[cig-commits] r16966 - in short/3D/PyLith/trunk/doc/userguide: . governingeqns materials tutorials/3dhex8 tutorials/3dhex8/gravity tutorials/3dhex8/gravity/figs

willic3 at geodynamics.org willic3 at geodynamics.org
Wed Jun 9 19:11:37 PDT 2010 

Author: willic3
Date: 2010-06-09 19:11:37 -0700 (Wed, 09 Jun 2010)
New Revision: 16966

Added:
   short/3D/PyLith/trunk/doc/userguide/tutorials/3dhex8/gravity/figs/
   short/3D/PyLith/trunk/doc/userguide/tutorials/3dhex8/gravity/figs/step15-displ-t200.jpg
   short/3D/PyLith/trunk/doc/userguide/tutorials/3dhex8/gravity/figs/step16-stress_xx-t200.jpg
   short/3D/PyLith/trunk/doc/userguide/tutorials/3dhex8/gravity/figs/step17-displ-t200.jpg
   short/3D/PyLith/trunk/doc/userguide/tutorials/3dhex8/gravity/gravity.lyx
Modified:
   short/3D/PyLith/trunk/doc/userguide/governingeqns/governingeqns.lyx
   short/3D/PyLith/trunk/doc/userguide/materials/materials.lyx
   short/3D/PyLith/trunk/doc/userguide/tutorials/3dhex8/3dhex8.lyx
   short/3D/PyLith/trunk/doc/userguide/userguide.lyx
Log:
Finished at least a draft of 3dhex8 tutorials.
Added some labels to other chapters for cross-referencing, and added a
new reference to userguide.lyx.



Modified: short/3D/PyLith/trunk/doc/userguide/governingeqns/governingeqns.lyx
===================================================================
--- short/3D/PyLith/trunk/doc/userguide/governingeqns/governingeqns.lyx	2010-06-10 00:23:57 UTC (rev 16965)
+++ short/3D/PyLith/trunk/doc/userguide/governingeqns/governingeqns.lyx	2010-06-10 02:11:37 UTC (rev 16966)
@@ -1,4 +1,4 @@
-#LyX 1.6.4 created this file. For more info see http://www.lyx.org/
+#LyX 1.6.6 created this file. For more info see http://www.lyx.org/
 \lyxformat 345
 \begin_document
 \begin_header
@@ -1509,6 +1509,13 @@
 
 \begin_layout Section
 Small Strain Formulation
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Small-Strain-Formulation"
+
+\end_inset
+
+
 \end_layout
 
 \begin_layout Standard

Modified: short/3D/PyLith/trunk/doc/userguide/materials/materials.lyx
===================================================================
--- short/3D/PyLith/trunk/doc/userguide/materials/materials.lyx	2010-06-10 00:23:57 UTC (rev 16965)
+++ short/3D/PyLith/trunk/doc/userguide/materials/materials.lyx	2010-06-10 02:11:37 UTC (rev 16966)
@@ -1,4 +1,4 @@
-#LyX 1.6.5 created this file. For more info see http://www.lyx.org/
+#LyX 1.6.6 created this file. For more info see http://www.lyx.org/
 \lyxformat 345
 \begin_document
 \begin_header
@@ -1997,6 +1997,13 @@
 
 \begin_layout Subsection
 Formulation for Generalized Maxwell Models
+\begin_inset CommandInset label
+LatexCommand label
+name "sub:Formulation-for-Gen-Max"
+
+\end_inset
+
+
 \end_layout
 
 \begin_layout Standard

Modified: short/3D/PyLith/trunk/doc/userguide/tutorials/3dhex8/3dhex8.lyx
===================================================================
--- short/3D/PyLith/trunk/doc/userguide/tutorials/3dhex8/3dhex8.lyx	2010-06-10 00:23:57 UTC (rev 16965)
+++ short/3D/PyLith/trunk/doc/userguide/tutorials/3dhex8/3dhex8.lyx	2010-06-10 02:11:37 UTC (rev 16966)
@@ -1,4 +1,4 @@
-#LyX 1.6.4 created this file. For more info see http://www.lyx.org/
+#LyX 1.6.6 created this file. For more info see http://www.lyx.org/
 \lyxformat 345
 \begin_document
 \begin_header
@@ -570,1362 +570,14 @@
 \end_inset
 
 
-\end_layout
+\begin_inset CommandInset include
+LatexCommand input
+filename "gravity/gravity.lyx"
 
