##  [Hooke's Law](/hookes-law) 

  ##  [Hooke's Law](https://natural.quantumdictionary.io/hookes-law-0) 

  

 [![Natural & Formal Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Natural%20%26%20Formal%20Sciences.png.webp?itok=2kCDRVQv)](/topic-specific-dictionaries/natural-formal-sciences)



**Natural & Formal Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A constitutive relation stating that, within the elastic limit, the restoring force (or stress) is proportional to displacement (or strain); commonly expressed for a spring as F = −k x and, in continuum elasticity, as linear relations between stress and strain.

 

 

 

 

 





 

 



 ##  [Hooke's Law](https://engineering.quantumdictionary.io/hookes-law-1) 

  

 [![Engineering & Applied Technologies Dictionary](/sites/default/files/styles/large/public/2026-01/Engineering%20%26%20Applied%20Technologies.png.webp?itok=_IKO7_-n)](/topic-specific-dictionaries/engineering-applied-technologies)



**Engineering & Applied Technologies Dictionary**

 







 

 

 

 



 

 

 

 

Definition

Linear constitutive relation for elastic solids in the regime of small, reversible deformations stating that, within the material’s proportional limit, stress is proportional to strain; in uniaxial form σ = E·ε, where σ is normal stress, ε is engineering strain and E is the elastic (Young’s) modulus.

 

 

 

 

 





 

 



 ##  [Hooke's Law](https://health.quantumdictionary.io/hookes-law-2) 

  

 [![Health & Life Sciences Dictionary](/sites/default/files/styles/large/public/2026-01/Health%20%26%20Life%20Sciences.png.webp?itok=yyyaiQOY)](/topic-specific-dictionaries/health-life-sciences)



**Health & Life Sciences Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The linear constitutive relation valid within the elastic limit of a material that states stress is proportional to strain; in uniaxial form σ = E·ε where σ is nominal stress, ε is nominal strain and E is the elastic (Young's) modulus. It applies to reversible, time‑independent elastic deformation under small strains for materials that behave approximately linearly.

 

 

 

 

 





 

 



 ##  [Hooke's Law](https://commerce.quantumdictionary.io/hookes-law-3) 

  

 [![Commerce, Trade & Industry Dictionary](/sites/default/files/styles/large/public/2026-01/Commerce%2C%20Trade%20%26%20Industry.png.webp?itok=nh8jKPLm)](/topic-specific-dictionaries/commerce-trade-industry)



**Commerce, Trade & Industry Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A linear constitutive relation between stress and elastic strain valid for materials within their linear elastic limit: for uniaxial tension σ = E ε (E = Young's modulus). In the most general small‑strain form for linear elasticity, stress and strain are related by a fourth‑order stiffness tensor: σ = C : ε.