The physics
Press on a body from all sides and its volume shrinks. The bulk modulus K is the extra pressure over the fraction the volume shrinks.
K = ΔP / (ΔV/V) ΔP = ρ g h under water
Take a small squeeze of a cube. Each edge shrinks by a third of the volume's fraction.
ΔL / L = (ΔV/V) / 3
Glue a block at its base and push along its top face. It leans. The shear modulus η is the push per area over the lean angle.
η = (F/A) / (x/h) x = F h / (η A)
Stretch a rod and it gets thinner. Poisson's ratio σ is the sideways strain over the length strain.
Δd / d = σ × (ΔL / L)
A gas has a bulk modulus too. A slow squeeze at a fixed temperature gives K = P. A fast squeeze gives K = γP.