REALIZABILITY OF NEGATIVE PORE COMPRESSIBILITY IN POROELASTIC COMPOSITES

For elastic materials containing fluid-saturated porosity, the pore co mpressibility is a measure of the deformation of a unit pore volume in response to a change in fluid pressure. Rather than being measured, t his quantity has been routinely set equal to an effective solid compre ssibility, since this equality is exact whenever a single solid compon ent is present. However, we show that the pore compressibility and sol id compressibility may be uncorrelated in general. In certain special circumstances they do not even share the same sign. Although thermodyn amic and mechanical stability constraints cause solid and drained-fram e bulk moduli of a porous composite to be positive and bounded by comp onent properties, the pore compressibility is unconstrained and, there fore, can have negative values. For special realizable model materials , the value of the pore compressibility can be found using an exact ex pression valid for a composite made up of one fluid and two solid comp onents, i.e., two porous components. In order to quantify how various factors affect the sign and magnitude of the pore compressibility, por e compressibilities were calculated for models that used two porous co mponents having the microgeometry of an assemblage of concentric spher es. This model implicitly assumes the pores are on a much smaller leng th scale than the concentric spheres. Modeling results show that with the stiffer porous material forming the outer shells of the concentric spheres, the pore compressibility of such materials is negative when solid component bulk moduli differ by at least a factor of 5, if in ad dition, the porosities and drained frame moduli of the two porous comp onents are relatively low. Negative pore compressibilities were found for realizable models whose two porous constituents had the properties of silicon nitride and either sandstone or clay. For models using com binations of alumina and glass foam properties, pore compressibilities were non-negative but smaller than the compressibilities of the solid components.