Better than linear strength scaling of multifunctional ceramic truss lattice materials

Driven by the goal of creating exceptionally strong and lightweight thermal insulators to enable the operation of a vacuum airship on Venus, conditions where ceramic truss lattice materials provide better than linear scaling of strength with respect to variations in relative density have been found. This enhanced scaling relationship is a consequence of the pressure sensitive shear strength of ceramic materials. A new Gibson-Ashby type scaling relationship is developed between strength and relative density. Elementary analysis is used to formulate theoretical limits for the compressive strength, minimum density, and minimum thermal conductivity for truss lattice materials subjected to hydrostatic pressure loads. Shape optimization using the covariance matrix adopted evolutionary strategy (CMA-ES) and highly resolved finite element models is conducted on silicon carbide Kelvin cells with variable cross-section axisymmetric struts considering three failure modes: buckling, tensile rupture, and shear failure. The optimized designs closely adhere to and validate the newly developed analytical scaling relationship with better than linear strength scaling. These optimized designs are found to withstand the extreme loading conditions on Venus while providing up to 43 $\frac{\mathrm{kg}}{m^3}$ of buoyancy. The thermal conductivity of the optimized designs are computed and found to be less than 0.5 $\frac{W}{mK}$, with one design outperforming silica aerogels at elevated temperature.