[cig-commits] r5491 - in long/3D/Gale/trunk: . documentation
walter at geodynamics.org
walter at geodynamics.org
Thu Dec 7 03:48:19 PST 2006
Author: walter
Date: 2006-12-07 03:48:18 -0800 (Thu, 07 Dec 2006)
New Revision: 5491
Modified:
long/3D/Gale/trunk/
long/3D/Gale/trunk/documentation/gale.lyx
Log:
r1140 at earth: boo | 2006-12-07 03:47:26 -0800
Add materials to the docs
Property changes on: long/3D/Gale/trunk
___________________________________________________________________
Name: svk:merge
- 3a629746-de10-0410-b17b-fd6ecaaa963e:/cig:1138
+ 3a629746-de10-0410-b17b-fd6ecaaa963e:/cig:1140
Modified: long/3D/Gale/trunk/documentation/gale.lyx
===================================================================
--- long/3D/Gale/trunk/documentation/gale.lyx 2006-12-07 11:48:12 UTC (rev 5490)
+++ long/3D/Gale/trunk/documentation/gale.lyx 2006-12-07 11:48:18 UTC (rev 5491)
@@ -594,18 +594,16 @@
Gale takes an agnostic approach to surface processes such as erosion.
Gale exposes a programming interface that allows us to modify the heights
of the surface.
- There is a simple example using diffusion in
-\family typewriter
-surface_process.xml
-\family default
-.
- Using a different surface process model requires modifying
+ See section
+\begin_inset LatexCommand \ref{sec:Surface-Processes}
+
+\end_inset
+
+ for details.
\end_layout
\begin_layout LyX-Code
-\family typewriter
-src/Gale/plugins/SurfaceProcess/SurfaceProcess.c
\end_layout
\begin_layout Subsection
@@ -613,29 +611,22 @@
\end_layout
\begin_layout Standard
-Gale incorporates a number of different Rheologies.
-\end_layout
+Gale incorporates a number of different rheologies, as well as letting you
+ create your own.
+ For details on the existing Rheologies, see section
+\begin_inset LatexCommand \ref{sec:Materials}
-\begin_layout Subsubsection
-Drucker-Prager
-\end_layout
+\end_inset
-\begin_layout Subsubsection
-Von Mises
-\end_layout
+.
+ To create your own rheology, see chapter
+\begin_inset LatexCommand \ref{cha:Modifying-Gale}
-\begin_layout Subsubsection
-Mohr-Coulomb
-\end_layout
+\end_inset
-\begin_layout Subsubsection
-Frank-Kamenetskii
+ for guidance.
\end_layout
-\begin_layout Subsubsection
-Moresi-Mülhaus
-\end_layout
-
\begin_layout Section
Gale History
\end_layout
@@ -690,7 +681,7 @@
The basic subduction model can be modified by introducing isostasy and/or
boundary mass fluxes.
(a) Flexural or local isostasy.
- Every Eularian column is displaced by the corresponding local or flexural
+ Every Eulerian column is displaced by the corresponding local or flexural
deflection
\emph on
w
@@ -898,6 +889,18 @@
There are also rough examples of shortening and subduction.
\end_layout
+\begin_layout Standard
+Gale uses PETSc for solvers, so you can easily change which solver to use.
+ The default solver is preconditioned conjugate gradient.
+ There are too many options of PETSc to go into it here.
