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Carolyn Small
06-28-1994, 12:28 AM
---------- Forwarded message ----------
Date: Tue, 28 Jun 1994 09:46:56 -0400 (EDT)
From: Carolyn Small
To: "Kenneth R. St. John"
Subject: Re: Von Mises Stresses



On Mon, 27 Jun 1994, Kenneth R. St. John wrote:

> I would appreciate a leg-up on a question someone has asked me...
> One of my colleagues walked in and asked me what von Mises stresses are.
> I recall that I should be able to answer the question since I have
> previously been exposed to the term but I can't remember and the texts
> available to me don't have the info. >
>
> ************************************************** ******************
> Kenneth R. St. John, Assistant Professor Voice: (601) 984-6199
> Orthopaedic Research and Biomaterials Fax: (601) 984-6087
> University of Mississippi Medical Center Fax: (601) 984-6014
> 2500 North State Street Fax: (601) 984-5151
> Jackson, MS 39216-4505 Internet: stjohn@fiona.umsmed.edu
> ************************************************** ******************

Dear Sir, you have pushed one of my buttons! There is no such thing as a
Von Mises "stress"; this is one of the most widely misused terms in
biomedical engineering, for my money. Three cheers for the colleague who
asked the question.

In solid mechanics, we try to predict failure of a material under
stress by comparing certain stress or strain parameters to the limits of
performance we observe when the material is subjected to uniaxial (usually
tension) loading. Some of the criteria include the maximum normal stress
at a point (generally good for brittle materials), the maximum normal
strain (not used much anymore in metals), the maximum shear stress (very
common usage; also known as the Tresca criterion), and the maximum
distortion energy criterion (the infamous Von Mises; also known as the
maximum octahedral shear stress criterion).

Glossing over the preamble and warnings about how this is an
engineering estimate of how to extrapolate from one situation (uniaxial
tension) to a completely different one (three-dimensional stress state),
the criterion boils down to this: failure is predicted when the sum of the
squares of the differences of the principal stresses at a point attain the
same level as they do at failure during a tensile test.

(S1-S2)^2 + (S2-S3)^2 + (S3-S1)^2 = 2*Sy^2

where S1, S2, S3 are the principal stresses, and Sy is the
material's yield stress from the tensile test.

I *think* what people are reporting as a Von Mises stress may be the
octahedral shear stress, which is one third of the square root of the left
hand side of the above equation; it's another imaginary "stress" engineers
dreamed up and is related to the distortion strain energy intensity.

Now, the reason we use the Von Mises criterion at all in engineering
is because for some ductile materials it has been shown experimentally to
predict failure better than the maximum shear stress criterion, and is a
bit less conservative, which has economic implications. Why it's in such
widespread use in biomechanics is beyond me; I am aware of no studies
which demonstrate the Von Mises criterion to be a better predictor of
multiaxial stress failures than the Tresca criterion. And the latter is a
whole lot simpler to use in design calculations.

Y'know, I think I just realized the "why".... Can it be that so many
use it because the calculation is easy for a computer to do? And so many
use finite element stress analysis packages? Hmmm... it has that ring of
truth.... (not to mention supporting all my belief systems about how
sloppy we can get in the face of raw computing power...!)

Carolyn F Small, PhD, PEng, CCE
Associate Professor, Mechanical Engineering
Queen's University
Kingston, Ontario
Canada K7L 3N6