Biophysics Q: Impact of stiffness (Young's modulus) on stress failure

[DNA105]

TL;DR

I'm trying to determine the impact of stiffness (Young's modulus) on the tendency of 'stress failure' with a given strain.

Hi. I'm a physician trying to understand the micromechanics of lung injury due to overdistension. The basic idea is that overstretching of the plasma membrane of the lung epithelial cell causes "stress failure" --> i.e. plasma membrane rupture --> cell death. The concepts of stress, strain, and Young's modulus (E) are utilized to study this: Stress = E x Strain, or Strain = Stress/E

Say object 1 has a stress = x, strain = y

Say object 2 has Young's modulus twice that of object 1, and the same stress (x) is applied
hence for stress = x, strain = y/2

So object 2 sees same stress (x) but half the strain (y/2) compared to object 1. What can be said about its chances/tendency for 'stress failure' compared to object 1: same or half?!

Would appreciate any insight.

Best.

 

[jrmichler]

One way to look at it:
Stress breaks things.
Strain is how far it stretches before it breaks.
That would imply that stress is the sole determinant of cell death.

But you have to be careful. Do the less flexible cells (higher Young's modulus) die at the same stress as the more flexible cells?

Side question: Is this related to the operation of ventilators?

 

[DNA105]

Thank you for the response. So the stress at which failure occurs may vary if alteration/remodeling occurs in an object. Makes sense!

And yes, this is in relation to ventilation induced lung injury (specifically overdistension injury due to large tidal volumes)

 

[Chestermiller]

The failure criterion of an object (or membrane) is somewhat separate from the stiffness behavior of the material. The failure is usually characterized by a critical stress level (expressed 3 dimensionally in terms of the principal stresses of the material). Google failure criteria.

 

[Tom.G]

This is just an information point for those interested. The following has been gleened from various on-line and off-line sources by an amateur and is not guaranteed 100% accurate. I'm sure @DNA105 can correct and expand on this!

A critical parameter during ventilator use is to not force a high tidal volume. During severe lung impairment, in COVID-19 for instance, some of the air sacs (alveoli) in the lung swell and the inner walls stick together; these are said to have 'collapsed'.

Just like a wet balloon or a wet plastic bag, the walls of the alveoli are then stuck together. It is sometimes possible to re-inflate them with a higher pressure from the ventilator (forcing a higher tidal volume), however the higher pressure can over-extend the non-collapsed alveoli, causing them to fail. A slight positive pressure is still used during exhalation though to help keep the functioning alveoli open and functioning.