What is Poisson's ratio: Definition and 43 Discussions

In materials science and solid mechanics, Poisson's ratio


{\displaystyle \nu }
(nu) is a measure of the Poisson effect, the deformation (expansion or contraction) of a material in directions perpendicular to the specific direction of loading. The value of Poisson's ratio is the negative of the ratio of transverse strain to axial strain. For small values of these changes,


{\displaystyle \nu }
is the amount of transversal elongation divided by the amount of axial compression. Most materials have Poisson's ratio values ranging between 0.0 and 0.5. Soft materials, such as rubber, where the bulk modulus is much higher than the shear modulus, Poisson's ratio is near 0.5. For open-cell polymer foams, Poisson's ratio is near zero, since the cells tend to collapse in compression. Many typical solids have Poisson's ratios in the range of 0.2-0.3. The ratio is named after the French mathematician and physicist Siméon Poisson.

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  1. A

    Poisson ratios for Orthotropic materials (composites)

    I'm new to composite materials. I've studied mechanical engineering but I am actually usually involved in hydrodynamics (in which I've done my masters). However for a project we do fluid structure interaction with composites, and as these things go, you cannot get away with the 'black box'...
  2. G

    Understanding Poisson's Ratio and Its Effects

    Hi everybody, Poisson's ratio determine that when applying force in one direction (let say z direction) it would cause a relative major strain at that direction, and also two additional strains at the two other directions (x & y). My question is, what is the explanation for the change in the...
  3. J

    Engineering What is Poisson's ratio and how does it relate to stress and strain?

    I'm working through the equations and I have a lot of information missing. I have calculated the longitudinal strain to be 0.4mm (4/90) is the lateral strain directly proportional to the longitudinal strain? As I need to work out poisson's ratio in order to calculate Bulk modulus, then youngs...
  4. J

    Engineering Calculating Poisson's Ratio: Young, Bulk, & Relation

    I've never really heard of Young, Bulk, or Poisson's ratio before. I have done some research but I can't seem to find the relationship between the three in order to calculate Poisson's ratio. Could someone please point me in the right direction? Thanks
  5. WhiteWolf98

    Calculating Dimensions of Titanium Disk Under Load

    Homework Statement A titanium disk (with ##E=107 ~GPa##, Poisson's ratio, ##v=0.34##) precisely ##l_0=8~mm## thick by ##d_0=30~mm## diameter is used as a cover plate in a mechanical loading device. If a ##P=20~kN## load is applied to the disk, calculate the resulting dimensions, ##l_{01}## and...
  6. T

    What Is the Correct Way to Calculate Poisson's Ratio?

    Hello all I was hoping someone could help clarify Poissons ratio. I understand that it is Lateral Strain / Axial Strain but I wanted to understand it in the context of an example. The question is:- At 5kN compression load Original Depth = 30mm Change in Depth = 2mm Original Height = 100mm...
  7. D

    Stiffness matrix for elastic materials

    For an anisotropic material, is there any way to analytically determine the elements of the stiffness matrix? For orthotropic and isotropic materials, there are analytical expressions relating the stiffness matrix elements to the elastic modulus and poisson's ratio, but I do not believe this...
  8. K

    B Exploring Poisson's Ratio in 3D Rectangles

    In poisson's ratio If we are stretching a a 3d rectangle L is hight A,B are the length and width Starching it in the L direction so that's the longitudinal strain we are making Why does the transverse strain in the "a " side equals the strain in "b" side So like that we can both use ∆a/a or...
  9. Hiero

    B Poisson's ratio, steel rod for example

    Steel has a "Poisson ratio" μ of 0.29 (in my book of problems at least). Am I understanding the meaning of this ratio correctly: if a steel cylinder is stretched along its symmetry axis by a factor p (something like 1.01 or 0.99) then the radius will change by a factor 1-μ(p-1)? [So then the...
  10. P

    Why Does Poisson's Ratio Differ for Different Materials?

    For any rod Poisson's ratio should be same i.e. 0.5 (we get this ans if we find (dr/r) / (dl/l) ) assuming that volume of rod always remains constant... But why it is not so ? We have different ratios for different materials..
  11. A

    Calculate variation in volume using given Poisson's ratio

    Homework Statement : A cylinder is elongated by 2% of its original length. If Poisson's ratio of its material is 0.3. Calculate the percentage variation in volume.[/B]Homework Equations V = πr^2l η= 0.3= Δl/l/Δr/r[/B]The Attempt at a Solution I tried using calculus to differentiate V to find...
  12. Z

    Calculate Young's modulus and Poisson's ratio

    Hi, I was looking some exercices on internet about the poisson's ratio. I have just one question. How can i calculate the young's modulus and poisson's ratio when i know that a material is purely elastical. I calculate circonferential et longitudinal contraints and i have write the cauchy...
  13. T

    How to find Poisson's ratio?

