= Unilateral contact complementarity
{title2=$g\geq0,\quad r\geq0,\quad gr=0$}
For a nonadhesive obstacle, $g$ is the signed separation and $r$ its outward <normal contact force>. Nonpenetration gives $g\geq0$, absence of adhesion gives $r\geq0$, and reaction is possible only at contact, giving $gr=0$. In a small-slope taut-string model, $g=w-f$ and force balance gives $r=p-Tw''$ for downward applied load $p$. The three conditions then become $(w-f)(Tw''-p)=0$, $w\geq f$, $Tw''-p\leq0$. Multiplication by admissible displacement differences and integration gives the associated <variational inequality>, connecting a local contact law to constrained energy minimization.
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