What Is Poisson's Ratio?
Poisson's ratio refers to the ratio of the absolute value of the transverse normal strain to the axial normal strain when the material is unidirectionally stretched or compressed. It is also called the transverse deformation coefficient. It is an elastic constant that reflects the lateral deformation of the material.
- Chinese name
- Poisson's ratio
- Foreign name
- Poisson ratio
- Definition
- Absolute value of transverse normal strain axial normal strain ratio
- discoverer
- Simon Denis Poisson
- Poisson's ratio refers to the ratio of the absolute value of the transverse normal strain to the axial normal strain when the material is unidirectionally stretched or compressed. It is also called the transverse deformation coefficient. It is an elastic constant that reflects the lateral deformation of the material.
Poisson's origin
- Poisson's ratio was first discovered and proposed by French scientist Simon Denis Poisson (1781-1840) [1] .
- Portrait of mathematician Poisson
- In the article "Elastomer Equilibrium and Motion Research Report" published in 1829, he used the theory of intermolecular interactions to derive the equation of motion of elastomers, and found that longitudinal and transverse waves can propagate in elastic media, and theoretically derived each When the isotropic elastic rod is stretched in the longitudinal direction, the ratio of the transverse contraction strain to the longitudinal elongation strain is a constant, and its value is one quarter.
- If loaded in the elastic range, the following relationship exists between the transverse strain x and the longitudinal strain y:
- x =- y
- Where is an elastic constant of the material, called Poisson's ratio. Poisson's ratio is a quantity with one dimension. [2]
Poisson's ratio in detail
- While the material undergoes elongation (or shortening) deformation along the direction of the load, it also undergoes shortening (or elongation) deformation in the direction perpendicular to the load. The negative value of the ratio of the strain l in the vertical direction to the strain in the load direction is called the Poisson's ratio of the material. If v is the Poisson's ratio, then v = - l / . During the elastic deformation phase of the material, v is a constant. In theory, only two of the three elastic constants E, G, and v of an isotropic material are independent, because they have the following relationship:
- G = E / [2 (1 + v)].
- The Poisson's ratio of a material is generally determined by a test method.
- For traditional materials, v is generally constant in the elastic working range, but beyond the elastic range, v increases with increasing stress until v = 0.5.
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- Difference between primary and secondary Poisson's ratio [1]
- The main Poisson's ratio PRXY refers to the compressive (or tensile) strain in the Y direction caused by the unit tensile (or compressive) strain in the X direction under a uniaxial action;
- The sub-Poisson's ratio NUXY, which represents the Poisson's ratio orthogonal to PRXY, refers to the compression (or tension) in the X direction caused by the unit tensile (or compression) strain in the Y direction under uniaxial action. strain.
- There is a certain relationship between PRXY and NUXY: PRXY / NUXY = EX / EY
- For orthotropic materials, the primary and secondary Poisson's ratios need to be entered separately based on the material data.
- But for isotropic materials, there is no difference in choosing PRXY or NUXY to enter Poisson's ratio, just enter one of them.
- The simple derivation is as follows:
- If under uniaxial action:
- (1) The compressive (or tensile) strain in the Y direction caused by the unit tensile (or compressive) strain in the X direction is b;
- (2) The compressive (or tensile) strain in the X direction caused by the unit tensile (or compressive) strain in the Y direction is a;
- Then according to Hook's law, = EX × a = EY × b
- EX / EY = b / a
- Again PRXY / NUXY = b / a
- PRXY / NUXY = EX / EY