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.

对于各种工程和工业应用，希望实现具有广泛可调弹性的机械系统，以灵活地响应外部环境。在这里，我们发现了二维和三维包装衍生网络中的仿射和非仿射弹性机制之间的拓扑相关转换。基于这种转变，我们通过数值设计和实验实现了具有可调弹性的多功能系统。在一个系统中，我们实现了类似固体的仿射响应、类似液体的非仿射响应以及两者之间的连续可调性。此外，该系统还表现出从正值到负值的广泛可调泊松比，这对于能量吸收和抗断裂材料具有实际意义。