We investigate the interplay between pre-stress and mechanical properties in
random elastic networks. To do this in a controlled fashion, we introduce an
algorithm for creating random freestanding frames that support exactly one
state of self stress. By multiplying all the bond tensions in this state of
self stress by the same number---which with the appropriate normalization
corresponds to the physical pre-stress inside the frame---we systematically
evaluate the linear mechanical response of the frame as a function of
pre-stress. After proving that the mechanical moduli of affinely deforming
frames are rigourously independent of pre-stress, we turn to non-affinely
deforming frames. In such frames, pre-stress has a profound effect on linear
response: not only can it change the values of the linear modulus---an effect
we demonstrate to be related to a suppressive effect of pre-stress on
non-affinity---but pre-stresses also generically trigger bistable mechanical
response. Thus, pre-stress can be leveraged to both augment the mechanical
response of network architectures on the fly, and to actuate finite
deformations. These control modalities may be of use in the design of both
novel responsive materials and soft actuators.Comment: 13 pages, 9 figure