-\begin_layout Subsection
-Shear Displacement Example
-\end_layout
-
-\begin_layout Standard
-The first example problem is shearing of the mesh along the y-direction,
- with displacement boundary conditions applied on the planes corresponding
- to the minimum and maximum x-values.
- Parameter settings that override or augment those in 
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file 
-\family typewriter
-shearxy.cfg
-\family default
-.
- These settings include:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.implicit Specifies an array of two output managers,
- one for the full domain, and another for a subdomain corresponding to the
- ground surface.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_pos Specifies the boundary conditions for the
- right side of the mesh, defining which degrees of freedom are being constrained
- (
-\family typewriter
-x
-\family default
- and 
-\family typewriter
-y
-\family default
-), providing the label (defined in 
-\family typewriter
-box_hex8_1000m.exo
-\family default
-) defining the points desired, assigning a label to the boundary condition
- set, and giving the name of the spatial database defining the boundary
- conditions (
-\family typewriter
-fixeddisp_shear.spatialdb
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_neg Specifies the boundary conditions for the
- left side of the mesh, defining which degrees of freedom are being constrained
- (
-\family typewriter
-x
-\family default
- and 
-\family typewriter
-y
-\family default
-), providing the label (defined in 
-\family typewriter
-box_hex8_1000m.exo
-\family default
-) defining the points desired, assigning a label to the boundary condition
- set, and giving the name of the spatial database defining the boundary
- conditions (
-\family typewriter
-fixeddisp_shear.spatialdb
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.z_neg Specifies the boundary conditions for the
- bottom of the mesh, defining which degrees of freedom are being constrained
- (
-\family typewriter
-x
-\family default
- and 
-\family typewriter
-y
-\family default
-), providing the label (defined in 
-\family typewriter
-box_hex8_1000m.exo
-\family default
-) defining the points desired, assigning a label to the boundary condition
- set, and giving the name of the spatial database defining the boundary
- conditions (
-\family typewriter
-fixeddisp_shear.spatialdb
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.formulation.output.subdomain Gives the label of the nodeset
- defining the subdomain and gives the base filename for VTK output over
- the subdomain corresponding to the ground surface (
-\family typewriter
-shearxy-groundsurf.vtk
-\family default
-).
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.materials.elastic.output Gives the base filename for
- state variable output files for the elastic material (
-\family typewriter
-shearxy-statevars-elastic.vtk
-\family default
-), and causes state variables to be averaged over all quadrature points
- in each cell.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.materials.viscoelastic.output Gives the base filename
- for state variable output files for the viscoelastic material (
-\family typewriter
-shearxy-statevars-viscoelastic.vtk
-\family default
-), and causes state variables to be averaged over all quadrature points
- in each cell.
-\end_layout
-
-\begin_layout Standard
-The values for the Dirichlet boundary conditions are described in the file
- 
-\family typewriter
-fixeddisp_shear.spatialdb
-\family default
-, as specified in 
-\family typewriter
-shearxy.cfg
-\family default
-.
- The files containing common information (
-\family typewriter
-box_hex8_1000m.exo
-\family default
-, 
-\family typewriter
-pylithapp.cfg
-\family default
-, 
-\family typewriter
-mat_elastic.spatialdb
-\family default
-, and 
-\family typewriter
-mat_viscoelastic.spatialdb
-\family default
-) along with the problem-specific files (
-\family typewriter
-shearxy.cfg
-\family default
-, 
-\family typewriter
-fixeddisp_shear.spatialdb
-\family default
-) provide a complete description of the problem, and we can then run this
- example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith shearxy.cfg
-\end_layout
-
-\begin_layout Standard
-The output file 
-\family typewriter
-shearxy-statevars-elastic_t0000000.vtk
-\family default
- contains the state variables for each cell in the material group 
-\family typewriter
-elastic
-\family default
-.
- The default fields are the total strain and stress fields and are computed
- at each quadrature point in the cell.
- There are eight quadrature points for each cell; however, we have requested
- that these values be averaged, so there is a single set of values per cell.
- The third file (
-\family typewriter
-shearxy-statevars-elastic
-\begin_inset Newline newline
 \end_inset
 
-_info.vtk
-\family default
-) gives the material properties used for the upper elastic material.
- Since we have not specified which properties to write, the default properties
- (
-\family typewriter
-mu
-\family default
-, 
-\family typewriter
-lambda
-\family default
-, 
-\family typewriter
-density
-\family default
-) are written.
- The files for the viscoelastic material 
-\family typewriter
-(shearxy-statevars-viscoelastic_t0000000.vtk
-\family default
- and 
-\family typewriter
-shearxy-statevars-viscoelastic_
-\begin_inset Newline newline
-\end_inset
 
-info.vtk
-\family default
-) are exactly analogous to the corresponding files for the elastic material.
- The file 
-\family typewriter
-shearxy-groundsurf
-\begin_inset Newline newline
-\end_inset
-
-_t0000000.vtk
-\family default
- is analogous to 
-\family typewriter
-shearxy_t0000000.vtk
-\family default
-, but in this case the results are only given for a subset of the mesh correspon
-ding to the ground surface.
- Also, the cells in this file are one dimension lower than the cells described
- in 
-\family typewriter
-shearxy_t0000000.vtk
-\family default
-, so they are quadrilaterals rather than hexahedra.
- If the problem ran correctly, you should be able to generate a figure such
- as 
-\begin_inset CommandInset ref
-LatexCommand ref
-reference "fig:3dhex8-shear"
-
-\end_inset
-
-, which was generated using ParaView.
 \end_layout
 