    Homework Statement I have some strain readings using a rosette gauge, but I want to know how to calculate the poissons ratio for the steel pressure vessel Homework EquationsThe Attempt at a Solution I tried Strain A/Strain B and got an average value of 0.4. But the provided value for steel is...
  14. Chrono G. Xay

    String Tension w/ Periodicity + Poisson's ratio =

    I've been trying to write an equation for the tension of a string where a segment of the string is suspended between two points a set distance apart (the string extends beyond both points in both its initial and final conditions), and involves not only the periodicity of the string's movement...
  15. W

    Poisson's ratio for a rigid rod

    I have a conceptual misunderstanding it seems. Poisson's ratio is the ratio of elastic strain deformation of the transverse and longitudinal components. That being said, if I were to induce thermal stress (heating up) to a rod by keeping its ends (longitudinal component) rigid, would there be a...
  16. A

    Prove Poisson's Ratio is .5 for Small Strains

    Homework Statement Poisson's ratio v is the negative ratio of the transverse strain to the axial strain. For an incompressible (density doesn't change), homogeneous (everything is the same molecule), isotropic (it doesn't matter which direction you pull or push on it, it will act the same way)...
  17. R

    Anisotropic Modulus of elasticity and Poisson's ratio

    Hi, I have some experimental data and I am interested to use this data to calculated modulus of elasticiy (young's modulus) and Poisson's ratio. The material for which the data is given in an anisotropic material, therefore I need to calculate modulus of elasticity and poisson's ration is x,y...
  18. R

    Anisotropic Modulus of elasticity and Poisson's ratio

    Hi, I have some experimental data and I am interested to use this data to calculated modulus of elasticiy (young's modulus) and Poisson's ratio. The material for which the data is given in an anisotropic material, therefore I need to calculate modulus of elasticity and poisson's ration is x,y...
  19. J

    Negative Poisson's Ratio in Rotated Orthotropic Material

    Hi all, I'm looking for physical and mathematical explanations for a phenomenon I've noticed when working with rotated material properties relative to an XYZ coordinate system. For certain rotations (~40 to ~50 degrees) about a single axis the S12, S13, or S23 components of the compliance...
  20. jtmbii

    Axial Deformation and Poisson's Ratio Calculation

    I've been studying this problem, trying to understand the given answer, but still no success. Homework Statement <<provided in attachment>> Homework Equations Longitudinal Strain Latitudinal Strain: where is the amount the radius contracts, r is original radius Average Normal Stress...
  21. M

    Calculating Poisson's Ratio with a Modulus of Rigidity & Young's Modulus

    Hi, I'm wondering if someone can point me in the right direction with this question. A material has a modulus of rigidity of 100 GNm-2 and a Young's Modulus of 250 GNm-2. Calculate the expected value of Poisson's Ratio for the material. Poisson's Ratio is expressed as transverse strain / axial...
  22. J

    Obtaining yield stress knowing only Poisson's ratio and UTS?

    Greetings all, I have been trying to find a method of calculating the yield stress for a material when only given; -The loading type (Two bars soldered together in tension) -The dimensions of the shaft and solder (ie thickness of solder, length, cross sectional area) -The Ultimate...
  23. F

    Radial variation in Poisson's ratio

    Hi, I am wondering why radial variation in Poisson's ratio exists when a cylinder is compressed? Ie, Poisson's ratio toward the center is lower than what is measured at the circumferential edge. Thanks M
  24. T

    Why would density increase when Poisson's ratio > 0.5?

    Homework Statement Does anyone understand why density would increase when the poisson ratio is greater than 0.5 as indicated in this slide from my professor: Does this density increase apply to a system undergoing tension or compression or both?
  25. T

    Determine the modulus of elasticity, Poisson's ratio and the shear modulus.

    Homework Statement A rod with a diameter of 1.00 in and length of 6.0 ft undergoes an axial deformation of 0.150 in when subjected to an axial force of 52.0 kip. The diameter of the rod decreases by 0.0007 in at this load. Determine the modulus of elasticity, Poisson's ratio and the shear...
  26. P

    A question about Poisson's Ratio

    Does Poisson's Ratio only apply to material still in the linear elastic range or is it still true for the material that has undergone plastic deformation?
  27. S

    How to find a value for poisson's ratio

    Homework Statement The question is: A rod of 50mm in diameter and 0.8m in length is subjected to an axial load of 150kn. If the rod entends by 1.4mm and there is a decrease in diameter of 0.01mm, determine: The value of poissons ratio? Homework Equations v=lateral strain/longitudinal...
  28. G

    Understanding Poisson's Ratio and Restrained Cylinders

    Hey. I have a couple of questions about Poisson's ratio I hope you guys can answer. If I have a cylinder made of, let's say steel. Steel has a Poisson's ratio of roughly 0.33. The cylinder is restrained in the vertical direction so no displacement can occur. If I apply an internal pressure...
  29. I

    How Can Poisson's Ratio Reach -1?

