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 volume fraction have been studied in the past. We studied the effective properties 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 provide accurate analytical predictions of the effective properties for all densities. Both the effective bulk modulus and effective conductivity are nearly extremal in the case of hexagonal honeycombs for the entire volume-fraction range, in contrast to the effective shear modulus. In the case of triangular honeycombs, all of the property values are relatively close to being optimal. Thus, the triangular honeycomb has desirable multifunctional performance for all densities in so far as the elastic moduli, conductivity, and dielectric constant are concerned.

[1]  O. Sigmund.  A new class of extremal composites , 2000 .

[2]  K. Lurie,et al.  Optimization of properties of multicomponent isotropic composites , 1985 .

[3]  S. Shtrikman,et al.  A variational approach to the theory of the elastic behaviour of multiphase materials , 1963 .

[4]  Salvatore Torquato,et al.  Effective mechanical and transport properties of cellular solids , 1998 .

[5]  Salvatore Torquato,et al.  Effective stiffness tensor of composite media : II. Applications to isotropic dispersions , 1998 .

[6]  Torquato,et al.  Link between the conductivity and elastic moduli of composite materials. , 1993, Physical review letters.

[7]  Graeme W. Milton,et al.  Bounds on the elastic and transport properties of two-component composites , 1982 .

[8]  M. Thorpe.  The conductivity of a sheet containing a few polygonal holes and/or superconducting inclusions , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[9]  Zvi Hashin,et al.  On elastic behaviour of fibre reinforced materials of arbitrary transverse phase geometry , 1965 .

[10]  M. Thorpe,et al.  Elastic Moduli of Two Dimensional Materials With Polygonal and Elliptical Holes , 1994 .

[11]  S. Torquato,et al.  GEOMETRICAL-PARAMETER BOUNDS ON THE EFFECTIVE MODULI OF COMPOSITES , 1995 .

[12]  Salvatore Torquato,et al.  Determining elastic behavior of composites by the boundary element method , 1993 .

[13]  Graeme W. Milton,et al.  Invariant properties of the stress in plane elasticity and equivalence classes of composites , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[14]  E. Garboczi,et al.  The elastic moduli of a sheet containing circular holes , 1992 .

[15]  Gilles A. Francfort,et al.  Homogenization and optimal bounds in linear elasticity , 1986 .