Mohr’s Circle—When Was the Last Time You Used It in Your Professional Engineering Work?

As a consultant in computational mechanics, I currently help write some FEM-related code, and while doing this job, an episode from a recent past came to my mind. Let me go right on to the technical issue, keeping aside the (not so good) particulars of that episode. (In case you are curious: it happened outside of my current job, during a job interview.)

If you are a design engineer, FE analyst, researcher, or any professional dealing with stress analysis in your work, I seek answers to a couple of questions from you:

Question 1:
When was the last time you used Mohr’s circle of strain/stress in your professional work? Was it a week ago? a month? a year? five years? ten years? longer? In what kind of an application or research context?

Please note, I do not mean to ask whether you directly or indirectly used the coordinate transformation equations—the basis for constructing Mohr’s circle—to find the principal quantities. The question is: whether you spoke of Mohr’s circle itself—and not of the transformation equations—in a direct manner, in a professional activity of yours (apart from teaching Mohr’s circles). In other words, whether, in the late 20th and early 21st century, there was any occasion to plot the circle (by hand or using a software) in the practice of engineering, did it directly illuminate something/anything in your work.

In case you are curious, my own answer to this question is: No, never. I would like to know yours.

Question 2:
The second question just pursues one of the lines indicated in the first.

In a modern FEM postprocessor, visualizations of stress/strain patterns are provided, usually via field plots and contour lines.

For instance, they show field plots of individual stress tensor components, one at a time.

Recently, there also have been some attempts to try to directly show tensor quantities in full directly, via systematically arranged ellipsoids of appropriate sizes and orientations. The view you get is in a way analogous to the arrow plots for visualizing vector fields in those CFD and EM software packages. Other techniques for tensor visualization are not, IMHO, as successful as the ellipsoids. Mostly, all such techniques still are at the research stage and have not yet made to the commercial offerings.

Some convenience can be had by showing some scalar measures of the tensors such as the von Mises measure, in the usual field/contour plots.

The questions here are:

(2.a) Would you like to see an ellipsoids kind of visualization in your engineering FEM software? If yes, would this feature be a “killer” one? Would you consider it to be a decisive kind of advantage?
(2.b) Would a simpler, colored cross-bars kind of visualization do? That is, two arrows aligned with the principal directions. The colors and the lengths of the arrows help ascertain the strength of the principal quantities.
(2.c) Would you like to see Mohr’s circles being drawn for visualization or any other purposes in such a context? If yes, please indicate the specific way in which it would help you.

My own answers to question 2 are: (a) Ellipsoids would be “nice to have” but not “killer.” I wouldn’t be very insistent on them. Having them is not a decisive adavantage. (b) For 2D, this feature should be provided. (c) Not at all.

Please note, the questions are directed rather at experienced professionals, even engineering managers, but not so much at students as such. The reason is that the ability to buy is an important consideration here, apart from the willingness. Of course, experienced or advanced PhD students and post-docs may also feel free to share their experiences, thoughts and expectations.

Thanks in advance for your comments.

Also posted at iMechanica, here [^].

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2 thoughts on “Mohr’s Circle—When Was the Last Time You Used It in Your Professional Engineering Work?

  1. I use Mohr’s circle plot a few time per year. Typically when I know the prinipal stresses and want to estimate the normal and shear stress on a plane. Usually I am just sketching the circle to get an estimate. The other condition where Mohr’s circles are sometimes used is in plots to obtain the failure envelope of rock based on uniaxial and triaxial compression tests on rock core. One method is to plot the principal stresses and the Mohr’s circle for each test and construct an envelop to be tangent to these.

    • Thanks.

      (1) What is the context in which prior computations (or computations) are done in such a way that you do have the principal stresses and directions at a point but not the normal and shear components (w.r.t. a local or a global coordinate frame).

      (2) Does the plane of interest lie within the volume, or does it coincide with a contact surface/free boundary?

      If the former, what kind of an application consideration requires separately knowing the normal and shear components w.r.t. a reference plane that is neither local nor global nor principal.

      If the latter, why doesn’t the computational tool already provide you with this information, and therefore recourse has to be made to Mohr’s circle?

      … Just wondering, that’s all!

      (3) BTW, I am not too clear on the use specifically of Mohr’s circle in building failure envelope in the stress space. Will have to look up a book or so before I come back on that respect.

      Thanks, again!

      –Ajit

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