Cai Shengqiang's blog

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Equations of state for ideal elastomeric gels

Submerged in a solvent-containing environment and subject to applied forces, a covalent polymer network absorbs the solvent and deforms, forming an elastomeric gel.  The equations of state are derived under two assumptions.  First, the amount of the solvent in the gel varies when the gel changes volume, but remains constant when the gel changes shape.  Second, the Helmholtz free energy of the gel is separable into the contribution due to stretching the network and that due to mixing the polymer and the solvent.  We demonstrate that these equations of state fit several sets of experimental data in the literature remarkably well.

The paper will be published in EPL and can be downloaded from


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Creasing instability of elastomer films

The creasing instability of elastomer films under compression is studied by a combination of experiment and numerical simulation.  Experimentally, we attach a stress-free film on a much thicker and stiffer pre-stretched substrate.  When the substrate is partially released, the film is uniaxially compressed, leading to formation of an array of creases beyond a critical strain.  The profile of the folded surface is extracted using confocal fluorescence microscopy, yielding the depths, spacings, and shapes of creases.  Numerically, the onset and development of creases are simulated by introducing appropriately sized defects into a finite-element mesh and allowing the surface of the film to self-contact.  The measurements and simulations are found to be in excellent agreement.


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Mechanics and chemical thermodynamics of phase transition in temperature-sensitive hydrogels


This paper uses the thermodynamic data of aqueous solutions of uncrosslinked poly(N-isopropylacrylamide) (PNIPAM) to study the phase transition of PNIPAM hydrogels.  At a low temperature, uncrosslinked PNIPAM  can be dissolved in water and form a homogenous liquid  solution.  When the temperature is increased, the solution separates into two liquid phases with different concentrations of the polymer.   Covalently crosslinked PNIPAM, however, does not dissolve in water, but can imbibe water and form a hydrogel.  When the temperature is changed, the hydrogel undergoes a phase transition:  the amount of water in the hydrogel in equilibrium changes with temperature discontinuously. While the aqueous solution is a liquid and cannot sustain any nonhydrostatic stress in equilibrium, the hydrogel is a solid and can sustain nonhydrostatic stressin equilibrium.  The nonhydrostatic stress can markedly affect various aspects of the phase transition in the hydrogel. 


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Poroelasticity of a covalently crosslinked alginate hydrogel under compression

This paper studies the poroelastic behavior of an alginate hydrogel by a combination of theory and experiment. The gel—covalently crosslinked, submerged in water and fully swollen—is suddenly compressed between two parallel plates. The gap between the plates is held constant subsequently, and the force on the plate relaxes while water in the gel migrates. This experiment is analyzed by using the theory of linear poroelasticity. A comparison of the relaxation curve recorded in the experiment and that derived from the theory determines the elastic constants and the permeability of the gel. The material constants so determined agree well with those determined by using a recently developed indentation method.


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Osmotic collapse of a void in an elastomer: breathing, buckling and creasing

This paper studies the collapse of a void in an elastomer caused by osmosis. The void is filled with liquid water, while the elastomer is surrounded by unsaturated air.  The difference in humidity motivates water molecules to permeate through the elastomer, from inside the void to outside the elastomer, leaving the liquid water inside the void in tension.  When the tension is low, the void reduces size but retains the shape, a mode of deformation which we call breathing.  When the tension is high, the void changes shape, possibly by two types of instability:  buckling and creasing.  The critical conditions for both types of instability are calculated.  A tubular elastomer collapses by buckling if the wall is thin, but by creasing if the wall is thick.  As the tension increases, a thin-walled tube undergoes a buckle-to-crease transition.

This paper can be found at http://www.seas.harvard.edu/suo/papers/233.pdf


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Dynamic fracture mechanics

Dynamic fracture mechanics is written by a very well known professro-L B Freund. Honestly, I have only read a small part of the book. However, I recommend this book because after reading this book, you can learn many things which haven't be touched in the class, as stated by Zhigang in the beginning of the class.

Generally speaking, dynamic fracture just include the inertia effect during the fracture process. The inertia effect can either from fast loading or the stress wave radiated from the crack tip. The concept of dynamic fracture in earthquake and other geophysics phenonmenon become extremmely import. The prediction of crack path and the instability of crack propagation also make the study of dynamic fracture important.


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A theory of constrained swelling of a pH-sensitive hydrogel

Many engineering devices and natural phenomena involve gels that swell under the constraint of hard materials. The constraint causes a field of stress in a gel, and often makes the swelling inhomogeneous even when the gel reaches a state of equilibrium. To analyze inhomogeneous swelling of a pH-sensitive gel, we implement a finite element method in the commercial software ABAQUS.  The program is attached here.  Contact Shenqiang Cai (shqcai@gmail.com) for a description of the program.


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Poroelasticity and diffusion in elastic solids

These are slides of poroelasticity and diffusion in elastic solids for final presentation based on ES241 notes.


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University lecturership in Engineering Science in Oxford

Here is a position for University lecturership in Engineering Science(Solid or Structural Mechanics)in association with a Tutorial fellowshiip at Pembroke College. 


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A University Lectureship in Solid Mechanics available in the Engineering Science Department at Oxford

Here is a Lectureship in Solid Mechanics available in the Engineering Science Department at Oxford posted by Prof.Alan Cocks.

We currently have a University Lectureship in Solid Mechanics available in the Engineering Science Department at Oxford.  I have attached a copy of the advert and further particulars. I would be grateful if you could pass this information on to anybody who you think would be interested in this post.  We would welcome applications from candidates with significant potential for research in solid mechanics and are particularly interested in strengthening our activity in the area of high strain rate mechanics.


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ES 240 Final Project

Attachment is my small final project. My name is Shengqiang Cai.


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A E Love -Treatise on the Mathematical Theory of Elasticity

I recommend this classic book to persons, who want to learn something more about elasticity that cannot be found in traditional books. It's a pretty valuable and inspiring book in elasticity today, although it was written by Love more than 100 years ago. It included many  impressive topics such as equilibirum of anistropic elastic solid bodies, the equilibrium of a elastic sphere, plates and shells. As far as I know, this book is frequently quoted in recent artilces. However, it will be very tough to read this book, even though you have some basic knowledge about elasticity.  I have only scanned some chapters.  Everyone should have a try.


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ES 240 Problem 6

I have got the master degree of Solid Mechanics in University of Science and Technology of China. Actually, I have taken several courses related to this subject, such as strength of materials and the theory of elasticity. So, my strength may be that I have some  knowledge about it, but my poor ability to solve PDE or even ODE could be the specific obstacle for studying this course. I will do research in Suo’s group(http://www.seas.harvard.edu/suo/), and my research may be related to soft matters, such as gels. Obviously, this course is essential for my future research, especially the topic about finite deformation.


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