Elastic and fracture property analyses of two-dimensional composite structure with lattice spring model

Abstract

Lattice spring models (LSMs) have been employed to simulate the mechanical behaviors of materials at a small computational cost such as the crack paths of heterogeneous materials and toughening mechanisms of nature-inspired composites. However, previous studies have mainly focused on the infinitesimal deformation range and the applicability of LSMs for the large deformation has not been thoroughly investigated. In the present study, we compare the mechanical properties of two-dimensional triangular and square LSMs (tLSM and sLSM) by systematically studying the nonlinearity and anisotropy of elastic response at finite strain range including the fracture behavior. We show that the mechanical responses of perfect lattices for both LSMs can be exactly predicted analytically. We also investigate the accuracy of the fracture behaviors of pre-cracked specimen under 3-point bending, tensile, and s fracture by varying the orientation of crack with respect to the lattice. Our results on both perfect and pre-cracked lattices indicate that the sLSM has significantly isotropic mechanical properties and is better suited to model isotropic materials. Following this study, a composite structure modeling was performed using a sLSM that can better simulate the mechanical behavior of isotropic materials. In many existing structural composite studies, a lot of analysis has been conducted on the composites which have stiffening/toughening mechanism and defect tolerance to only specific direction. In this study, to solve these problems, the four kinds of composites were constructed. We tried to construct a composite structure with toughening/stiffening mechanism and defects-tolerance in various directions. In this study, to reduce the anisotropy of previous structural composites, a rectangular / hexagonal structure which have aspect ratio of 1 and a penrose tiling which have symmetrical structure were constructed and analyzed. In order to analyze the mechanical behavior of each structure in various directions, the rotated samples are constructed and tension was applied, and the stress distribution, toughness, stiffness fracture strength and strain of each model were compared and analyzed. As a result, a composite material having defect resistance for various crack directions could be presented. As a result, we could present a composite with defect tolerance for the various direction of pre-crack.