+ But as a simple example, to use a direct LU solve, simply append arguments
+ to the command line
+\end_layout
+
+\begin_layout LyX-Code
+./Gale extension.xml -pc_type lu -ksp_type preonly
+\end_layout
+
\begin_layout Section
Output Format
\end_layout
@@ -1101,6 +1104,11 @@
\begin_layout Chapter
Modifying Gale
+\begin_inset LatexCommand \label{cha:Modifying-Gale}
+
+\end_inset
+
+
\end_layout
\begin_layout Section
@@ -1287,7 +1295,7 @@
\end_layout
\begin_layout Section
-System Decription
+System Description
\end_layout
\begin_layout Standard
@@ -3476,6 +3484,11 @@
\begin_layout Section
Shapes
+\begin_inset LatexCommand \label{sec:Shapes}
+
+\end_inset
+
+
\end_layout
\begin_layout Standard
@@ -3936,7 +3949,7 @@
\end_layout
-\begin_layout Subsubsection
+\begin_layout Subsection
BelowCosinePlane
\end_layout
@@ -4280,7 +4293,7 @@
\end_layout
-\begin_layout Subsubsection
+\begin_layout Subsection
Box
\end_layout
@@ -4409,7 +4422,7 @@
\end_layout
-\begin_layout Subsubsection
+\begin_layout Subsection
ConvexHull
\end_layout
@@ -4479,7 +4492,7 @@
creates a shape with vertices at (0,2), (4,-2), (-4,-2).
\end_layout
-\begin_layout Subsubsection
+\begin_layout Subsection
Cylinder
\end_layout
@@ -4568,9 +4581,7 @@
\begin_inset Text
\begin_layout Standard
-\begin_inset Formula \[
--\infty\]
-
+\begin_inset Formula $-\infty$
\end_inset
@@ -4593,9 +4604,7 @@
\begin_inset Text
\begin_layout Standard
-\begin_inset Formula \[
--\infty\]
-
+\begin_inset Formula $-\infty$
\end_inset
@@ -4618,9 +4627,7 @@
\begin_inset Text
\begin_layout Standard
-\begin_inset Formula \[
--\infty\]
-
+\begin_inset Formula $-\infty$
\end_inset
@@ -4643,9 +4650,7 @@
\begin_inset Text
\begin_layout Standard
-\begin_inset Formula \[
-\infty\]
-
+\begin_inset Formula $\infty$
\end_inset
@@ -4668,9 +4673,7 @@
\begin_inset Text
\begin_layout Standard
-\begin_inset Formula \[
-\infty\]
-
+\begin_inset Formula $\infty$
\end_inset
@@ -4693,9 +4696,7 @@
\begin_inset Text
\begin_layout Standard
-\begin_inset Formula \[
-\infty\]
-
+\begin_inset Formula $\infty$
\end_inset
@@ -4711,7 +4712,7 @@
\end_layout
-\begin_layout Subsubsection
+\begin_layout Subsection
Everywhere
\end_layout
@@ -4719,7 +4720,7 @@
This is a convenience shape simply meaning everywhere.
\end_layout
-\begin_layout Subsubsection
+\begin_layout Subsection
PolygonShape
\end_layout
@@ -4867,7 +4868,7 @@
\end_layout
-\begin_layout Subsubsection
+\begin_layout Subsection
Sphere
\end_layout
@@ -4933,7 +4934,7 @@
\end_layout
-\begin_layout Subsubsection
+\begin_layout Subsection
Superellipsoid
\end_layout
@@ -5094,8 +5095,1336 @@
\begin_layout Section
Materials
+\begin_inset LatexCommand \label{sec:Materials}
+
+\end_inset
+
+
\end_layout
+\begin_layout Standard
+Gale supports two kinds of rheologies: viscous and yielding.
+ We can combine these two rheologies to create a more realistic composite
+ rheology.
+ We then pair this composite rheology with a shape to actually lay down
+ material on the grid.
+ As a simple example, we can create a viscous rheology
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="viscousRheology">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">MaterialViscosity</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="eta0">10.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+and a Von Mises yielding rheology
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="strainWeakening">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">StrainWeakening</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="TimeIntegrator">timeIntegrator</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="MaterialPointsSwarm">materialSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="softeningStrain">0.1</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="initialDamageFraction">0.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="initialDamageWavenumber">0.5</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="initialDamageFactor">0.5</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="healingRate">0.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="yieldingRheology">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">VonMises</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="cohesion">10.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="cohesionAfterSoftening">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+and combine them together with
+\family typewriter
+materialShape
+\family default
+ (see section
+\begin_inset LatexCommand \ref{sec:Shapes}
+
+\end_inset
+
+ on how to create shapes)
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="yieldingMaterial">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">RheologyMaterial</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Shape">yieldingShape</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <list name="Rheology">
+\end_layout
+
+\begin_layout LyX-Code
+ <param>viscousRheology</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param>yieldingRheology</param>
+\end_layout
+
+\begin_layout LyX-Code
+ </list>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Subsection
+Viscous
+\end_layout
+
+\begin_layout Subsubsection
+MaterialViscosity
+\end_layout
+
+\begin_layout Standard
+This is the simplest rheology.
