Login |  Password

Elastic Deformations of a Solid Body

  • 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:
    $$u = \frac{E\epsilon^2}{2}, \; u = \frac{G \gamma^2}{2}.$$

 

Keywords: 
elastic, deformation, tensile, shear, compressibility, strain, sress, Young's modulus, Poisson's ratio, shear modulus
‹ Dynamics of a Solid BodyupHydrodynamics ›