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Elastic Strain Energy

  • Up to the elastic limit of a sample, all the work done in stretching it is stored potential energy, or Elastic Strain Energy. This value can be determined by calculating the area under the the force-extension graph. If the sample obeys Hooke's Law, and is below the elastic limit, the Elastic Strain Energy can be calculated by the formula:
E = ½Fx
  • Or, since F = kx (where k is the stiffness constant of the sample):
E = ½kx2
http://chart.apis.google.com/chart?chxl=0:|F|1:|x&chxp=0,100|1,100&chxs=0,676767,20,0.5,l,676767|1,676767,20,-0.5,l,676767&chxt=y,x&chs=300x225&cht=lxy&chco=000000&chd=s:A9,A9&chls=2&chma=10,0,0,10|10&chm=B,C564B5BB,0,0,0|@tElastic+Strain+Energy,000000,0,0.6:0.5,10
  • Some force-extension graphs have two curves, one measured when force was being applied (loading) and one where that force was being removed (unloading). The unloading curve may be below the loading curve, which would mean that less energy is given out when a force is removed from the sample than was put in, as the area under the unloading curve is less than that of the loading curve. This is because some of the energy put into the material was transferred as waste energy, like heat.
http://moon.ouhsc.edu/dthompso/namics/gifiles/hysttib.jpg