Strength of elasticity

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Strength of force - the force that causes the deformed body to return to its original shape. For small deformations, the elastic force is proportional to the deformation, as expressed by Hooke's law, which for linear deformation can be represented by the following formula: F & # x2192; = & # x2212; k & # x0394; x & # x2192; {\ displaystyle {\ vec {F}} = - to \ Delta {\ vec {x}}}

where & # x0394; x & # x2192; {\displaystyle \Delta {\vec {x}}} - elongation (shortening) of the body, k {\displaystyle k\,} - spring coefficient expressed in N / m, F & # x2192; {\displaystyle {\vec {F}}} - strength of elasticity.

Minus in the formula means that the force of elasticity is reversed to return the elongation vector (shortening) of the body. This force counteracts the deformation of the body and causes it to return to a non-deformed state when external forces, which deform the body, cease to function.

In the general case of any body of any structure, the elasticity of the body is more complex, both spatial and directional, and instead of the coefficient of elasticity, the stiffness tensor is used. This is due to the fact that different forces (eg, squeezing, shearing) and torque forces (eg twisting) acting on the body can cause different deformations, but not always the direction of force coincides with the direction of deformation. Bibliography

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