Fracture toughness of two-dimensional networks

The relationship between mechanical properties, such as Poisson’s ratio, and the fracture toughness of disordered materials ranging from metallic glasses to polymers is not well understood. Recent studies on the fracture of disordered mechanical metamaterials indicate that the trend in fracture toughness as a function of Poisson’s ratio is not universal across different constituent materials. Rather, it is dictated by the local elastic constants of the networks, specifically by the magnitude of the angle bending resistance relative to bond stretching resistance (k_angle/k_bond). To demonstrate this concept, we designed 2D ordered networks that allow for systematic control of k_angle/k_bond through geometric considerations, and conducted tensile tests to show that the enhancement in stiffness and toughness are related to how the local elastic constants resist bond reorientation during global deformation. Additionally, we demonstrate how different constituent materials can couple with this geometric control of the load bearing elements to enhance the mechanical properties of the entire network. The insights gained from this study can provide new manufacturing routes to the design of mechanical metamaterials with controlled toughness.