**Uniaxial loading**

- Tensile/compressive stress in the
*x*-direction produces tensile/compressive strain in the*x*-direction, with the stress and strain related through Young's modulus*E*: - Strain in the
*x*-direction produces strains the*y*- and*z*-directions. The strains in the*y*- and*z*-directions are proportional to the strain in the x-direction through the negative of the Poisson's ratio.

**Positive Poisson's ratio**

If the Poisson's ratio of the material if positive, then tensile/compressive strains in the x-direction produce compressive/tensile strains in the y- and z-directions, as shown below.

**Negative Poisson's ratio**

If the Poisson's ratio of the material if positive, then tensile/compressive strains in the x-direction produce tensile/compressive strains in the y- and z-directions, just the opposite of that for a positive Poisson's ratio.

* QUESTION*: Can a material possess a negative Poisson’s ratio? The answer is “yes”. Such materials are known as “

**”. From above, we see than an auxetic material will expand in the transverse directions for a tensile axial load. Consider the animation below of such a material, and study how a negative value for Poisson's ratio is possible with this material. As can be seen here, a compressive axial load produces contraction in the transverse direction, and a tensile axial load produces expansion in the transverse direction.**

*auxetic materials*There are a number of types of polyurethane foam materials with cell structures resembling the structure shown above. Kevlar woven composite materials used for body armor are also auxetic materials.