Discussion Forum

Hi Claire,

You are not solving the same problem as in the text book.

Now comes the interesting part: You are solving the correct problem from a physics point of view; the text book is not.

If you look at the stress contours in the text book, it evident that this is the effect of a force distribution on the surface, and not from actually having a mountain there. The caption under the figure actually says “Stresses below various loads…”

However, as you have noticed in your solution, the stress distribution when the mountain is included is quite different. The solution in the nearfield (which is the relevant part) is not even close to the textbook solution. The textbook solution is the mathematical solution to a different problem, one which is not relevant for the real-world problem.

Two other remarks:
* It looks to me like it is actually the square root of the second invariant that is plotted, and not the second invariant itself (but you need to check that).
* The appropriate boundary condition for infinite half spaces is the Infinite Element Domain (found under Definitions). Then you do not at all need to mesh all the way to infinity.

Bottom line: You cannot trust text books or papers, even by distinguished authors. We encounter that all the time in development. As one of my colleagues noted in passing while implementing the electromagnetic stress tensor: “It is easy to show that Einstein was wrong” (For that case, N.B.. General relativity can still be trusted :-) ).

Hi Henrik,

Thanks for your reply and pointing me toward the right boundary conditions for infinite half spaces.

The caption seems a little ambiguous to me, but it does sound like they might have just been considering a surface load distribution in the book. To check whether I got the solution from the book if I did that in COMSOL, I tried just setting a boundary load condition based on the weight of the mountain on the boundary between the mountain and the halfspace instead of applying gravity to both as I had been. The solution for the second invariant of the stress (which is what the book indicates is being plotted) doesn't look like the solution in the book but the solution for the second invariant of the deviatoric stress does look rather similar (except for higher stresses under the corners of the mountain). So maybe that is what the book is really showing.

Claire

Not my field- but-

Errors in technical books are not uncommon and can even persist through several editions.

Well, to get the text book solution, you should actually remove the mountain altogether. And just use the load.

I think you're right, when I remove the mountain and just use the load, the solution looks basically just like the book solution. Thanks for your help understanding this.