structural geology, propagation mechanics and - Stanford School of ...

(a)
(b)
σ 3
σ 1
x 3
x 1
x 1
(c) u 1
Figure 2.11. Schematic representations of the idealized compaction band model. (a)
Axisymmetric geometry of the eccentric ellipsoidal band aligned with the principal
remote stresses. (b) Cross-sectional area of the band (solid ellipse) relative to the precompacted
area originally occupied by the same detrital grains (dashed ellipse). As
inelastic compaction progresses, the boundary around the grains involved contracts as
indicated by the displacement arrows (u1). This inward displacement of the elliptical
boundary corresponds to the uniform uniaxial plastic strain of an Eshelby inclusion, and
the area between the dashed and solid ellipses corresponds to the volume loss associated
with the compaction. (c) Two-dimensional anticrack representation of the model band as
an elliptical distribution of closing-mode displacement discontinuity equivalent to the
uniform Eshelby compaction strain. In this virtual treatment, two material lines (solid
lines) interpenetrate by an amount equivalent to the volume loss associated with the
compaction (dashed ellipse) as shown by the displacement arrows (u1). Actual
interpenetration does not occur. Because of its extreme eccentricity, however, solutions
for the state of stress induced around the model band using the Eshelby and anticrack
approaches are substantially similar.
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u 1
x 2
x 2
u 1
σ 2