# How to Calculate Modulus

Three Methods:Understand the Difference Between Stress and StrainGet the Needed Input To the EquationsPerform the Calculations

Modulus is the ability of a material to resist stretching, compressing and shearing forces imposed on it by exterior causes. The modulus defines the amount that the material will deform under such external forces while retaining the memory of the original shape of the material. The material will return to its initial shape when the forces are removed. The ability of the material to return to the initial shape breaks down at a point called the yield stress point. If external forces deform the material past the yield strength point, the material will be permanently deformed and will not return to its initial shape when the external forces are removed. If the external forces drive the material past the tensile strength point of the material, it will cause the material to break. Use these tips to learn how to calculate modulus.

## Steps

### Method 1 Understand the Difference Between Stress and Strain

- 1
**Note that material stress is caused by axial stretching force.**For example, pulling straight out on a piece of taffy will stretch the taffy due to applied stress. - 2
**Understand that material strain is caused by shearing force perpendicular to the axis of the material.**For example, pushing on the middle of a tennis racket string will bend the string due to applied strain.

### Method 2 Get the Needed Input To the Equations

- 1
**Measure the proportional fractional volume change (also known as dilation) of the material.**Apply a known force to the material in both the stress and strain directions. Measure the dilation (dSs) that occurs in the material when stress only is applied. Measure the dilation (dSn) that occurs in the material when the external force applies only strain.

### Method 3 Perform the Calculations

- 1
**Calculate the bulk modulus.**Bulk modulus expresses the strength of the material when external force is applied in the axial direction, producing stress. The external pressure p (force times area over which the force is applied, expressed in MPa) applied to the material equals the dilation (a unitless number) times the bulk modulus K (expressed in MPa). As p = K times dSs, the bulk modulus K is determined as p divided by dSs. - 2
**Figure out the shear modulus.**Shear modulus expresses the strength of the material when external force is applied in the perpendicular direction, producing strain. The external pressure p (force times area over which the force is applied, expressed in MPa) applied to the material equals the dilation (a unitless number) times the shear modulus G (expressed in MPa). As p = G times dSn, the bulk modulus G is determined as p divided by dSn. - 3
**Determine the Young's Modulus.**Stressing a material will cause a proportional strain and vice versa. Young's modulus describes the relationship between stress and strain in the material. It is a linear relationship up to the yield point of the material. Young's modulus E equals stress divided by strain.

## Tips

- When applying external force to the material to measure proportional fractional volume change, do not apply so much force that the material crosses over the yield strength point. The resulting permanent material deformation will invalidate the data taken.
- A sinusoidal external force used to measure proportional volume change will yield more accurate values than will be achieved by applying a steady state external force.

## Article Info

Categories: Science