Auxeticity in Metals and Periodic Metallic Porous Structures Induced by Elastic Instabilities

Materials with a negative Poisson's ratio (auxetics) are counter intuitive because their mechanical response is unusual. On the other hand, instabilities are usually regarded as deleterious phenomena and thus their prevention is needed. Here, numerical and theoretical evidences have been provided to show that two different elastic instabilities are, rather than deleterious, useful phenomena that cause auxeticity. It has been shown that a negative Poisson's ratio can be found in some face-centered cubic (FCC) single crystals at a finite strain as they are under uniaxial stress along the [100]-direction. The auxeticity is associated with a phase transformation induced by the Born-Hill's elastic instability, i.e., an elastic material instability. In addition, it has been found that periodic metallic porous structures can also show a negative Poisson's ratio at finite compressive strain. In this case, buckling of the micro-structure of the porous structures, which is an elastic and geometric instability, is respondent for the auxeticity.