Poisson's Ratio Need Not Apply?

In summary, the rubber block is subjected to an elongation of 0.03in along the x-axis and its vertical faces are tilted at an angle of theta=89.3deg. Using Poisson's ratio (vr=0.5), the values of epsilonx, epsilony, and gammaxy can be calculated. The block is 4 in along the x-axis and 3 in along the y-axis. The solution states that epsilony = - epsilonx*vr = -.00375 in/in because of the definition of Poisson's ratio.
  • #1
kahless2005
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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 in/in

gammaxy = pi/2 - theta = pi/2 - 89.3(pi/180) = .0122 rad

epsilony = - epsilonx/vr using Poisson's ratio = -.015 in/in
HOWEVER
The solutions states that

epsilony = - epsilonx*vr = -.00375 in/in

Why is this? This has been bugging me for three days
 
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  • #2
.


Hello, let's break down the problem to understand why the solutions state that epsilony = - epsilonx*vr = -.00375 in/in.

Firstly, let's recall the definition of Poisson's ratio (vr):

vr = -epsilony/epsilonx

This ratio represents the relative change in the transverse strain (epsilony) to the axial strain (epsilonx).

In this case, we are given the value of vr = 0.5.

Now, let's substitute the values given in the problem into the equation:

0.5 = -epsilony/0.0075

Solving for epsilony, we get:

epsilony = -0.5*0.0075 = -0.00375 in/in

This is why the solutions state that epsilony = - epsilonx*vr = -.00375 in/in.

I hope this helps to clarify your doubt. If you have any further questions, please feel free to ask.
 
  • #3
... I would like to point out that Poisson's ratio is a material property that describes the relationship between the strain (deformation) in one direction and the strain in the perpendicular direction. It is typically denoted by the symbol "ν" (nu) and has a value between -1 and 0.5.

In the given scenario, the rubber block is being subjected to an elongation along the x-axis and a tilt on its vertical faces. This means that the strain in the y-direction (epsilony) is not solely caused by the elongation in the x-direction (epsilonx), but also by the change in shape due to the tilt (gammaxy). Therefore, using Poisson's ratio to calculate epsilony may not be appropriate in this case.

Instead, the solution provided uses the relationship between the strains and the tilt angle (theta) to find the value of epsilony. This approach takes into account the change in shape caused by the tilt, rather than just the elongation along the x-axis.

It is important to note that Poisson's ratio may not always apply in every situation, as it depends on the material and the type of deformation being considered. In this case, the given solution is a more appropriate approach to finding the strains in the rubber block.
 

1. What is Poisson's Ratio Need Not Apply?

Poisson's Ratio Need Not Apply is a concept in material science that challenges the traditional understanding of how materials behave under stress. It suggests that the relationship between a material's axial and transverse strains may not always follow the expected ratio, known as Poisson's ratio.

2. How does this concept differ from traditional material science theories?

In traditional material science, Poisson's ratio is considered a fundamental property of a material, describing how it responds to stress. However, Poisson's Ratio Need Not Apply suggests that this relationship may not always hold true, and that materials may exhibit different behaviors under certain conditions.

3. What is an example of a material that does not follow Poisson's ratio?

One example is auxetic materials, which have a negative Poisson's ratio. This means that when stretched, they become wider, rather than thinner like most materials. Another example is rubber, which can exhibit a Poisson's ratio of 0.5 or higher, meaning that it becomes thicker when stretched.

4. How does this concept impact engineering and design?

Poisson's Ratio Need Not Apply challenges traditional design principles, as it suggests that materials may behave differently under stress than previously thought. This can lead to the development of new materials and designs that take into account these unconventional behaviors.

5. What research is being done in this area?

Scientists and engineers continue to study and explore the implications of Poisson's Ratio Need Not Apply in various materials and applications. This includes investigating the underlying mechanisms that cause these non-traditional behaviors and developing new theories and models to better understand and predict material responses.

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