How many of us have thought about how surprisingly objects behave when exposed to them?
For example, why the fabric, if we stretch it in different directions, can stretch for a long time, and at one moment suddenly tear? And why is the same experiment much harder to do with a pencil? What determines the resistance of the material? How can one determine to what extent it lends itself to deformation or stretching?
All these and many other questions more than 300 years ago were asked by the English researcher Robert Hook. And he found the answers, now united under the general name "Hooke Law."
According to his research, each material has a so-called coefficient of elasticity . This property allows the material to stretch within certain limits. The coefficient of elasticity is a constant value. This means that each material can withstand only a certain level of resistance, after which it reaches the level of irreversible deformation.
In general, Hooke's Law can be expressed by the formula:
F = k / x /,
where F is the elastic force, k is the aforementioned coefficient of elasticity, and / x / is the change in the length of the material. What is meant by a change in this indicator? Under the influence of force, a certain subject under study, whether it is a string, rubber or any other, changes, stretching or contracting. The change in length in this case is the difference between the original and final length of the studied subject. That is, how much the spring stretched / compressed (rubber, string, etc.)
Hence, knowing the length and constant coefficient of elasticity for a given material, one can find the force with which the material is stretched, or the force of elasticity, as is often called the Hooke Law.
There are also special cases in which this law cannot be used in its standard form. We are talking about measuring the force of deformation under shear conditions, that is, in situations where the deformation is produced by a certain force acting on the material at an angle. Hooke's law on shear can be expressed as follows:
Ο = Gy,
where Ο is the desired force, G is a constant coefficient, known as the shear modulus, y is the shear angle, the value by which the angle of inclination of the object has changed.
The linear force of elasticity (Hooke's Law) is applicable only in conditions of small compressions and tension. If the force continues to influence the studied subject, then there comes a moment when it loses its elasticity qualities, that is, reaches its elastic limit. The force exerted exceeds the strength of resistance. Technically, this can be seen not only as a change in the visible parameters of the material, but also as a decrease in its resistance. The force required to change the material is now reduced. In such cases, there is a change in the properties of the object, that is, the body is no longer able to resist. In ordinary life, we see that it breaks, breaks, bursts, etc. Not necessarily, of course, a violation of integrity, but the quality is significantly affected. And the coefficient of elasticity, which is true for a material or body in an undistorted form, ceases to be significant in a distorted form.
Such a case allows us to say that a linear system (directly proportional to one parameter depending on another) has become non-linear when the interdependence of the parameters is lost and the change occurs according to a different principle.
Based on such observations, Thomas Jung created a formula for the modulus of elasticity, which was later named in his honor and became the basis for the creation of the Theory of Elasticity. The modulus of elasticity allows one to consider the deformation in cases where the changes in elasticity are significant. The law has the form:
E = Ο / Ξ·,
where Ο is the force applied to the transverse sectional area of ββthe studied body, Ξ· is the modulus of elongation or compression of the body, E is the modulus of elasticity, which determines the degree of stretching or compression of the body under the influence of mechanical stress.