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Micro-scale compression testing for hydrogel microspheres between two rigid plates

I am a last year Ph.D student at University of Toronto. During my study, I developed MEMS force sensor-based micro-scale compression testing for micrometer-sized spherical biomaterials. I applied this system for mechanical properties characterization of polymeric hydrogel microsphere for drug delivery.

I almost finished exprimental data acquisition and am trying to calculate mechanical properties such as Young's modulus and viscoelastic parameters using elastic and viscoelastic mechanics model. But I don't know which is the most appropriate mechanics model for describing this experimental situation. Could anybody please help me to find any elastic and viscoelastic mechanics model for the polymeric hydrogel microsphere in wet state compressed by two rigid plates. And I would like to verify this experiment with FEM analysis using ANSYS. Does anybody know how to analysis this problem using FEM? 

Thank you for your kind help in advance.

MichelleLOyen's picture

I'd suggest having a look at a few other pages here on iMechanica concerning mechanics of hydrogels and also concerning poroelasticity , which might be a better approach to consider than a standard viscoelastic response.  Good luck!  It's a very exciting research area.

Zhigang Suo's picture

My group is developing methods to compute large deformation due to swelling and mechanical loads.  It might be interesting for us to apply our methods to your experiment.  What hydrogles are you working with?  Are the polymers covalently cross-linked?  When you unload, does the gel recover its initial shape after some time?

Hi Prof. Suo,

Thank you for your interest about my experiment. The hydrogel microspheres which I am using are alginate microspheres with chitosan coating to reduce pore sizes and encapsulate drugs. Yes, it is covalently cross-linked natural polymeric hydrogels. When I unloaded the force sensor, the microspheres recovered its initial shape time-dependently. The size is about 20 um in diameter. I would like to discuss about your methods a little bit more detail. 

Wei Hong's picture

Hi Keekyoung,

 The FEM code we have now is for hydrogel is for the equilibrium or quasi-static deformation of a gel.  It might be able to tell you the final deformation of your gel spheres, but not the time-dependent process, at least for now.


Xuanhe Zhao's picture

Hi Keekyoung,

What do you mean by "the microspheres recovered its initial shape time-dependently"? Can you explain this point in more details? Thank you.


Hi Wei and Xuanhe,


Currently I have force-deformation data but I could not find an appropriate constitutive equation-the relationship between force and deformation to descrive the exprimental configuration such as a hydrogel sphere compressed by two rigid plate-to extract Young' modulus from the experimental data. Could you tell me there is any force-deformation euqation you derived to build FEM code? 


The time-dependently means the microsphere did not recover its initial shap immediately when I unload the compressive force. The shape was recovered slowly due to viscoelastic hysteresis.


Wei Hong's picture

Hi Keekyoung,

The material model we used to build the FEM code is described in our recent JMPS paper.  Lack of experimental data, we basically extends the Flory-Huggins Model to an arbitrary deformation state.  If you are interested, I am happy to run a FEM simulation of the compression of a gel sphere and show you the result.  But again, the current code is only for static response.  In your experiments, the Force-displacement relation is rate dependent, the result I can give you corresponds to the slowest limit of your experiments.  Let me know if you are interested.  And also, do you know the relative water concentration at the begining?


Xuanhe Zhao's picture

Dear Keekyoung

I would like to ask three more questions:

1. How long does the gel ball take to recover the initial state?

2. What type of covalent crosslink are you using(eg AAD, PEG et al)?

3. Would the mechanical behavior of the gel ball be a lot of difference if you did not use chitosan coating?

thank you. 

Aaron Goh's picture

I would have guessed that a simple hyperelastic + viscoelastic model would be ok?


By the way, I am rather curious.  Have you tried to eat these beads?  Do you know how they behave in the mouth?  Are they 'sticky'?


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