Sequential metamaterials with alternating Poisson's ratios

Mechanical metamaterials have been designed to achieve custom Poisson's ratios via the deformation of their microarchitecture. These designs, however, have yet to achieve the capability of exhibiting Poisson's ratios that alternate by design both temporally and spatially according to deformation. This capability would enable dynamic shape-morphing applications including smart materials that process mechanical information according to multiple time-ordered output signals without requiring active control or power. Herein, both periodic and graded metamaterials are introduced that leverage principles of differential stiffness and self-contact to passively achieve sequential deformations, which manifest as user-specified alternating Poisson's ratios. An analytical approach is provided with a complementary software tool that enables the design of such materials in two- and three-dimensions. This advance in design capability is due to the fact that the tool computes sequential deformations more than an order of magnitude faster than contemporary finite-element packages. Experiments on macro- and micro-scale designs validate their predicted alternating Poisson's ratios.