Its done using a mathematical calculation called hoop stress.
https://www.engineersedge.com/calculators/hoop-stress.htm
A quick and dirty example:
We will use 2 calculations. One, to find the pressure inside the suppressor and two, to find the maximum allowable hoop stress for the suppressor material. In this 'dirty' example im going to cut alot of corners fore the sake of explanation.
We will use the simple algebraic p=f/a and work it backwards and forwards a couple times.
A 6.5 creedmoor has a saami maximum chamber pressure of 62000 psi. So first we will set p to 62000.
So, now were at 62000=f/a
Now we will calculate the inner sirface area of a 6.5 creedmoor loaded round. (Im gonna cut corners). (.473×pi x1.75=2.4025"^2
So, we go with 62000=f/2.4025, then solve for f. F=148955
So now we will rework it for p, using the new calculations for f and a. But this time we recalculate a to include the area of the barrel. We will assume a 24" barrel. So for a, we use 2.4025+(.264)(pi)(24)=22.308
So, back to p=f/a we use p=148955/22.308 and solve for p. For p we have 6677.201 psi at the muzzle.
Now we work it over again, but include the area of the silencer. Again, dirty and cutting corners. We will assume a 1.5"od'8"long silencer. So, using the previous calculations for the area of the cartridge and bore, but now adding the silencer we get 22.308+(1.5)(pi)x8= 60.007 inches squared
So now, back to p=f/a to solve for p again.
P=148955/60.007 and we get 2482.294 psi inside the silencer.
So, now that we know the pressure inside the silencer, we can use the hoop stress for thin wall pressure vessels calculation to check to find the minimum wall thickness for the silencer.
This part gets complicated, so im going to use engineers edge hoop stress calculator linked above:
For a 4130 chromoly silencer, using a tensile rating of 63100 psi and assuming perfect surface finishes, welds, and assuming a bunch of other shit you should never assume, i get a minimum wall thickness of .030". Using the above numbers, below .030ish wall thickness, it blows up in your face.
So, obviously youd want lots of margine for error.
As the barrel length is reduced, pressure goes way up.
As the silencer inner area, aka volume, goes down, pressure goes way up.
Welds have heat affected zones that can create spots weaker than the steels max tensile load.
Poor surface finishes give sharp microtroughs that give cracks a place to start.
Baffles inside the suppressor reduce volume and increase pressure.
The algebraic formulas above can be increased in accuracy and reduced in complexity by integrating the increase of area with respect to the bullets movement down the bore with the change in pressure, but i figured a calculus function would be harder to follow and visualize.
For me anyway, using the algebraic solutions, while not as accurate, lets me see whats going on in my head.
I used to manufacture suppressors, and for a typical .308 suppressor that i intended to be used on and "rated for" use on barrels as short as 16", i used 4130 steel at a wall thickness of .062", with tig fusion welded end caps.
As an example of how barrel length changes pressure at the muzzle, the above example had the 24" creedmoor putting 6700ish psi at the muzzle.
The same gun with a 16" barrel produces 9500 psi at the muzzle.
Please please,! dont use any of the mathy shit above to make a silencer. I rushed through it, didnt double check or verify anything. Its just a dirty example of how its done! Overbuild it?
Another random thought, but cool as shit nonetheless.
You can use the above to calculate the force applied to the bullet at any given point as it moves down the bore, and using force mass acceleration method, f=m×a calculate the rate of change of velocity for the bullet. For example, in the throat the bullet has 3394 lbs of force pushing against the base.
So, the bullet has 3394lbs of force, so 3394=m×a
So now we find mass. A 140 grain bullet weighs .02lbs. So the mass is .0062 slugs.
So now 3394=.0062×a and we solve for accelleration. A=547419 feet per second squared.
So, at accelerating at 547,419 feet per second per second, how long does it take to get to 2700fps?
0.0027 seconds. ☺ not very long.
But, the formula above is an oversimplification too. But it wont be far off.
People dont like us nerds much, till theyre looking out the winder of their 747-8, looking down at a cloud layer 3 miles below them as its climbing through 35,000 feet. Then that shits a big deal. ? 900,000 lbs and 100,000 horsepower going 500mph
Seems like a miracle, but its engineering!
Time to go clean my pocket protector anf get another juice box.