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
-	filename figs/shear.jpg
-	lyxscale 50
-	scale 45
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Color contours and vectors of displacement for the shear displacement example
- using a mesh composed of trilinear hexahedral cells generated by CUBIT.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:3dhex8-shear"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Kinematic Fault Slip Example
-\end_layout
-
-\begin_layout Standard
-The next example problem is a right-lateral fault slip applied on the vertical
- fault defined by 
-\family typewriter
-x = 0
-\family default
-.
- The left and right sides of the mesh are fixed in the 
-\family typewriter
-x
-\family default
- and 
-\family typewriter
-y
-\family default
- directions, while the bottom is fixed in the 
-\family typewriter
-z
-\family default
- direction.
- Parameter settings that override or augment those in 
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file 
-\family typewriter
-dislocation.cfg
-\family default
-.
- 
-\end_layout
-
-\begin_layout Standard
-The fault example requires three additional database files that were not
- needed for the simple displacement example.
- The first file (
-\family typewriter
-finalslip.spatialdb
-\family default
-) specifies a constant value of 2 m of right-lateral fault slip that then
- tapers linearly to zero from 2 km to 4 km depth, and a linearly-varying
- amount of reverse slip, with a maximum of 0.25 m at the surface, linearly
- tapering to 0 m at 2 km depth.
- The data dimension is one since the data vary linearly along a vertical
- line.
- The default slip time function is a step-function, so we also must provide
- the time at which slip begins.
- The elastic solution is associated with advancing from 
-\begin_inset Formula $t=-dt$
-\end_inset
-
- to 
-\begin_inset Formula $t=0$
-\end_inset
-
-, so we set the slip initiation time for the step-function to 0 in 
-\family typewriter
-dislocation_sliptime.spatialdb
-\family default
-.
-\end_layout
-
-\begin_layout Standard
-The files containing common information (
-\family typewriter
-\size small
-box_hex8_1000m.exo
-\family default
-, 
-\family typewriter
-pylithapp.cfg
-\family default
-, 
-\family typewriter
-mat_elastic.spatialdb
-\family default
-\size default
-, and 
-\family typewriter
-mat_viscoelastic.spatialdb
-\family default
-) along with the problem-specific files (
-\family typewriter
-\size small
-dislocation.cfg
-\family default
-, 
-\family typewriter
-finalslip.spatialdb
-\family default
-, 
-\family typewriter
-sliptime.spatialdb
-\family default
-\size default
-) provide a complete description of the problem, and we can then run this
- example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith dislocation.cfg
-\end_layout
-
-\begin_layout Standard
-If the problem ran correctly, you should be able to generate a figure such
- as Figure 
-\begin_inset CommandInset ref
-LatexCommand vref
-reference "fig:3dhex-disloc"
-
-\end_inset
-
-, which was generated using ParaView.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
-	filename figs/dislocation.jpg
-	lyxscale 50
-	scale 45
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Color contours and vectors of displacement for the kinematic fault example
- using a mesh composed of trilinear hexahedral cells generated by CUBIT.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:3dhex-disloc"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Gravitational Body Force Example
-\end_layout
-
-\begin_layout Standard
-The next example is a simple problem where we apply the body forces due
- to gravitational acceleration.
- All sides are fixed in the normal direction, with the exception of the
- upper surface, which is left free.
- The resulting stress field is
-\begin_inset Formula \begin{equation}
-\sigma_{zz}=\rho gz,\:\sigma_{xx}=\sigma_{yy}=\frac{\nu\rho gz}{1-\nu},\end{equation}
-
-\end_inset
-
-where 
-\begin_inset Formula $\rho$
-\end_inset
-
- is the density of the material, 
-\begin_inset Formula $g$
-\end_inset
-
- is the gravitational acceleration, 
-\begin_inset Formula $h$
-\end_inset
-
- is the elevation (negative elevations for points below the upper surface),
- and 
-\begin_inset Formula $\nu$
-\end_inset
-
- is Poisson's ratio.
- Parameter settings that override or augment those in 
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file 
-\family typewriter
-gravity.cfg
-\family default
-.
- These settings include:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent Specifies an implicit formulation for the problem,
- the array of boundary conditions, and the specification of the 
-\family typewriter
-use_gravity
-\family default
- flag as 
-\family typewriter
-true
-\family default
-.
- The default values of 
-\family typewriter
-acceleration
-\family default
- and 
-\family typewriter
-gravity_dir
-\family default
- are used.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_pos Specifies the boundary conditions for the
- right side of the mesh, defining which degrees of freedom are being constrained
- (
-\family typewriter
-x
-\family default
-), providing the label (defined in 
-\family typewriter
-box_hex8_
-\begin_inset Newline newline
-\end_inset
-
-1000m.exo
-\family default
-) defining the points desired, and assigning a label to the boundary condition
- set.
- Rather than specifying a spatial database file to define the boundary condition
-s, we use the default spatial database (ZeroDispDB) for the Dirichlet boundary
- condition, which sets the displacements to zero.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_neg Specifies the boundary conditions for the
- left side of the mesh, defining which degrees of freedom are being constrained
- (
-\family typewriter
-x
-\family default
-), providing the label (defined in 
-\family typewriter
-box_hex8_
-\begin_inset Newline newline
-\end_inset
-
-1000m.exo
-\family default
-) defining the points desired, and assigning a label to the boundary condition
- set.
- Rather than specifying a spatial database file to define the boundary condition
-s, we use the default spatial database (ZeroDispDB) for the Dirichlet boundary
- condition, which sets the displacements to zero.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.y_pos Specifies the boundary conditions for the
- back of the mesh, defining which degrees of freedom are being constrained
- (
-\family typewriter
-y
-\family default
-), providing the label (defined in 
-\family typewriter
-box_hex8_1000m.exo
-\family default
-) defining the points desired, and assigning a label to the boundary condition
- set.
- Rather than specifying a spatial database file to define the boundary condition
-s, we use the default spatial database (ZeroDispDB) for the Dirichlet boundary
- condition, which sets the displacements to zero.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.y_neg Specifies the boundary conditions for the
- front of the mesh, defining which degrees of freedom are being constrained
- (
-\family typewriter
-y
-\family default
-), providing the label (defined in 
-\family typewriter
-box_hex8_1000m.exo
-\family default
-) defining the points desired, and assigning a label to the boundary condition
- set.
- Rather than specifying a spatial database file to define the boundary condition
-s, we use the default spatial database (ZeroDispDB) for the Dirichlet boundary
- condition, which sets the displacements to zero.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.z_neg Specifies the boundary conditions for the
- bottom of the mesh, defining which degrees of freedom are being constrained
- (
-\family typewriter
-z
-\family default
-), providing the label (defined in 
-\family typewriter
-box_hex8_1000m.
-\begin_inset Newline newline
-\end_inset
-
-exo
-\family default
-) defining the points desired, and assigning a label to the boundary condition
- set.
- Rather than specifying a spatial database file to define the boundary condition
-s, we use the default spatial database (ZeroDispDB) for the Dirichlet boundary
- condition, which sets the displacements to zero.
-\end_layout
-
-\begin_layout Standard
-The files containing common information (
-\family typewriter
-\size small
-box_hex8_1000m.exo
-\family default
-, 
-\family typewriter
-pylithapp.cfg
-\family default
-, 
-\family typewriter
-mat_elastic.spatialdb
-\family default
-\size default
-, 
-\family typewriter
-mat_
