Stiffness and strength of architected materials

In this thesis, methods for determining the effective stiffness, yield, and buckling strength of architected materials are presented. First, the theory of homogenization and the superposition principle is presented, which is used to determine effective stiffness properties. Then, the methods to determine the microstructural yield and buckling strength are presented. Floquet-Bloch wave theory is utilized, which enables capturing of local and global instabilities.

The methods are employed to determine the effective material properties for representatives of near-optimal microstructures from the literature. Furthermore,the effects of microstructural hierarchy are also investigated. The usual conclusion from the literature on optimality, that closed-walled plate lattice structures (PLSs) have higher stiffness and yield strength, while open walled truss lattice structures (TLSs) have higher buckling strength is shown to be more complex than that. Finding the optimal microstructure requires consideration of the macroscopic geometry and load case.

To verify the theoretically calculated stiffness and buckling strength, the microstructures are manufactured and experimentally tested. The microstructures are 3D printed in a soft elastomer, which enables the critical buckling mode to be observable during compression. It is illustrated that PLSs maybe stiffness optimal, but they are difficult to manufacture in practice and may require altercations that reduce performance.

A simplified model for buckling strength estimation of stretch-dominated microstructures is developed. The method is a compromise between simple analytical calculations and more sophisticated methods such as Floquet-Bloch.
It is based on individual member analysis where the topology of the unit cell is accounted for. The method is employed to determine the buckling strength surfaces under rotated uni-axial loads. The method is simple yet quite accurate and offers immense computational savings. It is illustrated that PLSs can have vastly different shaped yield and buckling strength surfaces, whereas TLSs have similar surfaces. Furthermore, based on the knowledge gained from the simplified model, a novel isotropic PLS configuration is proposed with an improved isotropic buckling strength surface without deterioration to the stiffness or yield strength.