Reducing greenhouse gas emissions is a major challenge of our time. In the transportation sector, reducing the mass of structures is a key lever for achieving this goal. To this end, it is essential to develop lighter materials without compromising their mechanical properties—elasticity, plasticity, and fracture resistance. The rapid advancement of additive manufacturing techniques has opened new avenues for creating ultra-lightweight materials, particularly micro-lattice materials. These consist of interconnected beams or tubes whose geometric arrangement (architecture) leads to novel properties. These mechanical metamaterials, combining high porosity with stiffness several orders of magnitude greater than traditional materials of equivalent density, pave the way for previously unexplored property spaces. While early generations of these materials were periodic, recent work has demonstrated the advantages of random architectures for optimizing performance and ensuring mechanical isotropy.
This thesis contributes to this field by exploring numerical methods to enhance compressive yield strength and fracture resistance. The approach is primarily computational and is structured into two parts.
In the first part, we investigate the potential of 2D and 3D micro-lattices with fractal architectures. We demonstrate how these architectures can be designed to spatially modulate the size and shape of individual beams in a statistically isotropic and scale-invariant manner. We then analyze the impact on the elastic behavior and yield strength of the resulting mechanical metamaterials. Notably, we show that, in certain cases, a linear relationship between yield strength and relative density can be achieved, replacing the traditionally observed quadratic relationship.
The second part focuses on the properties of nacre-inspired metacomposites. The architecture of these micro-lattices features highly connected, rigid regions analogous to composite reinforcements and weakly connected, soft regions, akin to the matrix in composite materials. We first present the design process for such materials. We then explore how modulating the sizes and proportions of hard and soft regions enables on-demand elastic properties in these metacomposites. Finally, we examine the tensile fracture resistance enhancement induced by these architectures in mechanical metamaterials.