A novel cellular substrate for flexible electronics with negative Poisson ratios under large stretching

Recently, open cellular substrates instead of traditional solid substrates have been used in flexible electronics, catering to the need for high permeability of bio-fluids through the device. The Poisson ratio of the existing open cellular designs, however, remains positive, which is inappropriate for the cellular substrates mounting on some biological auxetic materials, as the resulting mismatch in deformation may cause irritation. In the current work, a type of triangular lattice networks is presented with satisfactory negative Poisson ratio effect over large strains. A finite deformation model is developed for the deformed angles, constitutive relation and maximum strain of the building block, with nonlinear finite element method (FEM) validations. Results demonstrate desired negative Poisson ratios and mechanical properties can be achieved in an isotropic manner by tailoring three geometric parameters (arc angle θ₀, length/radius ratio L/R and width/radius ratio w/R). Thereinto, longer arm lengths not only yield lower equivalent modulus and maximum strain, but also enable wider range of isotropic negative Poisson ratios (from -0.35 to 0) and applied strains (from 0% to 80%), providing more flexibility in network designs and new possibilities to emerging biomedical applications.