A Computational Model of Bio-Inspired Soft Network Materials for Analyzing Their Anisotropic Mechanical Properties

Soft network materials constructed with horseshoe microstructures represent a class of bio-inspired synthetic materials that can be tailored precisely to match the nonlinear, J-shaped, stress–strain curves of human skins. Under a large level of stretching, the nonlinear deformations associated with the drastic changes of microstructure geometries can lead to an evident mechanical anisotropy, even for honeycomb and triangular lattices with a sixfold rotational symmetry. Such anisotropic mechanical responses are essential for certain targeted applications of these synthetic materials. By introducing appropriate periodic boundary conditions that apply to large deformations, this work presents an efficient computational model of soft network materials based on the analyses of representative unit cells. This model is validated through comparison of predicted deformed configurations with full-scale finite element analyses (FEA) for different loading angles and loading strains. Based on this model, the anisotropic mechanical responses, including the nonlinear stress–strain curves and Poisson's ratios, are systematically analyzed for three representative lattice topologies (square, triangular and honeycomb). An analytic solution of the geometry-based critical strain was found to show a good correspondence to the critical transition point of the calculated J-shaped stress–strain curve for different network geometries and loading angles. Furthermore, the nonlinear Poisson's ratio, which can be either negative or positive, was shown to depend highly on both the loading angle and the loading strain.