+ There is only one variable, the viscosity
+\family typewriter
+eta0
+\family default
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="2" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+eta0
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+1
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Frank-Kamenetskii
+\end_layout
+
+\begin_layout Standard
+This is a temperature dependent viscosity
+\begin_inset Formula \[
+eta=eta0*\exp\left(-theta*T\right).\]
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+eta0
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+1
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+theta
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsection
+Yielding
+\end_layout
+
+\begin_layout Standard
+Yielding rheologies are a bit more complicated.
+
+\end_layout
+
+\begin_layout Subsubsection
+StrainWeakening
+\end_layout
+
+\begin_layout Standard
+First we need to create a
+\family typewriter
+StrainWeakening
+\family default
+ component.
+
+\family typewriter
+StrainWeakening
+\family default
+ is mainly used to define an initial distribution of strain in a material
+ and to calculate the accumulated strain on each particle.
+ To that end, it requires a number of parameters.
+\end_layout
+
+\begin_layout Description
+TimeIntegrator This is the component used for time integration to accumulate
+ strain.
+ Given the standard components in section
+\begin_inset LatexCommand \ref{sec:Basic-Components}
+
+\end_inset
+
+, this will be
+\family typewriter
+timeIntegrator
+\family default
+.
+\end_layout
+
+\begin_layout Description
+MaterialPointsSwarm This is the swarm of particles that this rheology will
+ tie itself to.
+ Given the standard components in section
+\begin_inset LatexCommand \ref{sec:Basic-Components}
+
+\end_inset
+
+, this will be
+\family typewriter
+materialSwarm
+\family default
+.
+\end_layout
+
+\begin_layout Description
+healingRate With this parameter, accumulated strain can decrease.
+ Specifically, the time derivative of accumulated strain becomes
+\begin_inset Formula \[
+\frac{\sigma_{yield}}{\eta}\left(\frac{\beta}{1-\beta}-healingRate\right),\]
+
+\end_inset
+
+ where
+\begin_inset Formula $\beta\equiv\sigma_{yield}/\sigma$
+\end_inset
+
+,
+\begin_inset Formula $\sigma_{yield}$
+\end_inset
+
+ is the yield stress,
+\begin_inset Formula $\sigma$
+\end_inset
+
+ is some measure of the current stress (e.g.
+ the second invariant of the stress tensor), and
+\begin_inset Formula $\eta$
+\end_inset
+
+ is the isotropic viscosity.
+ Note that the healing rate should be between 0 and 1.
+\end_layout
+
+\begin_layout Description
+softeningStrain The strain at which the material has fully yielded.
+\end_layout
+
+\begin_layout Description
+initialDamageFraction The chance that an individual material particle will
+ have a non-zero initial strain.
+\end_layout
+
+\begin_layout Description
+initialDamageWaveNumber The wavenumber for the initial random strain.
+ To avoid having initial strain on the edges of the box, this should be
+ set to the inverse of the horizontal length of the box.
+\end_layout
+
+\begin_layout Description
+initialDamageFactor The maximum initial random strain for a particle is
+
+\family typewriter
+initialDamageFactor
+\family default
+*
+\family typewriter
+softeningStrain
+\family default
+.
+
+\end_layout
+
+\begin_layout Description
+randomSeed A random number seed used when computing which particles are
+ initially yielded.
