= Homogeneous stress-intensity field of a semi-infinite antiplane crack
{title2=$F'_h(z)=iC/\sqrt z$}
For real $C$, this analytic homogeneous field has real boundary values on both faces of the negative-axis crack, so it adds no face shear <traction>. Ahead of the tip it adds <stress> $-\mu C/\sqrt x$. Its <stress> tends to zero at infinity, but its primitive grows like $\sqrt z$, producing unbounded remote <displacement> and infinite total <elastic energy>. Thus merely requiring vanishing far <stress> does not uniquely fix the face-loaded crack solution. Excluding an added remote stress-intensity field, for example through the localized-load bounded-displacement far condition, removes this homogeneous ambiguity. Ordinary inverse-square-root tip <stress> remains allowed and has finite energy in any bounded neighbourhood of the tip.
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