  For various engineering and industrial applications it is desirable to
realize mechanical systems with broadly adjustable elasticity to respond
flexibly to the external environment. Here we discover a topology-correlated
transition between affine and non-affine regimes in elasticity in both two- and
three-dimensional packing-derived networks. Based on this transition, we
numerically design and experimentally realize multifunctional systems with
adjustable elasticity. Within one system, we achieve solid-like affine
response, liquid-like non-affine response and a continuous tunability in
between. Moreover, the system also exhibits a broadly tunable Poisson's ratio
from positive to negative values, which is of practical interest for energy
absorption and for fracture-resistant materials. Our study reveals a
fundamental connection between elasticity and network topology, and
demonstrates its practical potential for designing mechanical systems and
metamaterials.
