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How to understand the shear modulus of polymers

Hi everybody,

I have a question about the shear modulus of polymers. As we know, the general engineering polymers (rubbers) are highly extensible and elastic. The shear modulus,G, for the polymers subjected to the small-strain conditions, can be defined by G=NkT, where N is the number of network chains, k is Boltzmann's constant and T is temperature in Kelvins.

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Maxwell stress of a dielectric elastomer subjected to electric field


Hello everyone,

As reported in some references, Maxwell stress of a dielectric  elastomer subjected to electric field can be determined by the following formula

P=e*E^2    (1) -------e=e0*e1, e0 is the dielectric permittivity of vacuum, e1 is the relative dielectric permittivity of the elastomer, and E is the applied electric field.

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Some problem concerning the position of increment in ABAQUS subroutines.

Dear all,


 I have a puzzling question. 

As we know, the positions of a increment in a FEM analysis ( in abaqus) include :

 1.  the start of the increment    2.    the end of the increment   3.     the current increment     etc

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Deduction of derivatives of free-energy density function in ABAQUS UHYPER

Dear xuanhe and all,

I have reviewed the paper "Method to analyze programmable deformation of dielectric elastomer layers". (Xuanhe zhao, Zhigang Suo)

It is very insteresting.

I have one question you would like to ask you.  Hope to get your reply.

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About osmotic pressure

Recently, I studied  Prof.Suo's lecture "Advanced Elasticity", node/725.

The following is explaination about osmosis pressure in the lecture.

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ABOUT Work done by a pressure applied to a system

I have one question  about work done by a pressure applied to a system.  The book of Thermodynamics often always present pdV (where dV is the change in the volume of the system. )but never Vdp, Why is that? Is it because we don't treat p as a variable? In a grand canonical ensemble is pressure constant for any system?

Acording to Thermodynamics first law,  du=dq-dw , where dw denotes work done by pressure and external force.  dw=pdv+dw' .   dq=Tds (Thermodynamics second law)

so, dU=TdS-Pdv-dw' 

finally, dG=vdp-sdT-dw'

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Cell mechanics-----Soft Tissue (MICROSCOPIC BIOMECHANICS )

The cells of our bodies represent a very large class of systems whose structural components often are both comlex and soft. Most cells have a complex internal structure of biological rods,ropes and sheets.

cell mechanics is vital to tissue formation!

I need some introductory materials to be familiar with cell mechanics and soft tissues in biomechanics. I will appreciate your help and guidance!



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continuity e.q.,equilibrium e.q. ,N-S , constitutive e.q. for elastic solid and compressible fluid in the space-frequency domain

continuity e.q.,equilibrium e.q. ,N-S , constitutive e.q. for elastic solid and compressible fluid in the space-frequency domain, as shown in the following Fig.

i don't understand how can this author deduce? why v=iwu? is this assumption?  why is this necessary?    thanks for your help and guidance!


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