How to differentiate Young’s modulus, spring constant, biaxial

modulus, and bulk modulus?

1) Young’s modulus: The modulus corresponding to axial loading.

Material shape: axial or 1-D.

Young’s modulus is usually obtained from tensile test.

The loading, hence stress and strain, is axial in the tensile test.

2) Spring constant: The stiffness of a spring during deflection loading.

Material shape: beam, 1-D.

2.1 The beam is axial, so does stress and strain.

à Young’s modulus is used to calculate spring constant:

3) Biaxial modulus: The modulus corresponding to biaxial loading.

Material shape: thin film, sheet. 2-D.

3.1 What is biaxial loading? à.

3.2 Biaxial modulus is:

Why? You have to know the definition of Poisson Ratio and derive generalized Hook’s

law.

Therefore,

Now, use what we have learned in 2.1 you will get.

1 (1 )xx xxEε ν σ= − ##

Finally, you get the biaxial modulus is xx and yy direction.

4) Bulk modulus: the volume change due to pressure loading.

Material shape: rigid bulk, 3-D.

4.1 Definition:

4.2 The relationship with Young’s modulus.

3(1 2 )E

Kν

=−

You can also use generalized Hook’s law to derive it. How?

Hint: (1 3 ), ....o xxV V ε ε ε∆ = − = = , clear enough?

4.3 Need more details, check this link:

http://scienceworld.wolfram.com/physics/BulkModulus.html