🎬Visualize how the Poisson's ratio approaches the incompressibility limit as the stiffness ratio incr

The visualization confirms the complete interdependency of the elastic constants ( $E, \nu, K, G$ ) by showing the simultaneous limiting behavior as the stiffness ratio ( $K / G$ ) increases. For near-incompressible materials ( $K \gg G$ ), two critical limits are reached: first, the Poisson's ratio ( $\nu$ ) approaches 0.5 , signifying a maximum resistance to volume change (high K ); and second, the Young's Modulus ( E ) approaches 3 G, establishing a fixed relationship between axial and shear stiffness that is independent of the increasingly dominant bulk modulus K. This combined behavior, characteristic of materials like rubber, means the material easily changes shape ( G ) but strongly resists changes in volume ( K ), with its overall stiffness ( E ) being dictated solely by its shear rigidity ( G ) in this limit.

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