    v = \epsilontrans/ \epsilonaxial where ν is the resulting Poisson's ratio, \epsilontrans is transverse strain \epsilonaxial is axial strain and Poissions Ratio have range and its not more then 0.5 and not less then -1? so my question is how its value can turn "-1"? As...
  30. N

    Rate of change of volume and poisson's ratio

    Homework Statement Consider a rectangular block of isotropic material of dimensions a, b and c, with c >> a or b. It is characterised by its elastic constants: Young's modulus E, shear modulus G and Poisson's ratio . The block of material is subjected to axial deformation along the c...
  31. J

    Find Poisson's Ratio of Aluminum from Torsion and Tensile Tests

    1. Torsion test showed aluminum to have shear modulus of 4.60x10^6psi. Under a tensile test, the same specimen showed a modulus of elasticity of 12.2x10^6psi. Find Poisson's Ratio. 2. Poisson's Ratio=lateral strain/axial strain 3. The ratio is a function of both strains. The...
  32. A

    Bulk modulus and poisson's ratio

    Homework Statement derive the equation for the bulk modulus, K = E/3(1 - 2v), where v is poisson's ratio. Homework Equations E = stress/e, where e is strain The Attempt at a Solution e_v = e_x + e_y + e_z e_y = e_z = -v*e_x e_v = (1 - 2v)*e_x K = stress/e_v therefore K =...
  33. L

    Poisson's Ratio Coursework: Urgent Help Needed!

    Poisson's Ratio coursework - Urgent help needed! hello, I'm currently working on a coursework for my A2 physics on Poisson's ratio i'm finding the ratio for aluminuim using aluminuim foil and strain gauges, adding masses to a clamp on the end of the foil (so foil is under tension) and...
  34. K

    Poisson's Ratio Need Not Apply?

    A rubber block is subjected to an elongation of 0.03in along the x-axis, and its vertical faces are given a tilt so that theta=89.3deg. Find epsilonx, epsilony, and gammaxy. vr=0.5. The block is 4 in along the x-axis and 3 in along the y-axis. My solution epsilonx = 0.03/4 = .0075...
  35. S

    Calculating Cross Sectional Area After Cold Working?

    Hello, Is using Poisson's ratio to calculate the cross sectional area accurate after a material has been extensively cold worked and deformed. For example say I have a wire at some nominal length and thickness (which is too small for me to precisely measure, but I know at the start). So can...
  36. D

    Poisson's Ratio and Ultrasonic Velocity for Isotropic Material

    For an isotropic material, the relation between the longitudinal ultrasonic velocity(VL), the transverse (shear) ultrasonic velocity(VT) and the Poisson's ratio (nu) is given by (VT/VL)^2 = (1-2*nu)/(2*(1-nu)) From the above relation, one gets that VL=0 when nu=1 which is not...
  37. B

    Computing Poisson's Ratio for AISI 1020 Steel Rod

    If you had a 2 inch diameter AISI 1020 steel rod that is 10 feet long. Under an applied load, the rod elongates by 0.48 inches. A). How would you compute the axial strain in the bar? and B). How would you compute Poisson's ratio for the material, if the transverse deformation of the rod is...
  38. L

    Finding yield stress with only modulus of elasticity and Poisson's ratio?

    Is it possible to find the yield stress of a material with only modulus of elasticity and Poisson's ratio? I was given a problem that: What is the min. aluminum needed to support a block (10 Newton) to 1 meter high? E=70GPa and v=0.3 are the only given aluminum properties. I would know...
  39. B

    Calculating Poisson's Ratio and Modulus of Elasticity for a Solid Cylinder

    Hi, I am new to this so bear with me, I'm stuck on a question, basically, i need to work out the poissons ratio for a solid cylinder 140mm dia by 4.0m long to find out if it's steel or aluminium. I know the formula for poisson ratio is lateral strain / axial strain. The question states that...
  40. S

    How is the Poisson's Ratio Formula Derived?

    can anybody please tell me how this equation has been arrived? dA=A(1-m dL/L)^2 -A where A=Area of cross section L=length
  41. S

    Calculating Poisson's Ratio: Step-by-Step Guide

    please help on this formula how it has been arrived? dA=A(1-m dL/L)^2-A where m= Poisson's ratio A=area of cross section L=length
  42. C

    Understanding Poisson's Ratio Limits

    I'm doing A2 course work on properties of materials and have been looking at Youngs modulus, Bulk modulus, Poissons ratio and Shear stress strain etc.:uhh: Was wondering if any kind person would be able to explain why Poissons ratio has theoretical limits of -1 to 0.5? Have tried to search on...
  43. U

    Calculate Poisson's ratio of NaCl crystal

    hello to all here is a problem i designed myself. i don't know whether it can be solved. Question: Consider NaCl lattice of edge length 'x' m. Let Na+ carry +1 C and each Cl- carry -1 charge. Calculate Poisson's ratio of NaCl crystal. Assume no heat loss when deformation takes place...