📢The Interdependence of Elastic Constants

The relationship between the elastic constants, derived from the general constitutive equations, establishes that Young's modulus and Poisson's ratio can be fully expressed by the Bulk modulus and the Shear modulus for an isotropic material. This derivation fundamentally relies on separating stress and strain into volumetric and deviatoric components. The key intermediate result is the relationship, which connects the stiffness to the resistance to shear and lateral contraction. The final expressions show how the material's resistance to volume change and resistance to shape change combine to define its overall elastic behavior.

Young's Modulus and Poisson's Ratio in Terms of Bulk and Shear Moduli | Proof and Derivationviadean on Notion