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# 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.

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