Derive the relation between young's modulus shear modulus and bulk modulus?

Answer 1

Type your from the hook's law,

stress is directly proportional to the strain under the elastic limits.

σ α ε

where,

σ - tensile stress.

ε - strain.

now σ =E ε

where, E is the proportionality constant or the young's modulus of the material.

the extension of the hook's law

where the shear stress is directly proportional to the shear strain.

ζ α γ

ζ - shear stress.

γ - shear strain.

ζ = Gγ

where G is the modulus of rigidity.

A pure shear stress at a point can be alternatively presented by the normal stresses at 450 with the directions of the shear stress.

σ1 = -σ2 = ζ.

using this principle you get

G = E/(2(1+ ν)) is the 1 equation.

where, ν is the poisson's ratio.this is the basic relation between E,G, ν.

the change in volume per unit volume referred to as the dilation.

e = εx + εy + εz

the shear strains are not taken into account because they do not contribute to any volume change.

for an isotropic linearly elastic materials for use with Cartesian coordinates

εx = σx/E - νσy/E - νσz/E

similar equations are formed for εy ,εz .

e = εx + εy + εz = ((1 - 2ν)/E)( σx+ σy+ σz)

if σx= σy = σz = -p like a hydrostatic pressure of uniform intensity

then

-p/e = k = E/3(1 - 2ν) is the 2 equation

where k is the bulk modulus.

Addin 1 & 2 by bringing only the poisson's ratio to left side and taking all other constants to the right side the equation formed is the

9/E = 3/G + 1/k is the relation between the three modulus.

here...

Answer 2

For isotropic materials the relation of Young's modulus, E, and rigidity, G, is

G = E divided by 2(1+u) where u = poisson ratio which is generally 0 to 0.5 depending on material.

G is also known as the shear modulus

Answer 3

Let young's modulus = E, Shear modulus = G, Bulk Modulus = K and poisson's ratio = v E = 3K(1-2v) E = 2G(1+v)

Answer 4

3/y = 1/3k +1/n y - youngs modulus k - bulk modulus n(eta) - shear or rigidity modulus

Answer 5

the worst answer i have ever get .. just get lost

Answer 6

E=3K(1-(2/m))

Answer 7

G= E/2(1+U) k=E/3(1-2U)