavior simple
  coefficient of restitution
• Large-scale macro-porosity cannot smear into a
  continuum

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Part 1 Introduction
But, there is lots of data, and it is consistent
if organized in appropriate ways..
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Part 1 Introduction
And, while much of it is for explosions, Impacts
and Explosions are (almost) the same
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Part 1 Introduction
The Siren of CPU Power!
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Understanding the processesRegions of Impact
Processes
Part 1 Introduction

• r 0-gt a Coupling of the energy and momentum
  of the impactor into the asteroid
• 2. r a -gt 2a Transition into point source
  solution, shock breakaway.
• 3a. r 2a -gt Shock decays with distance,
  strength (and gravity) become important
• 3b. r 5a -gt 15a Crater boundary, depending on
  problem

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What do we need?
Part 1 Introduction

• Balance Laws (easy continuum mechanics balance
  of mass, momentum, energy)
• Material behavior (very hard 100 Mbar down to
  partial bars!)
• Robust computer codes

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Material Behavior Three regimes
Part 1 Introduction
EOS
Pgtgtr c2
Solids
Pr c2
Flow, fracture, failure
Pltltr c2
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Region 1 Source Coupling
Part 2 Source region, EOS

• Other Names
• Penetration region
• Contact and Compression region
• Coupling region
• Early-time region
• Isobaric Core region

• ? Characteristics
• High Pressure gtgt c2
• gt Hydrodynamic
• gt Primarily determined by EOS

In this regime, the energy and momentum of the
impactor are transferred into the target.
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This is the bailiwick of the EOS..
EOS
Pgtgtr c2
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Part 2 Source region, EOS

• It is the EOS that determines the initial
  high-pressure response, including
• The Maximum Initial Pressure
• The Transition into the Point-Source field
• The exponent m of that point source
• The source effect on all subsequent scaling

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Stress Waves Pressure Decay
Part 2 Source region, EOS
PROPERTIES
4. But every impact velocity case approaches a
Point-Source Solution (but not self-similar)
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And, pressure decay is problem dependentPressur
es decay much faster in a porous material, the
point source has m1/3, Pr-6
Part 2 Source region, EOS
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Point-Source Impacts
Part 2 Source region, EOS

• Initially, the flow field depends on all three of
  the impactor measures
• radius a, velocity U and mass density r
• However, soon all signatures of those disappear,
  and there remains but a single measure of the
  impactor
• aUmdn

Then all aspects of the process can depend only
on aUmdn and not separately on the three
measures..
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Scaled Pressure Decay
Part 2 Source region, EOS
All Velocity Cases in a given material approach
the same Point-Source Solution after a few
impactor radii
Thus, there is no signature of the impact
velocity except in the source region rlt2a
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EOS gt EOS
Part 2 Source region, EOS

• Different sources have the same far-field results
  whenever the point-source property holds!
• The EOS determines the EOS The Equation Of State
  determines Equivalence Of Sources

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Equivalent Sources mass x Q0.82
Part 2 Source region, EOS
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So, what do we need to define the EOS?
Part 2 Source region, EOS

• 1. Equations of State for solid
• 2. modified by mixtures
• 3. modified by Porosity

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Analytical Single-phase EOS Models
Part 2 Source region, EOS

• Murnaghan Non-linear elastic, no thermodynamics,
  limited uses.
• Tillotson (1962) Powers in density thermal
  componentE vapor interpolation
• Mie-Gruneisen Linear Us-up thermal componentE
  vapor interpolation
• Puff (1966) vapor

Simple algebraic descriptions, no phase changes
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Analytical, Explicit Three-Phase
Part 2 Source region, EOS

• Gray (1971), ESA, Philco-Ford (1969), Barnes et
  al. (1967 and on)
• Aneos (1970) solid, liquid, vapor
• No molecules, no mixture theory, limited solid
  phase changes
• Panda (1981) Various combinations of cold,
  thermal, electron and multi-phase models
• Allows mixtures of molecular species, multiple
  phases

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Complete Equations of State E(r,P)(ColdThermal
Electron components)
Part 2 Source region, EOS
Electrons
T h e r m a l C o m p o n e n t
ltlt--Cold Component--gtgt
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What properties are sometimes available for
calibration??
Part 2 Source region, EOS
4. Other data at one bar such as specific heat,
thermal expansion.
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Porosity Addition..solid voids
Part 2 Source region, EOS

• Herrmanns P-alpha (1969)
• Carroll-Holt (1972)
• Seaman and Linde POREQST (1969)
• Holt et al. (1971)

