What is Poisson's ratio: Definition and 43 Discussions
In materials science and solid mechanics, Poisson's ratio
ν
{\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,
ν
{\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.
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'...
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...
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...
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
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...
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...
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...
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...
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...
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..
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...
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...
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...
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...
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...
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)...
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...
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...
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...
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...
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...
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...
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
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?
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...
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?
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...
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...
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...
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...
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...
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 =...
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...
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...
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...
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...
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...
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...
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...
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...
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...