Elasticity
Stress
The
concept of the rigid body, body that always keeps its form, is the
mathematic abstraction, introduces to describe the work of the outer
forces on the real bodies. Each body, under the influence of the
work of outer forces changes its position, but also changes its
form. The value of that change depends on the inner properties of
the body. It is practical in that case to define the two extreme
cases: perfectly elastic bodies, which completely return their basic
form when the work of the outer forces stops and perfectly plastic
bodies, bodies that keep the deformed form even when the outer forces
stop working. Real bodies are in fact somewhere in between those
two types.
The
pressure of the outer forces on the surface of the rigid body causes
the disturbance in the body, which can be seen in the change of
the distance among the material particles. Those shifts cause additional
stress forces among the particle of the body. Since body is in the
state of static balance, those stress forces will be equal to the
outer pressure forces. But, when two bodies touch, the contact forces
that act among them will not act only in one point, but through
out all the touching surface. The ratio of force value and surface
on which the force acts will be called sress : p=F/S. Stress is
neither scalar nor vector quantity. Stress is the quantity that
is called tensor in mathematics.
Deformations
The
rigid bodies on which sides the pressure is imposed deform under
the influence of this force. The work of the forces and deformation
that appears as the result of the force work in a rigid body are
seen as deformation. Deformation is like stress, the tensor quantity. The
relation between deformation and stress is not a simple one, as
each component of the deformation depends on each component of the
stress.
Most
of the materials is isotropic and that means that stress deformations
spread equally in all directions.
Hook's law
The
ratio of the change in the stress and the corresponding deformation
in the material we call the elasticity module. The elasticity module for
the tensile and compressive forces is called the Young elasticity
module and appear in the form E. It the experimental fact that the
Young module is equal for the tensile and compressive forces, and
it is in given limitations independent of the present stress. That
fact is caused by Hook's law: if we enlarge the pressure force F
for the quantity (delta) F, under which the existing linear deformation
of the bar 1 enlarges for (delta) 1, the change in stress, (delta)
F/S, and deformation, (delta) 1/L, are correlated by relation: page
148 xf.