Hooke Law (Linear Elasticity)

Available identifiers

WikidataQ170282 ScholiaQ170282MaRDI QIDQ6674324

force to extend or compress a spring by distance scales linearly with distance

Description

An empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F = kx. Also the stresses and strains of material inside a continuous elastic material are connected by a linear relationship that is mathematically similar to Hooke's spring law, and is often referred to by that name.

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Defining Formula: $𝝈=𝖢:𝜺\text{ where }𝜺(u)=\frac{1}{2}(\mathrm{\nabla }u+(\mathrm{\nabla }u{)}^T)$

$𝖢$ symbol represents Elastic Stiffness Tensor

$𝜺$ symbol represents Mechanical Strain

$𝝈$ symbol represents Mechanical Stress

$u$ symbol represents Displacement of Atoms

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Related URL

https://en.wikipedia.org/wiki/Linear_elasticity

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