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index.html

@@ -254,5 +254,5 @@ <h2 id="initialize">Initialize</h2>
 
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-Build Date UTC : 2024-01-26 07:40:26.763245+00:00
+Build Date UTC : 2024-01-26 11:03:23.017974+00:00
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plastic-spin/index.html

@@ -125,13 +125,13 @@
 
                 <h1 id="plastic-spin">Plastic spin</h1>
 <p><img alt="" src="https://raw.githubusercontent.com/nicholasmr/specfab/main/images/tranisotropic/plastic-spin.png" style="width:380px" /></p>
-<p>In bulk simple shear, the orientation of slip systems generally tends towards the bulk shear-plane axes. 
+<p>In bulk simple shear, the orientation of a grain's dominant slip system tends to align itself with the bulk shear-plane system. 
 Thus, if the two are perfectly aligned, the slip-system orientation should be unaffected by continued shearing (i.e. be in steady state).
-Clearly, slip-system orientations do therefore not simply co-rotate with the bulk spin (<span class="arithmatex">\(\bf W\)</span>) like passive material line elements (plane elements) subject to a flow field, i.e. 
+Clearly, slip systems do therefore not simply co-rotate with the bulk continuum spin (<span class="arithmatex">\(\bf W\)</span>) like passive material line elements embedded in a flow field, i.e. 
 <span class="arithmatex">\({\bf \dot{n}} \neq {\bf W} \cdot {\bf n}\)</span>.
-Rather, slip systems must experience an additional spin contribution &mdash;a plastic spin <span class="arithmatex">\({\bf W}_\mathrm{p}\)</span>&mdash;such that, in the case of perfect alignment, the bulk spin is exactly counteracted to achieve steady state:</p>
+Rather, slip systems must be subject to an additional contribution &mdash; a plastic spin <span class="arithmatex">\({\bf W}_\mathrm{p}\)</span> &mdash; such that the bulk spin is exactly counteracted to achieve steady state:</p>
 <div class="arithmatex">\[
-{\bf \dot{n}} = ({\bf W} + {\bf W}_{\mathrm{p}}) \cdot {\bf n} = {\bf 0} .
+{\bf \dot{n}} = ({\bf W} + {\bf W}_{\mathrm{p}}) \cdot {\bf n} = {\bf 0} \quad\text{for ${\bf b}$&ndash;${\bf n}$ shear}.
 \]</div>
 <p>Here, the functional form of <span class="arithmatex">\({\bf W}_\mathrm{p}\)</span> is breifly discussed following <a href="https://doi.org/10.1016/0749-6419(91)90028-W">Aravas and Aifantis (1991)</a> and <a href="https://www.doi.org/10.1088/0965-0393/2/3A/005">Aravas (1994)</a> (among others). </p>
 <p>For a constant rate of shear deformation (<span class="arithmatex">\(1/T\)</span>) aligned with the <span class="arithmatex">\({\bf b}\)</span>&mdash;<span class="arithmatex">\({\bf n}\)</span> system, </p>
@@ -143,7 +143,7 @@ <h1 id="plastic-spin">Plastic spin</h1>
 \frac{1}{T} {\bf b}\otimes{\bf n}
 ,
 \]</div>
-<p>the bulk stretching (strain rate) and spin tensors are, respectively,</p>
+<p>the bulk strain-rate and spin tensors are, respectively,</p>
 <div class="arithmatex">\[
 {\bf D} = \frac{1}{2T} ({\bf b}\otimes{\bf n} + {\bf n}\otimes{\bf b}),
 \\