Design considerations for negative Poisson ratio structures under large deflection for MEMS applications

Negative Poisson ratio (NPR) materials based on a re-entrant honeycomb structure expand in the direction perpendicular to an externally exerted tension. This feature makes NPR structures attractive for use in microsensors and actuators as versatile motion transformers. When implemented in microdevices, where slender and flexible micromachined elements are widely used, the NPR material can tolerate large deflections. In the present work, motivated by the development of an optical sensor based on a photonic crystal device attached to a NPR based structure, we analyze the behavior of re-entrant honeycomb structures under large deflections. The model of the structure is built using extensible elastica theory for the description of geometrically nonlinear beams with an extensible axis. Results provided by the analytical model are compared with numerical results obtained by the finite element method. It is shown that the Poisson ratio (ν), which is defined entirely by the initial geometry of the structure undergoing small deflections, becomes strain dependent at large deflections. The extensibility of the beam's axis has a strong influence on the ν of the structure at large deflections and leads to the appearance of a minimum on the strain-ν curve. An example of design is demonstrated which yields a desired strain-independent ν of the NPR structure under large deflections.