Optimizing properties on the critical rigidity manifold of underconstrained central-force networks

This dataset can be used to generate the figures from the article of the
same name published in Physical Review E. These include images of examples
of optimized network configurations, distributions and size scaling of
several metrics describing network structure and elastic response,
optimization time series data, and movies of the optimization process for
several objective functions. 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.