What will be the shear modulus of the material with elastic modulus of 240 GPa and Poisson's ratio is 0.2?

Concept:

The relationship between elastic modulus, bulk modulus and Poisson's ratio is given by

\(E=3K(1-2μ)\)

The relationship between elastic modulus, modulus of rigidity and Poisson's ratio is given by

\(E=2G(1+μ)\)

The relationship between elastic modulus, modulus of rigidity and bulk modulus is given by

\(E={9KG\over{G+3K}}\)

Hence, combining all these equations and solving it together we can get,

\(\begin{array}{l} μ = \frac{{3K - 2G}}{{6K + 2G}} \end{array}\)

Calculation:

Given data;

E= 240 GPa

μ = 0.2

The relationship between elastic modulus, modulus of rigidity and Poisson's ratio is given by

\(E=2G(1+μ)\)

\(G={E\over2(1+μ)}\)

\(G={240\over2(1+0.2)}\)

G= 100 GPa