Solid Mechanics Part I
5.1 Energy in Deforming Materials
There are many different types of energy: mechanical, chemical, nuclear, electrical,
Energies can be grouped into
(which are due to
(which are stored energies - energy that a piece of
matter has because of its position or because of the arrangement of its parts).
A rubber ball held at some height above the ground has (gravitational) potential energy.
When dropped, this energy is progressively converted into kinetic energy as the ball’s
speed increases until it reaches the ground where all its energy is kinetic.
When the ball
hits the ground it begins to deform elastically and, in so doing, the kinetic energy is
progressively converted into
elastic strain energy
, which is stored
elastic energy is due to the re-arrangement of molecules in the ball – one can imagine this
to be very like numerous springs being compressed inside the ball.
The ball reaches
maximum deformation when the kinetic energy has been completely converted into strain
The strain energy is then converted back into kinetic energy, “pushing” the ball
back up for the rebound.
Elastic strain energy is a potential energy – elastically deforming a material is in many
ways similar to raising a weight off the ground; in both cases the potential energy is
is done in stretching a rubber band.
This work is converted into elastic
strain energy within the rubber.
If the applied stretching force is then slowly reduced, the
rubber band will use this energy to “pull” back.
If the rubber band is stretched and then
released suddenly, the band will retract quickly; the strain energy in this case is converted
into kinetic energy – and sound energy (the “snap”).
When a small weight is placed on a large metal slab, the slab will undergo minute strains,
too small to be noticed visually.
Nevertheless, the metal behaves like the rubber ball and
when the weight is removed the slab uses the internally stored strain energy to return to
its initial state.
On the other hand, a metal bar which is bent considerably, and then laid
upon the ground, will not nearly recover its original un-bent shape.
It has undergone
Most of the energy supplied has been lost; it has been converted
into heat energy, which results in a very slight temperature rise in the bar.
deformations of this type are accounted for by
, which is treated in Part
In any real material undergoing deformation, at least some of the supplied energy will be
converted into heat.
However, with the ideal elastic material under study in this chapter,
it is assumed that all the energy supplied is converted into strain energy.
When the loads
are removed, the material returns to its precise initial shape and there is no energy loss;
for example, a purely elastic ball dropped onto a purely elastic surface would bounce
back up to the precise height from which it was released.