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Herrmanns P-alpha
Part 2 Source region, EOS

• Distension ratio arsolid/rtotal
• ranges from r0 (initial) to (fully crushed)
• A crush curve defines crushing decrease of the
  void volume
• af(P,Pe,Ps)
• Instantaneous state variable
• P(r, T,a) Psolid(rsolid,T)/a
• e(r,T,a) esolid(rsolid,T)

Ps
Pe
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Part 2 Source region, EOS
Crush curves for porous Sands Crush begins at
Pe, complete at Ps
(From Kevin Housen)
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Part 2 Source region, EOS
The P-Alpha model Pe1e7 Ps2e9 Crush is
limited to one decade!
You dont always get what you think!!
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Part 2 Source region, EOS
Furthermore The actual path followed in CTH with
Ps20 mpa
P85 mpa
You dont always get even what you think you
didnt get!!
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Finally, supposing we have a reasonable EOS, how
do we use it in Wave Codes?
Part 2 Source region, EOS

• Direct analytical evaluation, or..
• Tabular Data Tables (Sesame)
• We have Sesame tables from Panda, Aneos, Seslan
  (Los Alamos) and others

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Summary of EOS
Part 2 Source region, EOS

• The model choice will fix the scaling and other
  important features of a solution
• The tools are there for complex models, but it is
  very hard to get the data to calibrate the
  models, even for simple ones like Aneos (24
  constants)
• I think many users are unaware of the major
  uncertainties the very existence of a
  pre-existing model gives it unwarranted
  credibility
• It is Extremely complex to construct a
  multiple-species model using Panda.

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But wait, theres more
Part 2 Source region, EOS

• Porosity adds yet another large uncertainty
• Phase changes
• Kinetic Effects
• Multiple Species

And all of that assumes we know the actual
material, which we dont in most or our
applications!
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Stress-Strain
Part 3, Stress-Strain
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Stress-Strain behavior
Part 3, Stress-Strain
When Prc2 the material no longer behaves as a
fluid. Then we need a constitutive equation
for the stress-strain behavior Almost always,
in wave codes that is simply an isotropic linear
elastic relation (which is undoubtedly extremely
crude).
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Which brings us to the strength parts..
Part 4, Strength
EOS
Pgtgtr c2
Solids
Pr c2
Flow, fracture, failure
Pltltr c2
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The F words Flow, Fracture and Failure
Part 4, Strength

• Models for these fall into three groups

• Degraded Stiffness, no explicit flow or
  fracture.
• Flow including plasticity and damage, used to
  model microscopic voids and cracks leading to an
  inability to resist stress.
• Fracture, involving actual macroscopic cracks
  and voids which are tracked, leading to an
  inability to resist stress.

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In a continuum theory, the first two can be
included directly, the latter is difficult,
unless some statistical approach is used to smear
them out.
Part 4, Strength
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Some Real Data
Part 4, Strength
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Yield depends on pressure
Part 4, Strength
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Damage and degradation leading to ultimate
failure occur at some limiting strain
Part 4, Strength
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Pressure-Dependent DuctilityFailure Strain
depends on pressure..
Part 4, Strength
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Pressure Dependent Yield and Ductility
Part 4, Strength
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Bulking increase in volume at failure
Part 4, Strength
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Damaged material Cohesionless,but not Fluid.
Part 4, Strength
Grady Kipp, failed
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Tensile fracture depends strongly on strain rate
Part 4, Strength
Codes
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Flow and Fracture Models should include
Part 4, Strength
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Part 4, Strength
We can do all of that using

• An Explicit Yield Envelope

• Envelope is pressure dependent

• A damage measure

• Envelope changes with damage

• Damage accumulation depends on pressure

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Flow and Fracture Yielding and CrackingLets put
it all together Start with the yield envelope
Part 4, Strength
Initial YieldF(stresses) or G(strains)

• Isotropicgt s1, s2, s3
• (Or three stress invariants)
• Commonly only 2, e.g.
• J2F(P)
• Or max shearf(pressure)

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Special Case VonMises (metals)
Part 4, Strength
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Special Case Mohr-Coloumb Drucker-Prager
Part 4, Strength
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Mohr-Coloumb with Mises Cutoff
Part 4, Strength
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Yield Functions in Shear-Pressure Space
Part 4, Strength
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Now add Improvements
Part 4, Strength

• A Damage measure. e.g. accumulated plastic strain
  or plastic work

• Then the envelope degrades with damage

• Damage accumulates slower at higher pressure
  leading to more ductility at higher pressure

