Improving the buckling performance of topology designed periodic microstructures

A formulation of linearized buckling for cellular microstructured solids is developed. The goal is to include instability modes in the design of a microstructure. An asymptotic method provides us with the equations for stability analysis at macroscopic and microscopic level and its range of applicability is analyzed. This is then used to address the problem of the buckling performance of cellular microstructures, leading to a buckling performance index concept that provides the basis for a comparative analysis between different distributions of material in the microstructure, as well as the influence of length scale of the buckling mode (single cell or multiple cell modes). This concept is then used to improve the buckling performance of microstructures designed for, e.g., maximal bulk modulus.