*Egregia
menziesii* Stress and Strain

The material properties of *Egregia menziesii* are really quite
remarkable. Its tough, leathery stipe makes it one of the strongest
macroalga in the Monterey Bay, and perhaps on the whole west coast.
There are two main factors to look at in quantifying the material
properties of an alga.

**Stress **

Stress is an applied force, in this case a force applied to an alga by a wave
passing by. Stress acts in a direction normal to a cross-sectional
area of the plant, like taking two ends of a rachis and pulling.

** Strain **

Strain is the actual deformation of the alga caused by the stress
applied (i.e. the change in length of the alga).
** Strain= e = Change in length / Initial length = D L/ Lo **

Using an extensometer here at Hopkins Marine Station in Mark Denny's
lab, I was able to graph a **stress vs. strain** curve for a piece
of *Egregia menziesii*. This machine exerts a stress force on
a piece of algae while recording its deformation (change in length).

Here is the graph I got from that:

The stress force at the breaking point was found to be 80 Newtons,
quite a lot for an alga, but not uncommon for *Egregia.* The "r" shape of the curve is also not uncommon for *Egregia*.
The slope of the stress vs. strain curve ( s/e ) is a measure of the
stiffness of the material, the **Young's Modulus (E)**. The
non-linearity shows that *Egregia*, unlike other algae, is very
stiff, and you could also say very strong, up to a certain point. As
the force on the alga increases, it gets weaker and weaker before it
breaks, rather than maintaining the same stiffness. I do not know the
mechanism for this. Where the graph begins to loose its linearity, this is where **elasticity** is
lost. As long as the curve is linear, the alga can return to
its original length after the stress is released. Past this point,
though, some permanent deformation has occurred.

Here is a graph showing only the elastically extending portion:

The Youngs Modulus for this piece of *Egregia* is 4 E 7. This
is very stiff for an alga. This also means that *Egregia* is
not as ductile as other algae. That is, the deformation (change
in length) will not be as great before the alga breaks. Above
the elastic area, the alga will be more ductile per unit force.
I would have liked to do more of these tests using the extensometer
to compare the stress vs. strain curves of different pieces of *Egregia
menziesii*. However, I was unable. To make up for
this, I attempted a more low-tech method of gaining the same information. By
attaching a piece of *Egregia menziesii* to a bar, and tying a
bucket to the bottom end, I was able to get some data by adding increments
of water to the bucket, and measuring the length of the algal specimen
with increasing stress. My data were not very good, however,
so a thourough analysis of it would be a bit useless.

However, here are graphs of stress vs. strain to two specimens
of the alga that I tested in this way. Cross sectional area is
not taken into consideration, but was similar for the two. Also,
the force acted upon the alga by the bucket is also not factored in. The
graphs both show **force on the alga due solely to water vs. total
length of the algal specimen**.

The first graph is an intact algal specimen.

For the second graph, I made a small cut on the side of the rachis, to very
crudely simulate damage by, for example, limpet scars.

Unfortunately, there is no great difference between the two graphs.
The slope (what could be the Youngs Modulus with further calculations)
was about 500.4 in both. Also, the total change in length of
the cut rachis was only .2mm greater than that of the intact rachis,
definitely a measurement that could be due to experimental error.
The breaking point of the intact rachis occured at 4500 g of water,
and the cut rachis, 5000 g of water. This is also a measurement
that I can easily say could be due to experimental error.
Fortunately, a great deal of study has been done and published on
the biomechanical properties of *Egregia menziesii*, much of it
in the lab of Mark Denny (owner of the extensometer). Click here to
see some of this work on drag on *Egregia menziesii.*

BACK TO EGREGIA

© 1999 Sarah Present. Contact spresent@stanfordalumni.org for any non-educational use.