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

helps to explain why the oblique approach of one band to the flank of another rarely leads
to intersection, as the local direction of σθθ max can never be parallel to the band flank and
thus cannot lead the propagating tip on a direct collision course with the adjacent band
flank.
Finally we note that, unlike opening-mode cracks, which generally are modeled as
shear traction-free boundary surfaces pressed open by an internal fluid pressure that
constitutes an independently variable driving force for propagation (e.g. Cotterell and
Rice, 1980), anticrack CBs are compaction structures whose propagation can only be
driven by near-tip compressive stress concentrations generated as a consequence of
previous compaction, which must ultimately result from the failure of grain-scale flaws
within the ambient remote stress field (Sternlof et al., 2005). This amounts to a stringent
constraint on initiation and propagation that renders the dense variety of band patterns
pervading the Aztec sandstone all the more remarkable.
5. Numerical model
In order to examine the stress and strain fields generated by CBs and model their
propagation and interaction as anticracks, we developed a MATLAB® code based on the
displacement discontinuity boundary element method of Crouch and Starfield (1983). In
our formulation of this 2-D, linear elastic plane strain model, which corresponds well
with the character of the field data and interpretations described above, we consider an
infinite whole space subjected to uniform principal stresses at infinity and represent the
bands as segmented traces of linear boundary elements (Figure 4.15). Across each of
these elements, two independent and uniformly distributed components of displacement
discontinuity, or dislocation, can be accommodated: Dn (normal) and Ds (shear). The
displacements realized on each element affect those on all others and depend on the
remote loading, as well as the traction boundary conditions (normal and shear) which
must be specified for every element. In order to determine the two unknown components
of displacement for all N elements, while matching the specified traction boundary
conditions, requires the formulation and solution of a traction boundary value problem
consisting of a linear system of 2N equations that can be summarized in matrix notation
as:
tn = E·dn + F·ds (1)
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