External work will always equal the internal work only in case of a linear elastic response.
External work could be defined as"a force acting upon an object to cause a displacement".
Suppose the object is absolutely rigid(just imaginary) then it may not displace at all.In such a case it is clear from the definition that external work done is zero.But i think in such a case internal work is not zero as there will deinitely be internal forces developed and hence energy stored.It would be better if someone expands on this para.I am sure of the former part of my answer(para 1) but someone plz. expand your thoughts on para 3.
surely in your theoretically rigid solid, since all the internal strains are zero, the internal stresses/forces still do zero work. (work being force*distance - if either is zero, the work is zero).
Austim has clarified the para3 of your post but I was expecting something on para1 and para2 as well because my understanding on what you have stated is different. As per the law of coservation of energy, external work equals internal work in ALL the systems, be they elastically linear or non-linear.
Para2 is in error due to bad framing of your sentence. It appears to state that external work is a force whereas external work is vector product of force and displacement caused by that force.
A small correction. The external work and the internal energy stored ( otherwise called the work done by the internal forces) are equal only in a conservative system. This means, the system does not have any energy dissipating mechanisms such as friction.
One typical example is a rubber ball thrown on the floor. Even though the collision of the ball with the floor is elastic, some energy is lost in every collision due to friction. That is why the ball bounces back to lesser heights in every successive collision befoere it comes to rest.
The definition of work as stated by flest is of course not correct. The work is a product of the force and displacement.
Flame, I think work is only a scalar product of the force and displacement vectors. Work has got only magnitude and does not have a direction.
You might be right. I am not sure but its likely that the energy dissipation is due to the conversion of part of the kinetic energy to heat during the impact.
However, I stated that as an example of a process which is not conservative.
What about the strain hardening region of the structural steel specimen subjected to simple tension? The material undergoes strain hardening(increase in strength as it strains) due to change in molecular structure of the material.Is this also part of internal energy stored?Will in this case external work=internal work??