-\begin_inset Newline newline
-\end_inset
-
-viscoelastic.spatialdb
-\family default
-) along with the problem-specific file (
-\family typewriter
-\size small
-gravity.cfg
-\family default
-\size default
-) provide a complete description of the problem, and we can then run this
- example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith gravity.cfg
-\end_layout
-
-\begin_layout Standard
-If the problem ran correctly, you should be able to generate a figure such
- as
-\begin_inset CommandInset ref
-LatexCommand vref
-reference "fig:3dhex-gravity"
-
-\end_inset
-
-, which was generated using ParaView.
- Note that the stress values for the example problem match the analytical
- solution given at the beginning of this problem description, recalling
- that the solution is at the center of each cell.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\noindent
-\align center
-\begin_inset Graphics
-	filename figs/hex8-gravity.jpg
-	lyxscale 50
-	scale 45
-
-\end_inset
-
-
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Color contours of vertical stress and vectors of displacement for the gravitatio
-nal body force example using a mesh composed of trilinear hexahedral cells
- generated by CUBIT.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:3dhex-gravity"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Gravitational Body Forces With Initial Stresses
-\end_layout
-
-\begin_layout Standard
-In the previous example, the application of body forces resulted in large
- amounts of vertical deformation, which is generally not desirable in a
- simulation.
- To avoid this difficulty, initial stresses may be specified to exactly
- balance the stresses due to gravitational body forces.
- The problem is identical to the previous problem, except for the use of
- initial stresses.
- The stress solution should be identical, but there should be no displacements
- or strains.
- Parameter settings that override or augment those in 
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file 
-\family typewriter
-gravity_istress.cfg
-\family default
-.
- These settings include:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent Specifies an implicit formulation for the problem,
- the array of boundary conditions, and the specification of the 
-\family typewriter
-use_gravity
-\family default
- flag as 
-\family typewriter
-true
-\family default
-.
- The default values of 
-\family typewriter
-acceleration
-\family default
- and 
-\family typewriter
-gravity_dir
-\family default
- are used.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.materials.elastic Sets the 
-\family typewriter
-use_initial_state
-\family default
- flag to 
-\family typewriter
-True
-\family default
- and provides the initial state database file (
-\family typewriter
-initial_state.spatialdb
-\family default
-) as the filename for 
-\family typewriter
-initial_state_db.iohandler.
-\begin_inset Newline newline
-\end_inset
-
-filename
-\family default
-.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.materials.viscoelastic Sets the 
-\family typewriter
-use_initial_state
-\family default
- flag to 
-\family typewriter
-True
-\family default
- and provides the initial state database file (
-\family typewriter
-initial_state.spatialdb
-\family default
-) as the filename for 
-\family typewriter
-initial_state_db.
-\begin_inset Newline newline
-\end_inset
-
-iohandler.filename
-\family default
-.
-\end_layout
-
-\begin_layout Standard
-The files containing common information (
-\family typewriter
-\size small
-box_hex8_1000m.exo
-\family default
-, 
-\family typewriter
-pylithapp.cfg
-\family default
-, 
-\family typewriter
-mat_elastic.spatialdb
-\family default
-\size default
-, 
-\family typewriter
-mat_
-\begin_inset Newline newline
-\end_inset
-
-viscoelastic.spatialdb
-\family default
-, 
-\family typewriter
-initial_state.spatialdb
-\family default
-) along with the problem-specific file (
-\family typewriter
-\size small
-gravity_istress.cfg
-\family default
-\size default
-) provide a complete description of the problem, and we can then run this
- example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith gravity_istress.cfg
-\end_layout
-
-\begin_layout Standard
-If the problem ran correctly, you should be able to generate a figure such
- as 
-\begin_inset CommandInset ref
-LatexCommand vref
-reference "fig:3dhex-gravity_istress"
-
-\end_inset
-
-, which was generated using ParaView.
- Note that the stress values are identical to those for the previous example,
- while the displacements are zero.
-\end_layout
-
-\begin_layout Standard
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
-	filename figs/hex8-gravity_istress.jpg
-	lyxscale 50
-	scale 45
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Color contours of vertical displacement for the gravitational body force
- example with initial stresses using a mesh composed of trilinear hexahedral
- cells generated by CUBIT.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:3dhex-gravity_istress"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Subsection
-Multiple Kinematic Ruptures Example
-\end_layout
-
-\begin_layout Standard
-The next example problem involves right-lateral slip applied on the vertical
- fault defined by 
-\family typewriter
-x = 0,
-\family default
- where the slip is constant aseismic creep below 
-\family typewriter
-z=-2km
-\family default
- and repeated earthquake ruptures every 200 years above 
-\family typewriter
-z=
-\family default
--2km.
- The left and right sides of the mesh are fixed in the x direction and have
- constant velocities 
-\family typewriter
-in the y
-\family default
- directions, while the bottom is fixed in the 
-\family typewriter
-z
-\family default
- direction.
- This is similar to the Savage-Prescott problem for repeated strike-slip
- earthquakes on an infinite strike-slip fault.
- Parameter settings that override or augment those in 
-\family typewriter
-pylithapp.cfg
-\family default
- are contained in the file 
-\family typewriter
-savageprescott.cfg
-\family default
-.
- These settings include:
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent Specifies an implicit formulation for the problem,
- the array of boundary conditions, and the array of interfaces.
- The total time of the simulation is 700 years with a time step of 10 years.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_pos Specifies the boundary conditions for the
- right side of the mesh, defining which degrees of freedom are being constrained
- (
-\family typewriter
-x
-\family default
- and 
-\family typewriter
-y
-\family default
-), providing the label (defined in 
-\family typewriter
-box_hex8_1000m.exo
-\family default
-) defining the points desired, and assigning a label to the boundary condition
- set.
- Rather than specifying a spatial database file to define the boundary condition
-s, we use the default spatial database (ZeroDispDB) for the Dirichlet boundary
- condition, which sets the displacements to zero.
- We also assign nonzero rates for the y degree of freedom, corresponding
- to a velocity of -1.0 cm/year.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.x_neg Specifies the boundary conditions for the
- left side of the mesh, defining which degrees of freedom are being constrained
- (
-\family typewriter
-x
-\family default
- and 
-\family typewriter
-y
-\family default
-), providing the label (defined in 
-\family typewriter
-box_hex8_1000m.exo
-\family default
-) defining the points desired, and assigning a label to the boundary condition
- set.
- Rather than specifying a spatial database file to define the boundary condition
-s, we use the default spatial database (ZeroDispDB) for the Dirichlet boundary
- condition, which sets the displacements to zero.
- We also assign nonzero rates for the y degree of freedom, corresponding
- to a velocity of 1.0 cm/year.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.bc.z_neg Specifies the boundary conditions for the
- bottom of the mesh, defining which degrees of freedom are being constrained
- (z), providing the label (defined in 
-\family typewriter
-box_hex8_1000m.
-\begin_inset Newline newline
-\end_inset
-
-exo
-\family default
-) defining the points desired, and assigning a label to the boundary condition
- set.
- Rather than specifying a spatial database file to define the boundary condition
-s, we use the default spatial database (ZeroDispDB) for the Dirichlet boundary
