Overview of Hooke’s Law and Its Limitations
Hooke’s law of physics defines a linear relationship between the strain of a solid and the stress applied to it, and as one increases, the other also increases. However, this law is limited to the region of minor deformations, and it loses its relevance when it goes beyond the elasticity of the material.
The point of this problem is that at small deformations, stress and strain are indeed related in a directly proportional manner, and an equation constructed according to Hooke’s law can be used to predict one variable when the other is known. However, due to the atomic-molecular structure of solid materials, the relationship between strain and stress ceases to be linear as the deformation further increases beyond the elastic limit. The rationale for this behavior is the displacement of particles in the crystalline structure of the material, which becomes the cause of irreversible deformation.
Behavior of Materials Beyond the Elastic Limit
In particular, at minor deformations, the atoms or molecules that form a solid’s structure also undergo displacements. However, these displacements are in equilibrium regions, which means that the particles move back when the stress is removed. In contrast, if the stress continues to be applied, atoms and molecules are displaced beyond equilibrium, collisions and discontinuities can occur between them, and other additional effects can occur that prevent the strain-stress relationship from remaining linear.
The Need for New Physics
It is unlikely that new physics is required to explain these patterns of disobedience to linear Hooke’s law since the application of Hooke’s law is only appropriate within the elastic limit. Instead, the focus should be on extending the existing knowledge of microstructural deformation and the phenomena observed when solids exceed elasticity thresholds. It is not excluded that the behavior of objects at high values of applied stress may also obey some laws, so instead of creating new physics, attention should be paid to finding regularities in such behavior.
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