The effect of pore shape on the Poisson ratio of porous materials

Abstract

A brief review is given of the effect of porosity on the Poisson ratio of a porous material. In contrast to elastic moduli such as K, G, or E, which always decrease with the addition of pores into a matrix, the Poisson ratio (Formula presented.) may increase, decrease, or remain the same, depending on the shape of the pores, and on the Poisson ratio of the matrix phase, (Formula presented.). In general, for a given pore shape, there is a unique critical Poisson ratio, (Formula presented.), such that the addition of pores into the matrix will cause the Poisson ratio to increase if (Formula presented.), decrease if (Formula presented.), and remain unchanged if (Formula presented.). The critical Poisson ratio for spherical pores is 0.2, for prolate spheroidal pores is close to 0.2, and tends toward zero for thin cracks. For two-dimensional materials, (Formula presented.) for circular pores, 0.306 for squares, 0.227 for equilateral triangles, and again approaches 0 for thin cracks. The presence of a “trapped” fluid in the pore space tends to cause (Formula presented.) to increase, and for the range of parameters that may occur in rocks or concrete, this increase is more pronounced for thin crack-like pores than for equi-dimensional pores. Measurements of the Poisson ratio therefore may allow insight into pore geometry and pore fluid. If the matrix phase is strongly auxetic, small amounts of porosity will generally not cause the Poisson ratio to become positive.