- condition, which sets the displacements to zero.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.interfaces Gives the label (defined in 
-\family typewriter
-box_hex8_1000m.exo
-\family default
-) defining the points on the fault, provides quadrature information, the
- array of kinematic ruptures, and the database names for material properties
- (needed for conditioning), fault slip, and fault slip time.
- The origin time determines when each earthquake source begins, and the
- corresponding slip and slip time databases are then applied beginning at
- that time.
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.formulation.output.output.writer Gives the base filename for
- VTK output over the entire domain (
-\family typewriter
-savageprescott.vtk
-\family default
-).
- To simplify the names of the generated VTK files, the timestamp is created
- in units of one year.
-\end_layout
-
-\begin_layout Description
-pylithapp.problem.formulation.output.subdomain Gives the label of the nodeset
- defining the subdomain and gives the base filename for VTK output over
- the subdomain corresponding to the ground surface (
-\family typewriter
-savageprescott-groundsurf.vtk
-\family default
-).
- To simplify the names of the generated VTK files, the timestamp is created
- in units of one year.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.interfaces.fault.output.writer Gives the base filename
- for cohesive cell output files (
-\family typewriter
-savageprescott-fault.vtk
-\family default
-).
- To simplify the names of the generated VTK files, the timestamp is created
- in units of one year.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.materials.elastic.output Gives the base filename for
- state variable output files for the elastic material (
-\family typewriter
-savageprescott-elastic.vtk
-\family default
-), and causes state variables to be averaged over all quadrature points
- in each cell.
- To simplify the names of the generated VTK files, the timestamp is created
- in units of one year.
-\end_layout
-
-\begin_layout Description
-pylithapp.timedependent.materials.viscoelastic.output Gives the base filename
- for state variable output files for the viscoelastic material (
-\family typewriter
-savageprescott-viscoelastic.vtk
-\family default
-), and causes state variables to be averaged over all quadrature points
- in each cell.
- To simplify the names of the generated VTK files, the timestamp is created
- in units of one year.
-\end_layout
-
-\begin_layout Standard
-The multiple earthquake ruptures and fault creep each require their own
- spatial database files to specify the slip.
- With the depth variation in slip for the creep and earthquake ruptures,
- the data dimension in the slip spatial database files is one since the
- data vary linearly along a vertical line.
- Because we use identical, repeating ruptures for the earthquakes, we use
- the same set of spatial database files for each rupture.
- The file (
-\family typewriter
-sliprate_creep.spatialdb
-\family default
-) specifies a constant, uniform right-lateral slip rate of 2 cm/yr over
- the bottom half (z < -2 km) of the fault.
- The creep commences at the beginning of the simulation, so the origin time
- of the creep is 
-\family typewriter
-t=0
-\family default
- s.
- Each earthquake rupture prescribes 4.0 m of uniform right-lateral slip for
- z > -2.0 km repeat every 200 years with the first rupture at 
-\family typewriter
-t=200
-\family default
- years.
- We use the step-function for the slip-time function in the earthquake ruptures
- with origin times of 200, 400, and 600 years.
-\end_layout
-
-\begin_layout Standard
-The files containing common information (
-\family typewriter
-\size small
-box_hex8_1000m.exo
-\family default
-, 
-\family typewriter
-pylithapp.cfg
-\family default
-, 
-\family typewriter
-mat_elastic.spatialdb
-\family default
-\size default
-, and 
-\family typewriter
-\size small
-mat_viscoelastic.spatialdb
-\family default
-\size default
-) along with the problem-specific files (
-\family typewriter
-\size small
-savageprescott.cfg
-\family default
-, 
-\family typewriter
-finalslip_
-\begin_inset Newline newline
-\end_inset
-
-rupture.spatialdb
-\family default
-, 
-\family typewriter
-sliprate_creep.spatialdb
-\family default
-, 
-\family typewriter
-sliptime.spatialdb
-\family default
-\size default
-) provide a complete description of the problem, and we can then run this
- example by typing
-\end_layout
-
-\begin_layout LyX-Code
-pylith savageprescott.cfg
-\end_layout
-
-\begin_layout Standard
-Running the problem produces a number of output files.
- The solution over the entire volume and state variables are output once
- every 100 years (skipping 9 time steps) while the fault and ground surface
- information is output every time step.
- The time stamp in the VTK files is normalized by the value of 1 year, so
- the numbers in the VTK filenames correspond to the time in years.
- As in the other simulations, the files in the form 
-\family typewriter
-savageprescott_tXXXX.vtk
-\family default
- contain the displacement values at the mesh vertices.
- The files of the form 
-\family typewriter
-savageprescott-elastic_tXXXX.vtk
-\family default
- contain the state variables for each cell in the material group 
-\family typewriter
-elastic
-\family default
-.
- The default fields are the total strain and stress fields.
- These values are computed at each quadrature point in the cell.
- There are eight quadrature points for each cell; however, we have requested
- that these values be averaged, so there is a single set of values per cell.
- The file 
-\family typewriter
-savageprescott-elastic_info.vtk
-\family default
- gives the material properties used for the elastic material.
- The files for the viscoelastic material,
-\end_layout
-
-\begin_layout LyX-Code
-
-\family typewriter
-savageprescott-viscoelastic_tXXXX.vtk 
-\family roman
-and
-\end_layout
-
-\begin_layout LyX-Code
-
-\family typewriter
-savageprescott-viscoelastic_info.vtk
-\end_layout
-
-\begin_layout Standard
-are exactly analogous to the corresponding files for the elastic material.
- The files of the form 
-\end_layout
-
-\begin_layout LyX-Code
-
-\family typewriter
-savageprescott-groundsurf_tXXXX.vtk
-\family default
- 
-\end_layout
-
-\begin_layout Standard
-are analogous to 
-\family typewriter
-savageprescott_t0000000.vtk
-\family default
-, but in this case the results are only given for a subset of the mesh correspon
-ding to the ground surface (and are output more frequently).
- The files of the form 
-\end_layout
-
-\begin_layout LyX-Code
-
-\family typewriter
-savageprescott-fault_tXXXX.vtk
-\family default
- 
-\end_layout
-
-\begin_layout Standard
-give the fault slip for each vertex on the fault, along with the computed
- traction change for the cohesive cell.
- The final file
-\end_layout
-
-\begin_layout LyX-Code
-
-\family typewriter
-savageprescott-fault_info.vtk
-\family default
- 
-\end_layout
-
-\begin_layout Standard
-provides information such as the normal direction and final slip and slip
- time for each vertex on the fault for each fault rupture.
- The desired output fields are specified as 
-\end_layout
-
-\begin_layout LyX-Code
-
-\family typewriter
-pylithapp.timedependent.interfaces.fault.output.vertex_info_fields
-\family default
- 
-\end_layout
-
-\begin_layout Standard
-in the file 
-\family typewriter
-savageprescott.cfg
-\family default
-.
- If the problem ran correctly, you should be able to generate a figure such
- as Figure 
-\begin_inset CommandInset ref
-LatexCommand vref
-reference "fig:3dhex:savageprescott"
-
-\end_inset
-
-, which was generated using ParaView.
-\end_layout
-
-\begin_layout Standard
-\noindent
-\align center
-\begin_inset Float figure
-wide false
-sideways false
-status open
-
-\begin_layout Plain Layout
-\align center
-\begin_inset Graphics
-	filename figs/savageprescott-t100.jpg
-	lyxscale 50
-	scale 45
-
-\end_inset
-
-
-\end_layout
-
-\begin_layout Plain Layout
-\begin_inset Caption
-
-\begin_layout Plain Layout
-Color contours and vectors of displacement at t = 100 years for the multiple
- kinematic fault rupture example using a mesh composed of trilinear hexahedral
- cells generated by CUBIT.
-\begin_inset CommandInset label
-LatexCommand label
-name "fig:3dhex:savageprescott"
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
-\end_inset
-
-
-\end_layout
-
 \end_body
 \end_document

