# Poisson’s Ratio

Reference work entry

First Online: 01 August 2018

**DOI:**https://doi.org/10.1007/978-3-319-73568-9_225

## Definition

Poisson’s ratio is the name given to a ratio of lateral strain to axial strain. Its recognition as a property of materials is attributed to Siméon-Denis Poisson (1781–1840), a French mathematician and student of Laplace. Uniaxial extension of a solid rod causes it not only to elongate a small amount but also to become more slender or to undergo a reduction in diameter. Conversely, uniaxial compression of a solid rod or rock core sample causes it to shorten a small amount, but also to expand in diameter or become thicker. Therefore, principal stress in only one direction (uniaxial extension or compression) produces strain in all three directions. Hooke’s law explained the proportional change in length of a spring to the application of a load. Generalized Hooke’s law (Pariseau,
2012) recognizes that strain (

*ε*_{x}= Δ*l*/*l*_{o}) is proportional to the applied stress (*σ*_{x}), and the constant of proportionality for an isotropic material being stressed and strained in the elastic range of...This is a preview of subscription content, log in to check access.

## References

- ASTM (2014) Standard test methods for compressive strength and elastic moduli of intact rock core specimens under varying states of stress and temperatures. American Society for Testing and Materials Test Designated D7012-14. http://www.astm.org/Standards/D7012.htm. Accessed April 2016
- Eberhardt E (2009) Stress & strain: a review. Course notes EOSC 433, University of British Columbia, Vancouver. https://www.eoas.ubc.ca/courses/eosc433/lecture-material/StressStrain-Review.pdf. Accessed April 2016
- Holmes DP (2016) Mechanics of materials: strain. Mechanics of slender structures. Boston University. http://www.bu.edu/moss/mechanics-of-materials-strain/. Accessed April 2016
- Pariseau WG (2012) Design analysis in rock mechanics, 2nd edn. CRC Press, LondonGoogle Scholar

## Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

## How to cite

- Cite this entry as:
- Keaton J.R. (2018) Poisson’s Ratio. In: Bobrowsky P.T., Marker B. (eds) Encyclopedia of Engineering Geology. Encyclopedia of Earth Sciences Series. Springer, Cham

## About this entry

- First Online 01 August 2018
- DOI https://doi.org/10.1007/978-3-319-73568-9
- Publisher Name Springer, Cham
- Print ISBN 978-3-319-73566-5
- Online ISBN 978-3-319-73568-9
- eBook Packages Earth and Environmental Science