Costi, John (rgh)

05-03-2004, 02:23 PM

Dear members

We do a considerable amount of testing (soft tissue and bone) using an

Instron servohydraulic testing machine that often involve the custom design

and manufacture of jigs and fixtures to allow clamping of specimens as well

as ensuring forces and moments are applied in as best a physiological manner

as possible. As you may appreciate, in some cases the stiffness of the test

rig (N/mm or Nm/degree) is substantially less than the stiffness of the

Instron. In these cases we quantify the stiffness of the test rig using

rigid steel blocks in place of the specimen to obtain a "system stiffness".

We then perform our tests on the specimen to obtain a "specimen stiffness".

The stiffness is calculated using linear regression over the most linear

portion of the final cycle of the loading curve (quite often Rsquared values

of 0.98 or better are achieved). The specimen stiffness therefore represents

components of the system stiffness as well as the true specimen stiffness

itself. Usually we are happy to use the specimen stiffness as calculated and

feel this is justified as studies are conducted using the same test rig

having the same system stiffness allowing direct comparisons.

However, in some cases, modifications may be made to test rigs thereby

changing its system stiffness and any subsequent specimen tests would

produce a stiffness that may be different due to the change in system

stiffness. Once again this is acceptable so long as we do not wish to

compare the specimen stiffnesses to specimens tested using the original test

rig. If we wish to compare specimen stiffnesses to earlier tests then the

differences in system stiffness between specimens must be taken into

account. This is particularly important if the system stiffness is not at

least an order of magnitude larger than the specimen stiffness.

My question is: has anyone encountered this before and if so what steps were

taken to adjust the specimen stiffnesses so that they were comparable?

I believe that the stiffness may be adjusted on the assumption that the

region where the stiffness is calculated is linear, which seems to be the

case in the majority of the testing we do, although it is clear that the

overall specimen behaviour is nonlinear and viscoelastic. The method I have

used to adjust the stiffness is quite simple and is outlined as follows

(apologies for the messy terminology in advance!):

Let: S represent the stiffness of the specimen tested in the rig

SRig represent the system stiffness of the rig using steel

blocks

SAdj represent the desired adjusted stiffness of the specimen

after taking into account the system stiffness

At the same force (F), the adjusted displacement (d_Adj) can be calculated

as the displacement of the specimen minus the displacement of the system

(d_S - d_SRig). It follows then that SAdj can be calculated between the

linear range of forces (F2 and F1) as:

SAdj = (F2 - F1) / (d_Adj2 - d_Adj1)

SAdj = delta_F / (d_Adj2 - d_Adj1)

And substituting for d_Adj we have:

SAdj = delta_F / [(d_S2 - d_SRig2) - (d_S1 - d_SRig1)]

Or:

SAdj = delta_F / [(d_S2 - d_S1) - (d_SRig2 - d_SRig1)]

Simplifying:

SAdj = delta_F / (delta_d_S - delta_d_SRig)

Assuming that the stiffnesses were calculated over the same force range

delta_F we have:

delta_d_S = delta_F / S and:

delta_d_SRig = delta_F / SRig

We know delta_F, S and SRig therefore we can substitute and simplify to

obtain:

SAdj = delta_F / [(delta_F / S) - (delta_F / SRig)]

I have verified this method using the above formula and also by using

experimental data and adjusting the displacements at the same force and then

using linear regression to calculate the adjusted stiffness and found that

both methods produce the same adjusted stiffness.

I'd appreciate any comments or suggestions with using this method and will

post a summary of replies in due course.

Kind regards

John Costi

Biomechanical Engineer, Final Year PhD Candidate & COES (SF-36 software)

Developer

Department of Orthopaedics

Division of Surgery

Repatriation General Hospital

Daws Road, Daw Park

SA, AUSTRALIA 5041

Phone: +61 8 8275 1126

Fax: +61 8 8374 1998

Email: John.Costi@rgh.sa.gov.au

http://som.flinders.edu.au/FUSA/ORTHOWEB/index.html

http://www.sf36.com.au

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We do a considerable amount of testing (soft tissue and bone) using an

Instron servohydraulic testing machine that often involve the custom design

and manufacture of jigs and fixtures to allow clamping of specimens as well

as ensuring forces and moments are applied in as best a physiological manner

as possible. As you may appreciate, in some cases the stiffness of the test

rig (N/mm or Nm/degree) is substantially less than the stiffness of the

Instron. In these cases we quantify the stiffness of the test rig using

rigid steel blocks in place of the specimen to obtain a "system stiffness".