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Added: short/3D/PyLith/trunk/doc/userguide/tutorials/3dhex8/gravity/gravity.lyx
===================================================================
--- short/3D/PyLith/trunk/doc/userguide/tutorials/3dhex8/gravity/gravity.lyx	                        (rev 0)
+++ short/3D/PyLith/trunk/doc/userguide/tutorials/3dhex8/gravity/gravity.lyx	2010-06-10 02:11:37 UTC (rev 16966)
@@ -0,0 +1,696 @@
+#LyX 1.6.6 created this file. For more info see http://www.lyx.org/
+\lyxformat 345
+\begin_document
+\begin_header
+\textclass book
+\begin_preamble
+
+\end_preamble
+\use_default_options false
+\language english
+\inputencoding latin1
+\font_roman default
+\font_sans default
+\font_typewriter default
+\font_default_family default
+\font_sc false
+\font_osf false
+\font_sf_scale 100
+\font_tt_scale 100
+
+\graphics default
+\paperfontsize default
+\spacing single
+\use_hyperref false
+\papersize default
+\use_geometry true
+\use_amsmath 0
+\use_esint 0
+\cite_engine basic
+\use_bibtopic false
+\paperorientation portrait
+\leftmargin 1in
+\topmargin 1in
+\rightmargin 1in
+\bottommargin 2in
+\secnumdepth 3
+\tocdepth 3
+\paragraph_separation indent
+\defskip medskip
+\quotes_language english
+\papercolumns 1
+\papersides 1
+\paperpagestyle default
+\tracking_changes false
+\output_changes false
+\author "" 
+\author "" 
+\end_header
+
+\begin_body
+
+\begin_layout Subsection
+\begin_inset CommandInset label
+LatexCommand label
+name "sec:Tutorial-3d-hex8-gravity"
+
+\end_inset
+
+Tutorial Using Hexahedral Mesh Created by CUBIT - Gravity Examples
+\end_layout
+
+\begin_layout Standard
+PyLith features discussed in this tutorial:
+\end_layout
+
+\begin_layout Itemize
+Gravitational body forces
+\end_layout
+
+\begin_layout Itemize
+Initial stresses
+\end_layout
+
+\begin_layout Itemize
+Finite strain
+\end_layout
+
+\begin_layout Itemize
+Generalized Maxwell linear viscoelastic material
+\end_layout
+
+\begin_layout Subsubsection
+Overview
+\end_layout
+
+\begin_layout Standard
+This set of examples describes a set of problems for PyLith involving gravitatio
+nal body forces.
+ All of the examples are quasi-static and all of them run for a time period
+ of 200 years.
+ These examples also demonstrate the use of a generalized Maxwell viscoelastic
+ material, which is used for the lower crust in all examples.
+ The final example (step17) demonstrates the usage of a finite strain formulatio
+n, which automatically invokes the nonlinear solver.
+ All of the examples are contained in the directory 
+\family typewriter
+examples/3d/hex8
+\family default
+, and the corresponding 
+\family typewriter
+.cfg
+\family default
+ files are 
+\family typewriter
+step15.cfg
+\family default
+, 
+\family typewriter
+step16.cfg
+\family default
+, and 
+\family typewriter
+step17.cfg
+\family default
+.
+ Each example may be run as follows:
+\end_layout
+
+\begin_layout LyX-Code
+pylith stepxx.cfg
+\end_layout
+
+\begin_layout Standard
+This will cause PyLith to read the default parameters in 
+\family typewriter
+pylithapp.cfg
+\family default
+, and then override or augment them with the additional parameters in the
+ 
+\family typewriter
+stepxx.cfg
+\family default
+ file.
+ Each 
+\family typewriter
+.cfg
+\family default
+ file is extensively documented, to provide detailed information on the
+ various parameters.
+\end_layout
+
+\begin_layout Subsubsection
+Step15 - Gravitational Body Forces
+\end_layout
+
+\begin_layout Standard
+The 
+\family typewriter
+step15.cfg
+\family default
+ file describes a problem with extremely simple Dirichlet boundary conditions.
+ On the positive and negative x-faces, the positive and negative y-faces,
+ and the negative z-face, the displacements normal to the face are set to
+ zero.
+ We then apply gravitational body forces.
+ Since all the material in the example has the same density, for the elastic
+ solution, the resultant stresses should be:
+\begin_inset Formula \begin{equation}
+\sigma_{zz}=\rho gh;\:\sigma_{xx}=\sigma_{yy}=\frac{\nu\rho gh}{1-\nu}\:.\label{eq:1-1}\end{equation}
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Standard
+We first set the gravity field, which by default has values of 9.80655 
+\begin_inset Formula $\unitfrac{m}{s^{2}}$
+\end_inset
+
+ for acceleration and 
+\begin_inset Formula $\left[0,0,-1\right]$
+\end_inset
+
+ for direction:
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent]
+\end_layout
+
+\begin_layout LyX-Code
+# Set gravity field (default is None)
+\end_layout
+
+\begin_layout LyX-Code
+gravity_field = spatialdata.spatialdb.GravityField
+\end_layout
+
+\begin_layout Standard
+We use adaptive time stepping, set the simulation time to 200 years, and
+ specify a maximum time step size of 10 years:
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent.implicit]
+\end_layout
+
+\begin_layout LyX-Code
+# Change time stepping algorithm from uniform time step, to adaptive
+\end_layout
+
+\begin_layout LyX-Code
+# time stepping.
+\end_layout
+
+\begin_layout LyX-Code
+time_step = pylith.problems.TimeStepAdapt
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout LyX-Code
+# Change the total simulation time to 200 years, and set the maximum time
+\end_layout
+
+\begin_layout LyX-Code
+# step size to 10 years.
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent.implicit.time_step]
+\end_layout
+
+\begin_layout LyX-Code
+total_time = 200.0*year
+\end_layout
+
+\begin_layout LyX-Code
