Intrinsic Correlation between Hardness and Elasticity in Polycrystalline   Materials and Bulk Metallic Glasses
  Though extensively studied, hardness, defined as the resistance of a material to deformation, still remains a challenging issue for a formal theoretical description due to its inherent mechanical complexity. The widely applied Teter's empirical correlation between hardness and shear modulus has been considered to be not always valid for a large variety of materials. Here, inspired by the classical work on Pugh's modulus ratio, we develop a theoretical model which establishes a robust correlation between hardness and elasticity for a wide class of materials, including bulk metallic glasses, with results in very good agreement with experiment. The simplified form of our model also provides an unambiguous theoretical evidence for Teter's empirical correlation. 
Xing-Qiu Chen, Haiyang Niu, Dianzhong Li, Yiyi Li
cond-mat.mtrl-sci