Ca. Andersson, DERIVATION OF THE EXPONENTIAL RELATION FOR THE EFFECT OF ELLIPSOIDAL POROSITY ON ELASTIC-MODULUS, Journal of the American Ceramic Society, 79(8), 1996, pp. 2181-2184
An analytical basis for the exponential relationship between elastic m
odulus and fraction porosity is derived, The exponential constant in t
he equation is shown to be a function of the pore shape and the orient
ation of the pores with respect to the stress axis and to be independe
nt of pore size, A similar exponential relationship between the modulu
s and the number of cracks per unit volume is crack-size dependent.