+max_dt = 10.0*year
+\end_layout
+
+\begin_layout LyX-Code
+stability_factor = 1.0 ; use time step equal to stable value from materials
+\end_layout
+
+\begin_layout Standard
+We use a generalized Maxwell model for the lower crust (see 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sub:Formulation-for-Gen-Max"
+
+\end_inset
+
+), and use a 
+\family typewriter
+SimpleDB
+\family default
+ to provide the properties.
+ We also request the relevant properties and state variables for output:
+\end_layout
+
+\begin_layout LyX-Code
+# Change material type of lower crust to generalized Maxwell viscoelastic.
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent]
+\end_layout
+
+\begin_layout LyX-Code
+materials.lower_crust = pylith.materials.GenMaxwellIsotropic3D
+\end_layout
+
+\begin_layout LyX-Code
+# Provide a spatial database from which to obtain property values.
+\end_layout
+
+\begin_layout LyX-Code
+# Since there are additional properties and state variables for the
+\end_layout
+
+\begin_layout LyX-Code
+# generalized Maxwell model, we explicitly request that they be output.
+\end_layout
+
+\begin_layout LyX-Code
+# Properties are named in cell_info_fields and state variables are named
+ in
+\end_layout
+
+\begin_layout LyX-Code
+# cell_data_fields.
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent.materials.lower_crust]
+\end_layout
+
+\begin_layout LyX-Code
+db_properties.iohandler.filename = spatialdb/mat_genmaxwell.spatialdb
+\end_layout
+
+\begin_layout LyX-Code
+output.cell_info_fields = [density,mu,lambda,shear_ratio,maxwell_time]
+\end_layout
+
+\begin_layout LyX-Code
+output.cell_data_fields = [total_strain,stress,viscous_strain_1,viscous_strain_2,
+viscous_strain_3]
+\end_layout
+
+\begin_layout Standard
+The boundary conditions for this example are trivial, so we are able to
+ use the default 
+\family typewriter
+ZeroDispDB
+\family default
+ for all faces.
+ When we have run the simulation, the output VTK files will be contained
+ in 
+\family typewriter
+examples/3d/hex8/output
+\family default
+ (all with a prefix of 
+\family typewriter
+step15
+\family default
+), and the results may be visualized using a tool such as ParaView or mayavi2.
+ Results using ParaView are shown in 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:step15-displ-t200"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename figs/step15-displ-t200.jpg
+	width 10cm
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Displacement field for example step15 at t = 200 years visualized using
+ ParaView.
+ The z-component of the displacement field is shown with the color contours,
+ and the vectors show the computed displacements.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:step15-displ-t200"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Step16 - Gravitational Body Forces with Initial Stresses
+\end_layout
+
+\begin_layout Standard
+The 
+\family typewriter
+step16.cfg
+\family default
+ file describes a problem that is identical to example step15, except that
+ initial stresses are used to prevent the initial large displacements due
+ to 'turning on' gravity.
+ Since all normal stress components are given an initial stress of 
+\begin_inset Formula $\rho gh$
+\end_inset
+
+, the initial stress state is lithostatic, which is an appropriate condition
+ for many tectonic problems in the absence of tectonic stresses (e.g., 
+\begin_inset CommandInset citation
+LatexCommand cite
+key "McGarr:1988"
+
+\end_inset
+
+).
+ When compared to example step15, this example should maintain a lithostatic
+ state of stress for the entire simulation, and displacements should remain
+ essentially zero.
+\end_layout
+
+\begin_layout Standard
+We set the gravity field, as for example step15, and we again use adaptive
+ time stepping and use a generalized Maxwell rheology for the lower crust.
+ We then must provide values for the initial stress for both the upper and
+ lower crust.
+ Since the materials have the same density, we are able to use the same
+ 
+\family typewriter
+SimpleDB
+\family default
+ with a linear variation for both (see file 
+\family typewriter
+examples/3d/hex8/spatialdb/initial_stress.spatialdb
+\family default
+):
+\end_layout
+
+\begin_layout LyX-Code
+# We must specify initial stresses for each material.
+\end_layout
+
+\begin_layout LyX-Code
+# We provide a filename for the spatial database that gives the stresses,
+\end_layout
+
+\begin_layout LyX-Code
+# and we change the query_type from the default 'nearest' to 'linear'.
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent.materials.upper_crust]
+\end_layout
+
+\begin_layout LyX-Code
+db_initial_stress = spatialdata.spatialdb.SimpleDB
+\end_layout
+
+\begin_layout LyX-Code
+db_initial_stress.iohandler.filename = spatialdb/initial_stress.spatialdb
+\end_layout
+
+\begin_layout LyX-Code
+db_initial_stress.query_type = linear
+\end_layout
+
+\begin_layout LyX-Code
+
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent.materials.lower_crust]
+\end_layout
+
+\begin_layout LyX-Code
+db_initial_stress = spatialdata.spatialdb.SimpleDB
+\end_layout
+
+\begin_layout LyX-Code
+db_initial_stress.iohandler.filename = spatialdb/initial_stress.spatialdb
+\end_layout
+
+\begin_layout LyX-Code
+db_initial_stress.query_type = linear
+\end_layout
+
+\begin_layout Standard
+Note that we use a 
+\family typewriter
+linear
+\family default
+ 
+\family typewriter
+query_type
+\family default
+ rather than the default type of 
+\family typewriter
