Uniaxial strain modulus ($M=E(1-\nu )/[(1+\nu )(1-2\nu )]$)

The uniaxial strain modulus relates longitudinal normal stress to longitudinal strain when both transverse normal strains vanish. For isotropic linear elasticity, solving the transverse compliance equations gives the transverse stresses $\nu {\tau }_1/(1-\nu )$ and hence the displayed modulus in terms of Young's modulus and Poisson's ratio. It differs from Young's modulus, which applies when the transverse stresses vanish. Their difference is crucial for thin elastic layers bonded to rigid faces.