2. Notes
  3. JEE Main & Advanced
  4. Physics
  5. Elasticity
  6. Relation between \[\mathbf{Y,}\,\mathbf{k,}\,\mathbf{\eta ,}\,\] and \[\mathbf{\sigma }\]

JEE Main & Advanced Physics Elasticity Relation between \[\mathbf{Y,}\,\mathbf{k,}\,\mathbf{\eta ,}\,\] and \[\mathbf{\sigma }\]

Relation between \[\mathbf{Y,}\,\mathbf{k,}\,\mathbf{\eta ,}\,\] and \[\mathbf{\sigma }\]

Category : JEE Main & Advanced

Moduli of elasticity are three, viz. Y, K and \[\eta \] while elastic constants are four, viz, Y, K, \[\eta \] and \[\sigma \]. Poisson's ratio s is not modulus of elasticity as it is the ratio of two strains and not of stress to strain. Elastic constants are found to depend on each other through the relations :

\[Y=3K(1-2\sigma )\]                                                      ...(i)

\[Y=2\eta (1+\sigma )\]                                                    ...(ii)

Eliminating s or Y between these, we get

\[Y=\frac{9K\eta }{3K+\eta }\]                                        ...(iii)

\[\sigma =\frac{3K-2\eta }{6K+2\eta }\]                            ...(iv)  

keyboard_arrow_leftRelation Between Volumetric Strain, Lateral Strain and Poisson's Ratio
Torsion of Cylinder keyboard_arrow_right

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