AN APPROXIMATE CALCULATION ON THE ELASTIC-CONSTANTS OF A SOLID CONTAINING VARYING VOLUME FRACTIONS OF CAVITIES

An approximate calculation for the elastic constants of a solid contai ning varying volume fractions of cavities is presented. The calculatio n is based on the mechanisms of deformation of solids containing varyi ng volume fractions of cavities namely straining, bending and stretchi ng. The work concentrates first on the deformation of solids containin g a small number of cavities and then secondly on the deformation of t he solid containing a large fraction of cavities. The analysis represe nts the unification of two modes of deformation of solids containing c avities in the dilute case with that of the concentrated case. It is f ound that [GRAPHICS] phi is the volume fraction, K is the bulk modulus of the material, K-f is the effective bulk modulus of the material wi th cavities, G is the shear modulus of the material, G(f) is the effec tive modulus of the material with cavities, e is the elastic modulus o f the material, nu is the Poisson ratio of the material, nu(f) Poisson ratio of the cellular material and phi(e) is the fraction of solid in the struts.