This paper presents a theoretical model that establishes a robust correlation between hardness and elasticity for a wide range of materials, including bulk metallic glasses (BMGs). The model is inspired by Pugh's modulus ratio, which relates the shear modulus (G) and bulk modulus (B) of materials. The study shows that the intrinsic correlation between hardness and elasticity can accurately predict Vicker's hardness for various crystalline materials and BMGs. The model provides a theoretical basis for Teter's empirical correlation between hardness and shear modulus, which has been widely used in materials science. The model is derived from the relationship between the shear modulus and the indentation geometry of a diamond pyramid indenter. It is shown that the hardness of materials can be expressed as a function of the shear modulus and the Pugh modulus ratio (k = G/B). The final formula derived is Hν = 2(k²G)^0.585 - 3, which demonstrates that hardness is not only correlated with the shear modulus but also with the bulk modulus. This formula is validated against experimental data for a wide range of materials, including BMGs, and shows excellent agreement with experimental results. The study also highlights the importance of the Pugh modulus ratio in understanding the mechanical behavior of materials. It is found that materials with a higher Pugh modulus ratio are more brittle, while those with a lower ratio are more ductile. This relationship is consistent with previous studies and provides a fundamental understanding of the mechanical properties of materials. The model is applied to a variety of materials, including superhard materials such as diamond, c-BN, and BC₂N, and shows that the formula accurately predicts their hardness. The study also addresses the limitations of previous semi-empirical models and emphasizes the importance of the Pugh modulus ratio in predicting the hardness of materials. The results demonstrate that the proposed model is a significant advancement in the understanding and prediction of hardness in materials science.This paper presents a theoretical model that establishes a robust correlation between hardness and elasticity for a wide range of materials, including bulk metallic glasses (BMGs). The model is inspired by Pugh's modulus ratio, which relates the shear modulus (G) and bulk modulus (B) of materials. The study shows that the intrinsic correlation between hardness and elasticity can accurately predict Vicker's hardness for various crystalline materials and BMGs. The model provides a theoretical basis for Teter's empirical correlation between hardness and shear modulus, which has been widely used in materials science. The model is derived from the relationship between the shear modulus and the indentation geometry of a diamond pyramid indenter. It is shown that the hardness of materials can be expressed as a function of the shear modulus and the Pugh modulus ratio (k = G/B). The final formula derived is Hν = 2(k²G)^0.585 - 3, which demonstrates that hardness is not only correlated with the shear modulus but also with the bulk modulus. This formula is validated against experimental data for a wide range of materials, including BMGs, and shows excellent agreement with experimental results. The study also highlights the importance of the Pugh modulus ratio in understanding the mechanical behavior of materials. It is found that materials with a higher Pugh modulus ratio are more brittle, while those with a lower ratio are more ductile. This relationship is consistent with previous studies and provides a fundamental understanding of the mechanical properties of materials. The model is applied to a variety of materials, including superhard materials such as diamond, c-BN, and BC₂N, and shows that the formula accurately predicts their hardness. The study also addresses the limitations of previous semi-empirical models and emphasizes the importance of the Pugh modulus ratio in predicting the hardness of materials. The results demonstrate that the proposed model is a significant advancement in the understanding and prediction of hardness in materials science.