## Compressibility Modulus

What material modulus property is used to characterize compressibility?

Hint
$$K=\frac{E}{3(1-2\upsilon)}$$$where $$E$$ is the modulus of elasticity (Young’s modulus), and $$\upsilon$$ is Poisson’s ratio. Hint 2 Poisson’s ratio is: $$\upsilon=-\frac{\varepsilon_{lateral}}{\varepsilon_{longitudinal}}$$$
where $$\varepsilon_{lateral}$$ is the lateral strain, and $$\varepsilon_{longitudinal}$$ is the longitudinal strain.
The Bulk (Volume) Modulus of Elasticity is a material property that characterizes a substance’s resistance to compression when subjected to pressure. The SI unit for the bulk modulus of elasticity is $$N/m^2$$ (Pa), while the imperial unit is $$lb_f/in^2$$ (psi). It is the ratio between increased pressure and decreased volume of a material, and it can be expressed in terms of Young’s modulus and Poisson’s ratio:
$$K=\frac{E}{3(1-2\upsilon)}$$$where $$K$$ is the bulk (volume) modulus of elasticity, $$E$$ is the modulus of elasticity (Young’s modulus), and $$\upsilon$$ is Poisson’s ratio. Poisson’s ratio measures a material’s deformation in directions perpendicular to the loading/pressure direction: $$\upsilon=-\frac{\varepsilon_{lateral}}{\varepsilon_{longitudinal}}$$$
where $$\varepsilon_{lateral}$$ is the lateral strain, and $$\varepsilon_{longitudinal}$$ is the longitudinal strain.
Young’s modulus describes the relationship between stress and strain during elastic loading. Applying Hooke’s Law:
$$E=\frac{\sigma}{\varepsilon}$$\$
where $$\sigma$$ is the stress and $$\varepsilon$$ is the strain.
Bulk (Volume) Modulus of Elasticity