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# Elastic Deformations of a Solid Body

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• Relation between tensile (compressive) strain $\epsilon$ and stress $\sigma$: $$\epsilon = \frac{\sigma}{E},$$ where $E$ is Young's modulus.
• Relation between lateral compressive (tensile) strain $\epsilon^\prime$ and longitudinal tensile (compressive) strain $\epsilon$: $$\epsilon^\prime = - \mu \epsilon,$$ where $\mu$ is Poisson's ratio.
• Relation between shear strain $\gamma$ and tangential stress $\tau$: $$\gamma = \frac{\tau}{G},$$ where $G$ is shear modulus.
• Compressibility: $$\beta = - \frac{1}{V}\frac{dV}{dp}.$$
• Volume density of elastic strain energy: $$u = \frac{E\epsilon^2}{2}, \; u = \frac{G \gamma^2}{2}.$$

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