• The envelopes also depend on rate, mostly the
  tension parts

• And they depend on temperature

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An example that has many of these is that of
Johnson Holmquist, 1990
Part 4, Strength
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But, Improvements Needed
Part 4, Strength

• Temperature dependence
• Tensile point depending most strongly on rate
• General EOS, not just non-thermo algebraic
• Porosity
• Interdependence between porosity, strength
• Size Dependence

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Another approach is to use Stiffness Degradation
rather than an explicit yield envelope (e.g.
Grady-Kipp Damage Model)
Part 4, Strength
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The Grady-Kipp Model
Part 4, Strength

• It is a Tensile Brittle Fracture Mechanism
• For fragmentation in mining
• One-Dimensional Model
• Synthesized for constant strain rate histories
  only
• Governed by Crack Distributions (Weibull) and
  growth
• Implies rate and size-dependent strength

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A Grady Kipp Implementation in 3D
Part 4, Strength

• Damage is isotropic, so that when a crack is
  formed in one directions, all directions lose
  stiffness

• As damage accumulates, the stiffness in both
  tension and in shear decrease, eventually to zero.

• Therefore, material failed by the outgoing shock
  behaves as water.

• Calibrated to disruption test, by adjusting the
  strength parameters

• But, for cratering, craters are way too large!

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The Grady-Kipp Approach
Part 4, Strength
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So how can we improve the models?
Part 4, Strength

• Compare, Compare, Compare
• to real experiments
• Large explosive field tests
• Carefully controlled lab tests
• to impact craters
• (but what was the impactor?)
• Test, Test, Test
• real materials
• Crushability
• Strength in different states

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Current Shortcomings
Part 5, Concluding Remarks

• Damage is a scalar not directional

• Behavior is isotropic, even after damage

• Most strength models do not address all types of
  strength

• Codes often have hidden features

• Even the limited models available usually greatly
  surpass the data

• We do not often enough make comparisons to any
  experiments

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Part 5, Concluding Remarks

• We are too anxious to get results and publish
• for the crater X on the moon Y of planet
• Z,
• and do not make enough effort of developing and
• checking the codes and models

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etc
Part 5, Concluding Remarks
We cannot model well enough to distinguish
details for a particular crater
We cannot handle mixtures well
We dont have a good handle on even the
mechanisms that give very significant features
e.g. late-stage adjustments.
Mixing rocks and atmospheres, and porosity makes
for very difficult code calculations
We do primarily continuum mechanics, and cannot
distinguish individual particles, size
distributions, ejecta particle characteristics
and fate
We dont do chemistry
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Part 5, Concluding Remarks

• Impact into a porous target

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Part 5, Concluding Remarks

• Porous cratering Marker particles

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Part 5, Concluding Remarks

• Impact into water

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Summary
Part 5, Concluding Remarks

• We have a long way to go
• Calculations should be considered order of
  magnitude at best
• Computer power will not save us and might even be
  detrimental.

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Part 5, Concluding Remarks

• On top of this, we observed that the current
  exponential increase in computer power is already
  leading to grave difficulties in assessing the
  content of simulations of complex phenomena, as
  well as comparing them with high quality
  experimental data. Among other challenges, this
  situation leads to the erroneous possibility of
  thinking that because output is complex, we must
  be successfully modeling complex phenomena.

T. G. Trucano, Prediction and uncertainty in
computational modeling of complex Phenomena A
whitepaper. SAND98-2776, 1998
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However
Part 5, Concluding Remarks

• We have learned a lot, especially qualitative, of
  cratering mechanics from codes.
• Cratering regimes strength, gravity, porous
• Ejecta transport and emplacement
• Effects of oblique impacts
• Thermodynamic histories of material
• Late-stage readjustments Scope, although not
  mechanism.
• Calibration to real results, followed by minor
  extrapolations are probably effective.

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And, some recent advances are promising
Part 5, Concluding Remarks

• Beginnings of all appropriate rock strength
  features
• Damage, bulking, thermal, strain softening
• E.g. OKeefe et al, 2001, Holsapple and Housen,
  2002
• Mixed materials
• Assuming non-equilibrium thermal
• (OKeefe et al. 2001 and others)
• Assuming phase equilibrium
• (Ivanov, 2003)
• Atmospheric transport
• e.g. Artemieva Pierazzo (2003)

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Part 5, Concluding Remarks
I believe it is the correct modeling of the
down-side of the Stress-strain curves that we
have not done well, and that is the key to
important aspects such as late-stage
readjustments.
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THE END, Thank You
Part 6, The End