suppose a body falls on a surface from a certain height. now due to sudden impact, an impulsive force will be generated which will vary with the time. so what will be that variation of impulsive force vs time? also, this variation will depend on the type of impact whether it is elastic impact or plastic impact.
Normally in standard impulse theory, the plot you are looking for is not given because the time of impulse is very small. The resultant force of impulse F acting on a body through time interval dt is equated with the change in momentum of body which is m.dv. m is the mass and dv change in velocity. This is given by
Fdt = m.dv.
Now the plot you are looking for can be obtained from above equation as follows.
F = m.dv/dt = m.a = m.d2x/dt2
where x represents total deformation of the body (plastic or elastic). If this total deformation is split up into i number of smaller deformations xi, then it will correspondingly split up the force of impact into equal number of smaller forces Fi acting during smaller unit of time ti. So the equation becomes
Fi = m.d2xi/dti2. This will give you desired plot of Fi against dti
DearVikram, the problem still remains .how to calculate the deformation gradient . can you suggest some research papers or some textbook related to the same
You can look into Atlas of Stress Strain curves for different materials.
https://www.saylor.org/site/wp-content/uploads/2012/09/ME1022.2.4.pdf
http://www.worldcat.org/title/atlas-of-stress-strain-curves/oclc/694732463
http://www.asminternational.org/materials-resources/results/-/journal_content/56/10192/06825G/PUBLICATION
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