# [cig-commits] r14217 - doc/snac

echoi at geodynamics.org echoi at geodynamics.org
Tue Mar 3 15:04:24 PST 2009

Author: echoi
Date: 2009-03-03 15:04:24 -0800 (Tue, 03 Mar 2009)
New Revision: 14217

Modified:
doc/snac/snac.lyx
Log:
* Minor changes.

Modified: doc/snac/snac.lyx
===================================================================
--- doc/snac/snac.lyx	2009-03-03 23:02:46 UTC (rev 14216)
+++ doc/snac/snac.lyx	2009-03-03 23:04:24 UTC (rev 14217)
@@ -1745,7 +1745,11 @@
\begin_inset Formula $\Delta\sigma^{n}=\mathbf{C}:(\Delta\varepsilon^{n}-\Delta\varepsilon^{p})$
\end_inset

-.
+ and
+\begin_inset Formula $\mathbf{C}$
+\end_inset
+
+ is the elastic moduli tensor.
In the principal component representation,
\begin_inset Formula $\sigma_{A}=a_{AB}^{e}e_{B}$
\end_inset
@@ -1762,13 +1766,13 @@
\begin_inset Formula $\mathbf{a}^{e}$
\end_inset

- is a corresponding elastic stiffness matrix of which components are given
+ is a corresponding elastic moduli matrix of which components are given
in terms of Lame's constants:
\begin_inset Formula $a_{AB}^{e}=\lambda+2\mu\delta_{AB}$
\end_inset

.
- By expanding each yield function using
+ By expanding each yield function and using
\begin_inset Formula $\sigma^{TR}=\sigma^{n}+\mathbf{C}:\Delta\varepsilon^{n}$
\end_inset

@@ -1853,10 +1857,10 @@
old mesh has moved too far away from the corresponding one of the new mesh.
Also, this remeshing works best in the case of lateral extension because
the nodes are moved back to their original positions.
- If a mesh has shrunk laterally and then remeshing moves all the nodes
- back to their original horizontal positions, it is impossible to remap
- variables for the regions of a new mesh that do not have overlapping parts
- in the deformed mesh.
+ If a mesh has shrunk laterally and then remeshing moves all the nodes back
+ to their original horizontal positions, it is impossible to remap variables
+ for the regions of a new mesh that do not have overlapping parts in the
+ deformed mesh.
In such a case, one would have to
\emph on
assume