[cig-commits] commit: More work on revisions. Added some words on difference between domain decomposition approach and TSN and double couples.

[Mercurial]

changeset:   156:71f4a93fa393
tag:         tip
user:        Brad Aagaard <baagaard at usgs.gov>
date:        Mon Jan 14 19:41:22 2013 -0800
files:       faultRup.tex
description:
More work on revisions. Added some words on difference between domain decomposition approach and TSN and double couples.


diff -r 3041d51e7728 -r 71f4a93fa393 faultRup.tex
--- a/faultRup.tex	Mon Jan 14 13:48:28 2013 -0800
+++ b/faultRup.tex	Mon Jan 14 19:41:22 2013 -0800
@@ -304,6 +304,37 @@ function and setting the integral over t
   \int_{S_f} \pmb{\phi} \cdot 
   \left(\bm{d} - \bm{u}_{+} + \bm{u}_{-} \right) \, dS = 0.
 \end{equation}\end{linenomath*}
+This constraint equation applies to the relative displacement vector
+across the fault and slip in both the tangential and fault opening
+directions.
+
+The domain decomposition approach for imposing fault slip or tractions
+on a fault is similar to the ``traction at split nodes'' (TSN)
+technique used in a number of finite-difference and finite-element
+codes \cite{ADD_CITATIONS_HERE}, but differs from imposing fault slip
+via double-couple point sources. The domain decomposition approach
+treats the fault surface as a frictional contact interface, and the
+tractions correspond directly to the Lagrange multipliers needed to
+satisfy the constraint equation involving the jump in the displacement
+field across the fault and the fault slip. As a result, the fault
+tractions are equal and opposite on the two sides of the fault and
+satisfy equilibrium.  The TSN technique ... ADD STUFF HERE.
+
+Imposing fault slip via double couple point sources involves imposing
+body forces consistent with an effective plastic strain associated
+with fault slip. These body forces resolved onto the fault surface do
+not directly correspond to the tractions on the fault
+surface. Instead, the fault tractions come from resolving the
+superposition of the stress from the elasticity equation and the body
+forces onto the fault surface.  Because the strain is imposed in a
+continuous medium, the body forces depend on the elastic modulii, so
+in the case of a contast in the elastic modulii across the fault, the
+body forces on the two sides of the fault differ. This introduces some
+greater complexity into imposing a desired fault slip and illustates
+the simplicity of the domain decomposition approach that directly
+relates the fault tractions to the enforcement of the constraint that
+the fault slip matches the jump in the displacement field across the
+fault.
 
 We express the weighting function $\pmb{\phi}$, trial solution
 $\bm{u}$, Lagrange multipliers $\bm{l}$, and fault slip $\bm{d}$ as