Consider one hypothesis and validate your results by self experimentation because no body knows what type of biopolymer you are going to use.

Please give more insight into what you mean by self experimentation. Thanks

You need to provide more data on the material. Is it a pure polymer or composite. If polymer what is the approx %crystallinity. Pls provide the details of all other curves in terms of materials, loading conditions etc. You have told it is axial loading. Pls share how exactly you did it. was it a standard set up or a customized set up made by you.

I would suggest this is a composite. If the matrix was on its own, you would probably have the same curve as the others, ie a rather elastic polymer. You probably have a second component in here which stiffens up (reinforces) your elastic matrix.

Hi Adesola,

• My 1st question - Did you zero the stress and strain in the begining?
• 2nd question -   Strain stiffening is a typical characteristic of soft tissues. Is this seeded or cultured biomaterial? If this is tissue engineered biomaterial, then this strain is a material characteristic. 

A little more information can be useful. But my inference is : -

• The curves were not normalized to zero
• If this is a polymeric biomaterial (and not a tissue engineered one) then the blue curve is an outlier. 

Hope this helps. 

Best

Sourav

Without knowing the exact material is quite difficult to determine possible explanations. Could it be some initial pre-stress?

Ademiloye, as others have stated, more information on the particulars of the material and test protocol would be helpful, but I can still take a shot at both questions.

1.  Regarding the negative stress question, this looks to be a case of either an initial prestress, or not zeroing out the load channel prior to testing.  All of the traces provided exhibit stress increasing with increasing strain, it simply appears to be a problem with the initial offset. (as pointed out by Javier and Sourav).

2.  Strain-stiffening is quite typical in biologic tissues and polymeric structures.  It is often attributed to the progressive recruitment of fibers with increasing stretch, either by recruiting slack fibers  (e.g., crimped collagen in tendon, or slackened polymer chains), or getting fiber to align to the direction of stretch and bear load (e.g., fiber rotation in skin, and polymer realignment in engineered mats).  Fiber alignment to the direction of stretch is what is responsible for the significant differences in low load behavior observed between aligned and randomly oriented electrospun fiber mats (scaffolds).  

I hope this is helpful.

Cheers,

-DTC

I agree with the suggestion to make sure that the load is zeroed in future tests.  I agree also with the interpretation given by several responders that the concave upward stress-strain curve is typical for tension of biological and soft polymeric materials. Stiffening occurs as some of the stretched long-chain molecules approach their total length between pinning points.

Rod Clifton

Also, how are you measuring strains?  If you are using a camera system to measure regional strains, rather than relying on actuator displacement and the triggers are not working correctly, this can also be a cause of apparent strain stiffening.   You can work around trigger issues by interpolating the regional strain camera data and load frame load data in Matlab.   If you are already doing this, check that the camera system is actually taking pictures at the frequency it is supposed to, or that the frequency was not inadvertently changed for this one test, but not accounted for. 

Hi Adesola,

I think that negative stiffness on the initial stage of curve was caused by stress relaxation in biomaterial. 

The stiffening mechanism have been explained enough in replies of our collegues just . 

Best,

Serge

material might have initial pre-stress due unknown loading... Please define your case precisely and the method of finding these negative stress...

Dear Adeshola,

The hooke's law itself states that it is valid only up to the elastic range of the material I.e. only to that limit where the material is behaving elastic. Compressive stress has stress units (force per unit area), usually with negative values to indicate the compaction. By convention, tensile axial stresses are positive, compressive axial stresses are negative. Compressive stress is defined in the same way as the tensile stress but it has negative values so as to express the compression since dL has the opposite direction.

If internal pressure is increasing or initial pre-stress occur on biomaterial than radial strain is become negative, but when the internal pressure decreases the materials constant is become positive in biomaterial and hence this shows positive stress. Negative stiffness brings the relaxation in biomaterials especially if it is soft tissue. This type of characteristics occur in the composites, biopolymer composites etc. This always occurs when Strain stiffening found in a typical characteristic of soft tissues. If this is tissue is engineered biomaterial, then this type of strain is a material characteristic.

Ashish