Calculate strain induced in a rubber(Elastosil 607) against applied force

[phani.kp]

Hello Team,
I have a rubber (harness A of 54 and elongation at break of 100%) on which 30N of force is applied over 45mm2 of ares. I would like to know the strain induced in the rubber against the force. The problem here is i could not find the exact Young's modulus value for this material. But i have tensile strength value, it is 3 N/mm2. Could anybody please let me know the approach to calculate the strain. And also i would like to know why Young's modulus is not an important property for rubbers.

 

[afreiden]

Young's Modulus is a constant that is used with linear infinitesimal elasticity. As you know, metals behave elastically under very small strains (infinitesimal ~ i.e. fraction of a percent strain) and also happen to behave linearly. Thus, Young's Modulus is a constant that is easy to find for metals.

Rubbers behave elastically out to very large ("finite") strains. Thus, linear infinitesimal elasticity won't apply, since your strains are likely too large. In addition, the stress vs. strain curve for rubber is nonlinear. For example, in tension, it usually has a "decreasing tangent stiffness" and it compression is will have an "increasing tangent stiffness" for the range of strains that you are probably interested in.

You can probably find some info on the "initial shear modulus," but that is a constant that is meant to be used with certain "hyperelastic" stress-strain relationships. Rubbers that are loaded very slowly can be idealized as "hyperelastic," where their stress strain curve is "finite," nonlinear, and the material loads and unloads along the same path (i.e. it conforms to the common definition of elasticity, albeit in a nonlinear fashion).
Having said all that, I'm sorry to say that there is no universal method for obtaining the strain that you seek. Whereas aluminum, steel, etc. obey Hooke's Law ($\sigma=E\cdot \epsilon$), silicone, adiprene, etc. have completely different constitutive relationships and there isn't one universal hyperelastic relationship that is analogous to Hooke's Law.

On top of that, you have to consider that under realistic rates of loading (even loading rates that may SEEM slow), "viscoelastic" effects will significantly influence your material behavior. Rubber behavior is usually understood to be a combination of hyperelasticity and viscoelasticity.

Rubber is complicated! Does that help?

 

[phani.kp]

Thank you very much for your explanation.
A few properties of this rubber material are as follows.

Hardness Shore A - 54
Tensile strength - 3N/mm^2
Elongation at break - 100%
Volume resistivity - 10^14 Ω cm
(For more details please see the attached data sheet)

In my application this rubber material should undergo 0.5 mm of elastic deformation against a load of 30N over a area of 45mm^2.
Having a look at the above mentioned properties could you please tell me whether this material will undergo 0.5 mm of elastic deformation or not?
Or else Please see if you can tell me the approximate or closer value of young's modulus for my calculations purpose.

 

[afreiden]

Thank you very much for your explanation.
A few properties of this rubber material are as follows.

Hardness Shore A - 54
Tensile strength - 3N/mm^2
Elongation at break - 100%
Volume resistivity - 10^14 Ω cm
(For more details please see the attached data sheet)

In my application this rubber material should undergo 0.5 mm of elastic deformation against a load of 30N over a area of 45mm^2.
Having a look at the above mentioned properties could you please tell me whether this material will undergo 0.5 mm of elastic deformation or not?
Or else Please see if you can tell me the approximate or closer value of young's modulus for my calculations purpose.

a) You didn't provide a length. To undergo .5mm of deformation will require less force for a longer specimen, compared to a shorter one...
b) You didn't specify if your force is a compression or tension. Recall that rubber behaves very differently in compression vs. tension.
c) You didn't specify the loading rate. Recall that rubber is viscoelastic (its stress vs strain behavior is dependent on strain rate).

Even if you gave me "a," "b," and "c," I wouldn't be able to give you a confident answer because:

"... whereas aluminum, steel, etc. obey Hooke's Law ... silicone, polyurethane, etc. have completely different constitutive relationships and there isn't one universal ... relationship that is analogous to Hooke's Law"


If you still want a simple solution, assuming your ".5mm of elastic deformation" is elongation (not shortening), and you are interested in very slow loading rates only:
1) Draw a straight line from (0,0), to the point ("tensile strength," "elongation at break").
2) Determine the slope
3) There you have it: you may call this the Young's Modulus of Elatosil 607 if you like.

But you didn't need to ask PF to figure that out, right?




note: Under tension, the actual stress-strain curve might lie well above your linear line and have a decreasing slope, for example. What does that curve look like, exactly? I don't know, because:

"[for rubber] there isn't one universal ... relationship that is analogous to Hooke's Law"

 

[phani.kp]

Now i understood the reason,Thank you for your explanation.