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# Modelling of a living plant cell (tubular shape)

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## Modelling of a living plant cell (tubular shape)

(OP)
First of all, I am biologist and know NOTHING about mechanical engineering or finite element analysis - so please forgive my amateur approach.
I would like to model the stiffness of a single plant cell, a pollen tube. It could be described as a fire hose kind of pipe (length up to several hundred micrometers), diameter ca. 6 micrometers, with an apical, half-sphere shaped dome (same diameter tubular part). The other end of the tube is more complicated and irrelevant in this context. This cellular pipe is filled with cytoplasm (for simplicity: homogeneous liquid). The resistance to local lateral deformation consists of 1. the turgor pressure (internal pressure of a living cell), 2. the cell wall (thickness ca. 100-200 nm).
Hypothetical case: The plasticity and thickness of the cell wall is identical at the apex and the remaining part of the cell. How can I calculate the force I would need to locally deform the apical part of the cell (i.e. cylindrical part directly adjacent to the half-sphere), compared to the more distal part (i.e. the purely cylindrical part further down the pipe). A ratio would be good enough (just to know, whether the apical, dome-shaped part would be stiffer or not)!
One more detail: local indentation of the cylindrical part under pressure needs about 20 times the force compared to indentation of the cylindrical empty tube, i.e. the wall only, without pressure.
Any kind of input, also reference to basic engineering literature (textbook? web site?) would be VERY welcome!!

PS: Any substantial calculations and ideas that would make their way into the scientific paper I am trying to write, will be honored with co-authorship!

### RE: Modelling of a living plant cell (tubular shape)

Roark's Formulas for Stress & Strain ( McGraw-Hill, 6th edition, 1998) by Warren C. Young, chapter 12 would be a good place to start.

I'll post some more information that may be of some use.
If you send me your email address or fax munber I'll will send you some calculations with graphics. ( I don't know if I link images into this forum.

My email address is WeldingEngineer@office.com

GL, Rich

### RE: Modelling of a living plant cell (tubular shape)

Another good reference is:

Timoshenko, S.: "Theory of Elastic Stability," Engineering Societies Monograph, McGraw-Hill Book Company.

Rich

### RE: Modelling of a living plant cell (tubular shape)

You may want to post this to the Aerospace Engineering discussion group.  That is not my area of expertise, but I know that some rockets rely on pressurization of the propellant tanks to stiffen the structure.  This could be analygous to your problem, but yours is probably much more nonlinear due to large (relative term) deflections.

### RE: Modelling of a living plant cell (tubular shape)

I don't think Elastic Stability is what you need but rather Timoshenko's Theory of Elasticity.  I believe I referenced this in the Structural forum.  I still believe that this is a non-linear, inelastic problem and thought it might be good to have some FEA engineers discuss the approach.

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