  We study the elastic response of concentrated suspensions of rigid wire frame
particles to a step strain. These particles are constructed from infinitely
thin, rigid rods of length $L$. We specifically compare straight rod-like
particles to bent and branched wire frames. In dense suspensions the wire
frames are frozen in a disordered state by the topological entanglements
between their arms. We present a simple, geometric method to find the scaling
of the elastic stress with concentration in these glassy systems. We apply this
method to a simple 2D model system where a test particle is placed on a plane
and constrained by a random distribution of points with number density $\nu$.
Two striking differences between wire frame and rod suspensions are found: 1)
The linear elasticity per particle for wire frames is very large, scaling like
$\nu^2 L^4$, whereas for rods it much smaller and independent of concentration.
2) Rods always shear thin but wire frames shear harden for densities less than
$\sim \sqrt{K/k_B T L^4}$, where $K$ is the bending modulus of the particles.
The deformation of wire frames is found to be important even for small strains,
with the proportion of deformed particles at a particular strain, $\gamma$,
being given by $(\nu L^2)^2 \gamma^2$. Our results agree well with a simple
simulation of the 2D system.
