My first test would be to use a rule of mixtures equation as though the system is a composite. Have you explored this option?

https://en.wikipedia.org/wiki/Rule_of_mixtures

Dear Khai,

pl go thru any book on  Mechanics of Composites. Your specimen seems to be similar to a composite specimen

 If the composite material is tested by loading in one of the directions of the adhesion plane you can use the following equation

Ec=E1*V1+E2*V2

Where Ec is the modulus of the composite system, E1 and E2 the moduli of the component materials and V1 and V2 the "Volume fractions" of the two component materials,

Please recall that V1+V2=1           (1)

From the figure you showed it seems to me that this is the case.

On the contrary if the tensile test is conducted in a direction perpendicular to the adhesion plane you can safely use the following equation:

Ec=(E1*E2)/(E1*V2+E2*V1)            (2)

with symbols having  the same  meaning as above. Equation 1 and 2 are the elemental upper and lower bound equations that can be found in any textbook on composites.

If the volume fractions of the constituent materials are similar,  the Ec value is dominated by the stiffer material in eq. (1),  whereas in it is close to that of the weaker material for the loading conditions expressed by eq. (2)

Dear all,

Thank you very much and sorry that not to reply to your comments earlier. I tried to collect more data for a broader view of this system.

The rule of mixtures that you all mentioned could be a good consideration and I have actually applied to check. However, the hybrid structure I'm working on is a bit different.

As can be seen from the attached image, I have a soft material that bonded to 2  slabs of stiffer material (stiff enough to be clamped on the machine). My aim was to characterise the bonding strength between that soft material and the stiffer material via different chemistries.

Since the bonding is not as excellent as what we can achieve in the case of a composite, the distribution of the applied force, and consequently deformation, is not homogenous throughout the hybrid structure.

From what I observed so far, we can only apply the rule of mixtures to the case that there are not significant difference between moduli of these materials. When we have either quite high modulus of the side slabs or too soft middle part, it always results in negative values after data correction. I think it could make sense in those cases when the force is mostly concentrated in the much weaker part rather than spreading throughout the structure. 

I think it could make sense in those cases when the force is mostly concentrated in the much weaker part rather than spreading throughout the structure. 

I am not sure if that could be valid, but would love to see your thought. I guess I would need a model (might be developed somewhere for other materials/structures) that takes into account how the force spreads, the difference in moduli of two materials and the interfacial strength of the bonding.

I'm not doing simulation or modelling, so it's a bit difficult to find this literature indeed; so please let me know if you have come across to any system similar to this.

Thanks all again for your valuable comments.

Khai

You have an iso-stress condition. Under standard cases, one of the two basic rules should apply. Otherwise, have you considered a complex rule of mixtures? It has an extra degree of freedom in an exponential n.

P^n = \sum f_v P^n

For simple, n = 1. For inverse, n = -1.

Alternatively, this is a flexible spring + a stiff spring system. You may find analogies in physics to such a picture.

Finally, when you cannot get direct information about the adhesion strength in your test, perhaps you can compare trends. Keep all else the same except the "glue" between the gel and silicon. Then compare differences in the force-distance plots, their integrals (energy - distance), or their derivatives.

Dear Prof. Weimer,

Thanks for your comment. Could I ask for your thought relating to the adhesion strength for such system? Doing the integration for the area beneath the stress-strain curve might relate more to the material's properties (e.g. toughness) so it's less representative for what happens at the interface.

Would the max tensile stress tell us more?

Yes. The failure points are determined by the adhesion strength. As I recall, they are classed as different types (I, II, or III), at least in iso-strain conditions.

You might consider how to increase the contributions of the interfaces to the failure points. This may happen by changing the ratio of gel to silicon. This effectively changes the volume fractions of the components in the composite. It could shift the break point. Alternatively, you may have to consider a test in an iso-strain configuration rather than an iso-stress configuration. As an example, what would happen when you would put the gel on two sides of a silicon wafer, clamp the system from the top and bottom, and  try to pull on the wafer to "slide it out" of the gel. This is a "fiber pull" test where the failure mode is directly dependent on the adhesion of the fiber (your silicon wafer) and the matrix (your gel).

When you are so inclined, I have a demo that shows model iso-strain behavior in fiber composites posted at the link below.

http://www.igorexchange.com/project/FiberCompositeDesigner

http://www.igorexchange.com/project/FiberCompositeDesigner