  Our goal is to develop a design framework for multifunctional mechanical
metamaterials that can tune their rigidity while optimizing other desired
properties. Towards this goal, we first demonstrate that underconstrained
central force networks possess a critical rigidity manifold of codimension one
in the space of their physical constraints. We describe how the geometry of
this manifold generates a natural parameterization in terms of the states of
self-stress, and then use this parameterization to numerically generate
disordered network structures that are on the critical rigidity manifold and
also optimize various objective functions, such as maximizing the bulk
stiffness under dilation, or minimizing length variance to find networks that
can be self-assembled from equal-length parts. This framework can be used to
design mechanical metamaterials that can tune their rigidity and also exhibit
other desired properties.