We then perform our tests on the specimen to obtain a "specimen stiffness".

The stiffness is calculated using linear regression over the most linear

portion of the final cycle of the loading curve (quite often Rsquared values

of 0.98 or better are achieved). The specimen stiffness therefore represents

components of the system stiffness as well as the true specimen stiffness

itself. Usually we are happy to use the specimen stiffness as calculated and

feel this is justified as studies are conducted using the same test rig

having the same system stiffness allowing direct comparisons.

However, in some cases, modifications may be made to test rigs thereby

changing its system stiffness and any subsequent specimen tests would

produce a stiffness that may be different due to the change in system

stiffness. Once again this is acceptable so long as we do not wish to

compare the specimen stiffnesses to specimens tested using the original test

rig. If we wish to compare specimen stiffnesses to earlier tests then the

differences in system stiffness between specimens must be taken into

account. This is particularly important if the system stiffness is not at

least an order of magnitude larger than the specimen stiffness.

My question is: has anyone encountered this before and if so what steps were

taken to adjust the specimen stiffnesses so that they were comparable?

I believe that the stiffness may be adjusted on the assumption that the

region where the stiffness is calculated is linear, which seems to be the

case in the majority of the testing we do, although it is clear that the

overall specimen behaviour is nonlinear and viscoelastic. The method I have

used to adjust the stiffness is quite simple and is outlined as follows

(apologies for the messy terminology in advance!):

Let: S represent the stiffness of the specimen tested in the rig

SRig represent the system stiffness of the rig using steel

blocks

SAdj represent the desired adjusted stiffness of the specimen

after taking into account the system stiffness

At the same force (F), the adjusted displacement (d_Adj) can be calculated

as the displacement of the specimen minus the displacement of the system

(d_S - d_SRig). It follows then that SAdj can be calculated between the

linear range of forces (F2 and F1) as:

SAdj = (F2 - F1) / (d_Adj2 - d_Adj1)

SAdj = delta_F / (d_Adj2 - d_Adj1)

And substituting for d_Adj we have:

SAdj = delta_F / [(d_S2 - d_SRig2) - (d_S1 - d_SRig1)]

Or:

SAdj = delta_F / [(d_S2 - d_S1) - (d_SRig2 - d_SRig1)]

Simplifying:

SAdj = delta_F / (delta_d_S - delta_d_SRig)

Assuming that the stiffnesses were calculated over the same force range

delta_F we have:

delta_d_S = delta_F / S and:

delta_d_SRig = delta_F / SRig

We know delta_F, S and SRig therefore we can substitute and simplify to

obtain:

SAdj = delta_F / [(delta_F / S) - (delta_F / SRig)]

I have verified this method using the above formula and also by using

experimental data and adjusting the displacements at the same force and then

using linear regression to calculate the adjusted stiffness and found that

both methods produce the same adjusted stiffness.

I'd appreciate any comments or suggestions with using this method and will

post a summary of replies in due course.

Kind regards

John Costi

Biomechanical Engineer, Final Year PhD Candidate & COES (SF-36 software)

Developer

Department of Orthopaedics

Division of Surgery

Repatriation General Hospital

Daws Road, Daw Park

SA, AUSTRALIA 5041

Phone: +61 8 8275 1126

Fax: +61 8 8374 1998

Email: John.Costi@rgh.sa.gov.au

http://som.flinders.edu.au/FUSA/ORTHOWEB/index.html

http://www.sf36.com.au

-----------------------------------------------------------------

To unsubscribe send SIGNOFF BIOMCH-L to LISTSERV@nic.surfnet.nl

For information and archives: http://isb.ri.ccf.org/biomch-l

Please consider posting your message to the Biomch-L Web-based

Discussion Forum: http://movement-analysis.com/biomch_l

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