Abstract
In this study, a plane-packed tessellated structure for modelling the natural structure of living organisms is discussed to find an alternative material that is tougher than currently used materials such as ceramic matrix composites. Hence, we generalize a method for generating a plane-packed tessellated structure of a regular polygon comprising n-tips and then develop a numerical procedure for analyzing the stress field in the tessellated structure based on the continuous distributed dislocation (CDD) method. The effects of n-tips and the loading direction, which is defined as the azimuthal angle measured from the side of the polygon, on the fracture toughness values are examined based on the fractal dimension D. It is revealed that the crack propagation path deflects significantly as the loading angle approaches the value of (2−n)π/2n. In this study, the deflected crack shape is characterized by D. It is discovered that D changed with the loading angle, and that the fracture toughness values changed with the loading angle, similar to the trend of D changing with the loading angle. The relation between the polygon shape and loading angle shows that the fracture toughness increases with D, which characterizes the complexity of the crack path, and increases with the number of vertices in the polygon. Therefore, it can be concluded that controlling D and plane geometry can effectively improve the fracture toughness of materials.
