A Mechanics Model of Soft Network Materials With Periodic Lattices of Arbitrarily Shaped Filamentary Microstructures for Tunable Poisson's Ratios

Soft network materials that incorporate wavy filamentary microstructures have appealing applications in bio-integrated devices and tissue engineering, in part due to their bio-mimetic mechanical properties, such as “J-shaped” stress–strain curves and negative Poisson's ratios. The diversity of the microstructure geometry as well as the network topology provides access to a broad range of tunable mechanical properties, suggesting a high degree of design flexibility. The understanding of the underlying microstructure-property relationship requires the development of a general mechanics theory. Here, we introduce a theoretical model of infinitesimal deformations for the soft network materials constructed with periodic lattices of arbitrarily shaped microstructures. Taking three representative lattice topologies (triangular, honeycomb, and square) as examples, we obtain analytic solutions of Poisson's ratio and elastic modulus based on the mechanics model. These analytic solutions, as validated by systematic finite element analyses (FEA), elucidated different roles of lattice topology and microstructure geometry on Poisson's ratio of network materials with engineered zigzag microstructures. With the aid of the theoretical model, a crescent-shaped microstructure was devised to expand the accessible strain range of network materials with relative constant Poisson's ratio under large levels of stretching. This study provides theoretical guidelines for the soft network material designs to achieve desired Poisson's ratio and elastic modulus.