+\end_layout
+
+\begin_layout Description
+initialStrainShape If defined, the initial random strain will only occur
+ within this shape (outside the shape the initial random strain will be
+ zero).
+\end_layout
+
+\begin_layout Standard
+We can also define a strain weakening ratio
+\begin_inset Formula $\alpha\equiv\min\left(1,\gamma/\gamma_{softening}\right)$
+\end_inset
+
+, where
+\begin_inset Formula $\gamma$
+\end_inset
+
+ is the accumulated strain, and
+\begin_inset Formula $\gamma_{softening}$
+\end_inset
+
+ is the softening strain.
+ This allows us to define quantities like the effective cohesion
+\begin_inset Formula $C_{effective}\equiv C_{pristine}\left(1-\alpha\right)+C_{yielded}\alpha$
+\end_inset
+
+ and effective friction coefficient
+\begin_inset Formula $\phi_{effective}=\phi_{pristine}\left(1-\alpha\right)+\phi_{yielded}\alpha$
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="10" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+TimeIntegrator
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+none
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+MaterialPointsSwarm
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+none
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+healingRate
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+softeningStrain
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+\begin_inset Formula $\infty$
+\end_inset
+
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+initialDamageFraction
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+initialDamageWaveNumber
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+-1.0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+initialDamageFactor
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+1.0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+randomSeed
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+initialStrainShape
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+none
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+VonMises
+\end_layout
+
+\begin_layout Standard
+This is the simplest yielding rheology in Gale.
+ The yielding stress is simply the effective cohesion, so this rheology
+ only has a few input parameters.
+
+\family typewriter
+cohesion
+\family default
+ and
+\family typewriter
+cohesionAfterSoftening
+\family default
+ have the obvious meanings.
+
+\family typewriter
+minimumYieldStress
+\family default
+ sets an absolute minimum to the stress required to make the material yield.
+\end_layout
+
+\begin_layout Standard
+
+\family typewriter
+StrainRateSoftening
+\family default
+ is a boolean variable that changes how the constitutive matrix is modified
+ when the material has yielded.
+ If
+\family typewriter
+StrainRateSoftening
+\family default
+ is
+\family typewriter
+True
+\family default
+, then the viscosity is set to
+\begin_inset Formula \[
+\eta_{effective}=2\sigma_{yield}^{2}\eta/\left(\sigma_{yield}^{2}+I_{2}^{2}\right),\]
+
+\end_inset
+
+ where
+\begin_inset Formula $I_{2}$
+\end_inset
+
+ is the second invariant of the stress tensor.
+ Otherwise the viscosity is set to
+\end_layout
+
+\begin_layout Standard
+\begin_inset Formula \[
+\eta_{effective}=\eta\sigma_{yield}/I_{2},\]
+
+\end_inset
+
+ which essentially sets the stress of the particle to the yield stress.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="5" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+cohesion
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+cohesionAfterSoftening
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+minimumYieldStress
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+StrainRateSoftening
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+False
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+DruckerPrager
+\end_layout
+
+\begin_layout Standard
+This rheology uses the same parameters as Von Mises, but also adds a friction
+ coefficient that can soften.
+ Specifically, the yield stress becomes
+\begin_inset Formula \[
+\sigma_{yield}=\alpha p+C_{p},\]
+
+\end_inset
+
+where
+\begin_inset Formula \[
+\begin{array}{ccc}
+C_{p} & = & \frac{6C_{effective}\cos\phi_{effective}}{\sqrt{3}\left(3-\sin\phi_{effective}\right)}\\
+\alpha & = & \frac{6\sin\phi_{effective}}{\sqrt{3}\left(3-\sin\phi_{effective}\right)}\end{array},\]
+
+\end_inset
+
+and
+\begin_inset Formula $p$
+\end_inset
+
+ is the pressure.
+
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="3" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+frictionCoefficient
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+frictionCoefficientAfterSoftening
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+(See also VonMises)
+\end_layout
+
+\begin_layout Subsubsection
+MohrCoulomb
+\end_layout
+
+\begin_layout Standard
+This rheology is like Drucker-Prager, but it uses the actual normal stress
+ instead of inferring a normal stress from the pressure.
