Tom Impelluso

07-10-1999, 04:02 AM

Hi all,

This may not be the best group to ask this... if not, could you

suggest a more appropriate one?

>From what I understand, there are three classifications of elastic

material properites:

hyper-elastic (strain energy function, integral formulation)

elastic (stress/strain law, algebraic formulation)

hypoe-lastic (rate dependent law, differential formulation)

It seems that most constitutive laws for biological tissues are

written as hyperelastic.

Could someone explain why?

I will hazard a guess...

The field of biomechanics took off before the very widespread

development of large scale finite element codes. At such a time, the

hyper elastic formulation was easier to work with since it postulated

an integral formulation for ONE parameter -- strain energy -- from

which stress could be found by the simple act of differentiation..

It seems that a HYPOelastic formulation seems more natural yet

I continue to see papers pushing hyperelasticity.

I claim HYPO- seems more natural because it is a rate dependent formulation

which accounts for change of frame (Jaumann stress rate). This, it seems

to me, is essential when modelling human tissue which typically

undergoes large deformation...

and while (and *if* you're at it)... try this one one for size...

(because, this too, has been frustrating me...

but this next question is not as essential as the previous so

I am boxing it in between the dashes)

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

A Hyperelastic material is one which possesses a strain energy function.

An elastic material is one where there is a natural stress free state,

AND

there is a one to one relationship between stress and strain.

A Hypoelastic material is one where the stress rates are linear

functions

of the strain rates (thus becoming a differential equation).

Now, typically, when I see hyper, hypo, etc, I feel the need to

contextualize

this in terms of comparatives... soft, softer, softest.... all embody

degrees of softness.

Yet, I try to search for comparatives in the three types of elasticity

above

and come out empty handed...

One person suggested that I view it this way:

Hyperelastic is one involving integration: the strain energy is the

INTEGRAL of stress, strain terms

Elastic is ALGEBRAIC

and

Hypoelastic is DIFFERENTIAL.

This only pushes my question back because then I cannot see how the

mathematical formulations introduce comparatives.

So... I try this...

If there is a strain energy function, then, internal stress work can

be related to the work of the applied loads. This definition causes

me to state that the material returns to the original configuration

if energy is conserved.

COntinuing...

It seems that NOTHING in the definition of elastic or hypoelastic

states the RETURN to a stress free state.

OK... Now I must see how hypoelastic differs from elastic.

Well, in a hypoelastic material, we are relating rates of deformation

while in an elastic material we at least still have the one to one

correspondence...

I think...

But, basically, I must conclude I am still baffled and ask if someone is

willing to respond to me...

Surely, I will read the response and answer back with a question unless

perhaps you can, hopefully, put this issue to rest in one clean

answer... (which I am coming to doubt is possible)

[where am I going wrong?]

Another way to phrase this is to ask for a definition of ELASTIC

than has the potential to demonstrate gradations of elastiticity,

and exactly how the integral, algebraic, and derivative formulations

embody these gradation...

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

Could someone tackle these for me?

Thanks

Tom

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

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

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

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

This may not be the best group to ask this... if not, could you

suggest a more appropriate one?

>From what I understand, there are three classifications of elastic

material properites:

hyper-elastic (strain energy function, integral formulation)

elastic (stress/strain law, algebraic formulation)

hypoe-lastic (rate dependent law, differential formulation)

It seems that most constitutive laws for biological tissues are

written as hyperelastic.

Could someone explain why?

I will hazard a guess...

The field of biomechanics took off before the very widespread

development of large scale finite element codes. At such a time, the

hyper elastic formulation was easier to work with since it postulated

an integral formulation for ONE parameter -- strain energy -- from

which stress could be found by the simple act of differentiation..

It seems that a HYPOelastic formulation seems more natural yet

I continue to see papers pushing hyperelasticity.

I claim HYPO- seems more natural because it is a rate dependent formulation

which accounts for change of frame (Jaumann stress rate). This, it seems

to me, is essential when modelling human tissue which typically

undergoes large deformation...

and while (and *if* you're at it)... try this one one for size...

(because, this too, has been frustrating me...

but this next question is not as essential as the previous so

I am boxing it in between the dashes)

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

A Hyperelastic material is one which possesses a strain energy function.

An elastic material is one where there is a natural stress free state,

AND

there is a one to one relationship between stress and strain.

A Hypoelastic material is one where the stress rates are linear

functions

of the strain rates (thus becoming a differential equation).

Now, typically, when I see hyper, hypo, etc, I feel the need to

contextualize

this in terms of comparatives... soft, softer, softest.... all embody

degrees of softness.

Yet, I try to search for comparatives in the three types of elasticity

above

and come out empty handed...

One person suggested that I view it this way:

Hyperelastic is one involving integration: the strain energy is the

INTEGRAL of stress, strain terms

Elastic is ALGEBRAIC

and

Hypoelastic is DIFFERENTIAL.

This only pushes my question back because then I cannot see how the

mathematical formulations introduce comparatives.

So... I try this...

If there is a strain energy function, then, internal stress work can

be related to the work of the applied loads. This definition causes

me to state that the material returns to the original configuration

if energy is conserved.

COntinuing...

It seems that NOTHING in the definition of elastic or hypoelastic

states the RETURN to a stress free state.

OK... Now I must see how hypoelastic differs from elastic.

Well, in a hypoelastic material, we are relating rates of deformation

while in an elastic material we at least still have the one to one

correspondence...

I think...

But, basically, I must conclude I am still baffled and ask if someone is

willing to respond to me...

Surely, I will read the response and answer back with a question unless

perhaps you can, hopefully, put this issue to rest in one clean

answer... (which I am coming to doubt is possible)

[where am I going wrong?]

Another way to phrase this is to ask for a definition of ELASTIC

than has the potential to demonstrate gradations of elastiticity,

and exactly how the integral, algebraic, and derivative formulations

embody these gradation...

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

Could someone tackle these for me?

Thanks

Tom

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

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

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

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