The Young Modulus

The Young Modulus is defined as the ratio of the tensile stress and the tensile strain.  

  So we can write:

            Young modulus = tensile stress

                                      tensile strain

  We know that

            tensile stress = force =  F

                                  area      A

  and that

            tensile strain =  ___extension __   = e

                                   original length        l

So we can write:

Units for the Young Modulus are Pascals (Pa) or newtons per square metre (Nm^-2).

The Young Modulus describes pulling forces. 

We can link the Young Modulus to a stress strain graph.

The Young Modulus is the gradient of the stress-strain graph for the region that obeys Hooke’s Law.  This is why we have the stress on the vertical axis when we would expect the stress to be on the horizontal axis.

The area under the stress strain graph is the strain energy per unit volume (joules per metre³).

Strain energy per unit volume = 1/2 stress x strain.

The units arise because stress is in Nm^-2 and strain is mm^-1 (NOTE: This unit here is not "millimetres to the minus one", but metres per metre which mean no units).

        Nm^-2 x mm^-1 = Nm m^-3.  Nm is joules, hence Jm^-3