P-wave modulus

In linear elasticity, the P-wave modulus ${\displaystyle M}$, also known as the longitudinal modulus or the constrained modulus, is one of the elastic moduli available to describe isotropic homogeneous materials.

It is defined as the ratio of axial stress to axial strain in a uniaxial strain state

where all the other strains ${\displaystyle \epsilon _{**}}$ are zero.

This is equivalent to stating that

where V_P is the velocity of a P-wave.

${\displaystyle S=\pm {\sqrt {E^{2}+9M^{2}-10EM}}}$

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