+nearest
+\family default
+, so that a linear interpolation is performed along the z-direction.
+ When we have run the simulation, the output VTK files will be contained
+ in 
+\family typewriter
+examples/3d/hex8/output
+\family default
+ (all with a prefix of 
+\family typewriter
+step16
+\family default
+), and the results may be visualized using a tool such as ParaView or mayavi2.
+ Results using ParaView are shown in 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:step16-stress_xx-t200"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename figs/step16-stress_xx-t200.jpg
+	width 10cm
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Stress field (xx-component) for example step16 at t = 200 years visualized
+ using ParaView.
+ Note that for this example, Stress_xx = Stress_yy = Stress_zz, and there
+ is no vertical displacement throughout the simulation.
+ Also note that the stresses appear as 4 layers since we have used 
+\family typewriter
+CellFilterAvgMesh
+\family default
+ for material output.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:step16-stress_xx-t200"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Subsubsection
+Step17 - Gravitational Body Forces with Small Strain
+\end_layout
+
+\begin_layout Standard
+The 
+\family typewriter
+step17.cfg
+\family default
+ file describes a problem that is identical to example step15, except that
+ we now use a small strain formulation (see 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "sec:Small-Strain-Formulation"
+
+\end_inset
+
+).
+ All of the problems up to this point have assumed infinitesimal (linear)
+ strain, meaning that the change in shape of the domain during deformation
+ is not taken into account.
+ In many problems it is important to consider the change in shape of the
+ domain.
+ This is particularly important in many problems involving gravitational
+ body forces, since a change in shape of the domain results in a different
+ system of forces.
+ By examining the stress and deformation fields for this example in comparison
+ with those of example step15, we can see what effect the infinitesimal
+ strain approximation has on our solution.
+\end_layout
+
+\begin_layout Standard
+We set the gravity field, as for example step15, and we again use adaptive
+ time stepping and use a generalized Maxwell rheology for the lower crust.
+ The only change is that we change the problem formulation from the default
+ 
+\family typewriter
+Implicit
+\family default
+ to 
+\family typewriter
+ImplicitLgDeform
+\family default
+.
+ Since the large deformation formulation is nonlinear, PyLith automatically
+ switches the solver from the default 
+\family typewriter
+SolverLinear
+\family default
+ to 
+\family typewriter
+SolverNonlinear
+\family default
+.
+ It is thus only necessary to change the formulation:
+\end_layout
+
+\begin_layout LyX-Code
+[pylithapp.timedependent]
+\end_layout
+
+\begin_layout LyX-Code
+# Set the formulation for finite strain.
+ The default solver will
+\end_layout
+
+\begin_layout LyX-Code
+# automatically be switched to the nonlinear solver.
+\end_layout
+
+\begin_layout LyX-Code
+formulation = pylith.problems.ImplicitLgDeform
+\end_layout
+
+\begin_layout Standard
+When we have run the simulation, the output VTK files will be contained
+ in 
+\family typewriter
+examples/3d/hex8/output
+\family default
+ (all with a prefix of 
+\family typewriter
+step17
+\family default
+), and the results may be visualized using a tool such as ParaView or mayavi2.
+ Results using ParaView are shown in 
+\begin_inset CommandInset ref
+LatexCommand ref
+reference "fig:step17-disp-t200"
+
+\end_inset
+
+.
+\end_layout
+
+\begin_layout Standard
+\begin_inset Float figure
+wide false
+sideways false
+status open
+
+\begin_layout Plain Layout
+\begin_inset Graphics
+	filename figs/step17-displ-t200.jpg
+	width 10cm
+
+\end_inset
+
+
+\end_layout
+
+\begin_layout Plain Layout
+\begin_inset Caption
+
+\begin_layout Plain Layout
+Displacement field for example step17 at t = 200 years visualized using
+ ParaView.
+ The z-component of the displacement field is shown with the color contours,
+ and the vectors show the computed displacements.
+ Note the larger displacements compared with example step15.
+\begin_inset CommandInset label
+LatexCommand label
+name "fig:step17-disp-t200"
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_inset
+
+
+\end_layout
+
+\end_body
+\end_document

Modified: short/3D/PyLith/trunk/doc/userguide/userguide.lyx
===================================================================
--- short/3D/PyLith/trunk/doc/userguide/userguide.lyx	2010-06-10 00:23:57 UTC (rev 16965)
+++ short/3D/PyLith/trunk/doc/userguide/userguide.lyx	2010-06-10 02:11:37 UTC (rev 16966)
@@ -1,4 +1,4 @@
-#LyX 1.6.5 created this file. For more info see http://www.lyx.org/
+#LyX 1.6.6 created this file. For more info see http://www.lyx.org/
 \lyxformat 345
 \begin_document
 \begin_header
@@ -754,5 +754,26 @@
 , 113, B09317, doi:10.1029/2007JB005553.
 \end_layout
 
+\begin_layout Bibliography
+\begin_inset CommandInset bibitem
+LatexCommand bibitem
+label "22"
+key "McGarr:1988"
+
+\end_inset
+
+McGarr, A.
+ (1988), On the state of lithospheric stress in the absence of applied tectonic
+ forces, 
+\shape italic
+Journal of Geophysical Research
+\shape default
+, 
+\shape italic
+93
+\shape default
+, 13,609-13,617.
+\end_layout
+
 \end_body
 \end_document

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