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

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