+ More explicitly, the yield shear stress is
+\begin_inset Formula \[
+\sigma_{yield}=\sigma_{n}\tan\phi_{effective}+C_{effective}.\]
+
+\end_inset
+
+ When the material is yielding, the viscosity is modified so that the stress
+ on the particle is the yield stress.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="6" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+cohesion
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+cohesionAfterSoftening
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+frictionCoefficient
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+frictionCoefficientAfterSoftening
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+minimumYieldStress
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+FaultingMoresiMulhaus2006
+\end_layout
+
+\begin_layout Standard
+This is a fairly complicated non-isotropic rheology.
+ The full details can be found in Moresi and Mülhaus (2006), but essentially
+ it keeps track of which direction a material is strained.
+ To do so, it uses a component called
+\family typewriter
+Director
+\family default
+.
+ For the standard components given in section
+\begin_inset LatexCommand \ref{sec:Basic-Components}
+
+\end_inset
+
+, this would be
+\end_layout
+
+\begin_layout LyX-Code
+<struct name="director">
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="Type">Director</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="TimeIntegrator">timeIntegrator</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="VelocityGradientsField">VelocityGradientsField</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="MaterialPointsSwarm">materialSwarm</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="initialDirectionX">0.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="initialDirectionY">1.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="initialDirectionZ">0.0</param>
+\end_layout
+
+\begin_layout LyX-Code
+ <param name="dontUpdate">True</param>
+\end_layout
+
+\begin_layout LyX-Code
+</struct>
+\end_layout
+
+\begin_layout Standard
+Otherwise, it adds one variable not present in
+\family typewriter
+MohrCoulomb
+\family default
+:
+\family typewriter
+ignoreOldOrientation
+\family default
+.
+ This tells Gale whether it should check to see whether material will weaken
+ further in the current direction, or it will try every direction equally
+ each time step.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Tabular
+<lyxtabular version="3" rows="7" columns="2">
+<features>
+<column alignment="center" valignment="top" leftline="true" width="0">
+<column alignment="center" valignment="top" leftline="true" rightline="true" width="0">
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+Defaults
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+cohesion
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+cohesionAfterSoftening
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+frictionCoefficient
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+frictionCoefficientAfterSoftening
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+minimumYieldStress
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" rightline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+0
+\end_layout
+
+\end_inset
+</cell>
+</row>
+<row topline="true" bottomline="true">
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+ignoreOldOrientation
+\end_layout
+
+\end_inset
+</cell>
+<cell alignment="center" valignment="top" topline="true" leftline="true" usebox="none">
+\begin_inset Text
+
+\begin_layout Standard
+False
+\end_layout
+
+\end_inset
+</cell>
+</row>
+</lyxtabular>
+
+\end_inset
+
+
+\end_layout
+
\begin_layout Section
Boundary Conditions
\end_layout
@@ -5452,7 +6781,7 @@
However, if the cloned particles have already undergone evolution (e.g.
they were strained), then the new particles would no longer be pristine.
To fix this, we can specify regions where particles should be created anew
- by adding
+ by adding something like
\newline
\family typewriter
@@ -5781,6 +7110,11 @@
\begin_layout Section
Surface Processes
+\begin_inset LatexCommand \label{sec:Surface-Processes}
+
+\end_inset
+
+
\end_layout
\begin_layout Standard
@@ -7033,6 +8367,18 @@
\begin_layout Bibliography
+\bibitem {key-3}
+ Moresi, L.N., and H.-B.
+ Mühlhaus (2006), Anisotropic viscous models of large-deformation MohrCoulomb
+ failure,
+\emph on
+Philosiphical Magazine, 86,
+\emph default
+ 3287-3305.
+\end_layout
+
+\begin_layout Bibliography
+
\bibitem {key-2}
Moresi, L.N., and V.S.
Solomatov (1995), Numerical investigation of 2D convection with extremely
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