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 $\nu$ may increase, decrease, or remain the same, depending on the shape of the pores, and on the Poisson ratio of the matrix phase, ${\nu }_o$. In general, for a given pore shape, there is a unique critical Poisson ratio, ${\nu }_c$, such that the addition of pores into the matrix will cause the Poisson ratio to increase if ${\nu }_o<{\nu }_c$, decrease if ${\nu }_o>{\nu }_c$, and remain unchanged if ${\nu }_o={\nu }_c$. 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, ${\nu }_c=1/3$ 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 ${\nu }_c$ 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.

简要回顾了孔隙率对多孔材料泊松比的影响。与K、G或E等弹性模量相反，弹性模量总是随着向基质中添加孔而减小，泊松比$\nu$ 可能会增加、减少或保持不变，这取决于孔的形状和基质相的泊松比， ${\nu }_{○}$. 一般来说，对于给定的孔隙形状，有一个独特的临界泊松比，${\nu }_C$，这样在基体中加入孔隙将导致泊松比增加，如果 ${\nu }_{○}<{\nu }_C$, 减少如果 ${\nu }_{○}>{\nu }_C$，并且保持不变，如果 ${\nu }_{○}={\nu }_C$. 球状孔的临界泊松比为 0.2，长球状孔的临界泊松比接近 0.2，薄裂纹趋于零。对于二维材料，${\nu }_C=1/3$对于圆形孔，正方形为 0.306，等边三角形为 0.227，对于细裂纹再次接近 0。孔隙空间中存在“被困”的流体往往会导致${\nu }_C$增加，对于岩石或混凝土中可能出现的参数范围，这种增加对于细裂缝状孔隙比等维孔隙更为明显。因此，泊松比的测量可以让我们深入了解孔隙几何形状和孔隙流体。如果基体相具有很强的拉胀性，少量的孔隙通常不会导致泊松比变为正值。