Effective elastic and transport properties of regular honeycombs for all densities

The effective planar elastic moduli and planar conductivity (or dielectric constant) of regular hexagonal and triangular honeycombs were investigated for the entire range of volume fractions. Only the extreme limits of the vo lume fraction have been studied in the past. We studied the effective prope rties both numerically, via finite elements, and analytically, via rigorous three-point bounds, three-point approximations, and cross-property bounds. We show here that the three-point bounds and approximations are generally in excellent agreement with the simulation data and are superior to the two -point Hashin-Shtrikman bounds. Therefore, the three-point estimates provid e accurate analytical predictions of the effective properties for all densi ties. Both the effective bulk modulus and effective conductivity are nearly extremal in the case of hexagonal honeycombs for the entire volume-fractio n range, in contrast to the effective shear modulus. In the case of triangu lar honeycombs, all of the property values are relatively close to being op timal. Thus, the triangular honeycomb has desirable multifunctional perform ance for all densities in so far as the elastic moduli, conductivity, and d ielectric constant are concerned.