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# Lianhua Ma's blog

## How to understand the shear modulus of polymers

Fri, 2010-12-10 01:56 - Lianhua MaHi 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

Sat, 2010-03-13 00:38 - Lianhua Ma

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.

Sat, 2009-07-04 01:01 - Lianhua MaDear 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

Fri, 2009-07-03 22:33 - Lianhua MaDear 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

Sun, 2008-12-14 03:32 - Lianhua MaRecently, 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

Sun, 2008-12-14 02:50 - Lianhua Ma
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 )

Mon, 2007-10-15 00:28 - Lianhua MaThe 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!

Best

Marc

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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

Sun, 2007-10-14 22:08 - Lianhua Macontinuity 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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