Gangming Luo

07-13-1999, 12:43 AM

Dear Biomch-l subscribers,

Last week I posted a message about FEA biphasic model for soft

tissues. I have received a lot of feedback. Thank to all people for

their encouraging and helpful replies. The following is a summary of

responses starting with my original question.

>>>> Original Message: >>>>

I am trying to use biphasical model to simulate soft issues, e.g.

muscle, fat..., mechanical behavior. At this time, I am using MARC 7.2

(MARC Analysis Research Corporation). In the FEA package, there is a

soil model that allows a fully solid-fluid coupled approach with

following features and limits.

(1) The fluid behavior is modeled using Darcy's law and the fluid is

assumed to be slightly compressible.

(2) The solid behavior is defined by

(a) linear elasticity: the Young's moduli and the Poisson ratio;

(b) non-linear elasticity: hypoelastic model.

(In MARC 'User Information' book, it states the solid grains are assumed

to be incompressible. It seems conflicting with the solid behavior as

defined above, because if Poisson ratio < 0.5, solid is compressible. I

prefer a FEA package that allows to use hyperelastic model for solid,

i.e. use a user defined strain energy function.)

Here are my questions:

(1) Is the above MARC FEA soil model appropriate for biphasic model to

simulate soft tissues?

(2) Are there other commercial FEA packages that have a biphasic model

to simulate soft tissues?

Any comments are welcome. Thank you in advance.

>>>>Summary of Responses >>>>

>>>>

> In MARC 'User Information' book, it states the solid

> grains are assumed to be incompressible. It seems

> conflicting with the solid behavior as defined above,

> because if Poisson ratio < 0.5, solid is compressible.

I believe that in this formulation, the individual solid

constitutents are incompressible, but the poisson's ratio

refers to the poisson's ratio of the drained solid

continuum. These two conditions do not conflict.

> (1) Is the above MARC FEA soil model appropriate for

> biphasic model to simulate soft tissues?

Commercial FEA software with soil elements has been shown to

adequately model "biphasic" tissues. See papers by

Prendergast, P.J. in 1996 (Proc.Instn.Mech.Eng.) and Wu, J.Z.

in 1998 (J.Biomech.)

>(2) Are there other commercial FEA packages that have a

>biphasic model to simulate soft tissues?

ABAQUS and DIANA come to mind. ABAQUS has quite a nice

selection of elements, with the ability to model

poroelastic objects in 3D, and also to model contact

between two poroelastic objects.

regards

Stephen

Stephen Ferguson

AO ASIF Research Institute

Davos, Switzerland

>>>>

Hello Gangming,

you might get a lot of replies with this answer, but ABAQUS is a good

choice to model poroelastic materials. It uses a similar model as

MARC, but it is more flexible in the sense of user material definitions.

If you look in the literature under Articular Cartilage, you will find

a lot of work has been done to qualify ABAQUS as a solver for cartilage

problems.

I myself used it for my MS thesis to examine osteoporosis in the rabbit

knee with very good results.

Give it a try if you can and let me know what you came up with.

Cheers, Michael

Michael Nilsson

Senior Research Engineer

Cleveland Clinic Foundation

Biomedical Engineering Department

>>>>

For details of using the program FiDAP, see:

SL Butler, SS Kohles, RJ Thielke, CT Chen, R Vanderby Jr. "Interstitial

Fluid Flow in tendons or Ligaments: A Porous Medium Finite Element

Simulation," Medical & Biological Engineering & Computing,

35(6):742-746, 1997.

Good luck,

Sean S. Kohles, PhD

Assistant Professor of Biomedical and

Mechanical Engineering

Dept. of Biomedical Engineering

Worcester Polytechnic Institute

100 Institute Road

Worcester, MA 01609-2280 USA

Ph1: 508-831-5384 (Office 414 Salisbury Labs)

Ph2: 508-831-5097 (Lab 306B SL)

Ph3: 508-831-5424 (Lab 124 Higgins Labs)

FAX: 508-831-5541

email: kohles@wpi.edu

http://www.wpi.edu/~kohles

>>>>

Gangming,

I use COSMOS/M for modelling bone tissue using my own constitutive

model. The package allows you to write your own fortran subroutines

for linking

with the solver module to define the stress and stress/strain matrices

given the current strain vector during the analysis (non-linear or say

pseudo-linear: ie. very few iterations to converge). A fellow student

here has used this approach to model bone as a biphasic material.

regards,

Dean

Dean Inglis, B. Eng., PhD candidate

Department of Civil Engineering \ Email: dean@numog.eng.mcmaster.ca

BSB B101A \ Voice: (905) 525-9140 x23167

McMaster University \ Fax: (905) 524-2121

Hamilton, Ontario, Canada L8S 4M1 \

>>>>

Dr Luo,

I am not familiar with MARC - but I use ABAQUS to do biphasic modelling

of articular cartilage.

In abaqus, a mixture theory is used - a typical example being a mixture

of a porous solid like sand and a fluid, like water. There can be two

types of fluid - a highly compressible and and an almost incompressible

type - there are also provisions of dealing with absorption/trapping of

some of the fluid by the solid particles.

The behaviour of the mixture is described by an effective stress

principle, where total stress at a point is the sum of the solid and

fluid stresses. The effective stress of the solid phase has regular

terms that can be derived from principles of elasticity, for example,

and an interaction term with fluid pressure components. You might be

able to implement a user defined strain energy function - but I have

never tried it.

For fluid flow Forchheimers's Law is used, which accounts for changes in

permeability as a function of fluid flow velocity - and reduces to

Darcy's law as fluid velocity reduces.

Equilibrium is expressed from virtual work principles.

A continuity equation is also enforced.

The material properties input into the model are really partially

structural, because the equations consider the interaction between the

two phases. Thus, it is possible to have both phases as intrinsically

incompressible and still have the mixture behave as a compressible

substance. This also means that the solid phase could have a high

modulus, but the mixture could behave as something with a much lower

modulus.

The biphasic theory proposed by Mow et al, 1980, uses similar

constitutive equations. They have a tutorial web page where they

derive all their equations.... I don't remember the exact URL - but

if you go to the Columbia University website - You can look for it

as a link from Dr Mow's page.

Wu et al. J Biomech 31( 1998)165-169..... showed that the two theories

(biphasic and the one used by ABAQUS) predict similar results if the

fluid phase is inviscid.

Mostly, I have seen ABAQUS being used to model cartilage, because that

is what I was looking for - but I am sure, it could be and probably has

been used for other soft tissues as well. I have seen ABAQUS being used

to model whole joints - but the ones I have seen, cartilage and

ligaments

are often used as elastic components.

I have tried to test the ABAQUS output in a variety of ways - and so far

I am satisfied with my test results. The model shows characteristic

properties of creep and stress relaxation. There is a transfer of stress

from fluid to solid when a load is applied and held... with the fluid

taking all the stress in the beginning, then a stress transfer, then

equilibrium reached at which point all the stress is taken by the solid

and fluid pressures are zero . For cyclic loading,for the right

frequencies,

you can see a significant time lag between the applied force and the

fluid pressures .

Hope this helps

Nilay

Nilay Mukherjee, Ph. D.

Cartilage and Connective Tissue Research Lab

Room 3-31, Medical Sciences Building

Mayo Clinic

Rochester, MN 55905

Ph : (507) 280-7826 (h)

(507) 284-3484 (w)

Fax: (507) 284-5075 (w)

>>>>

Gangming,

We have been using MARC 7.2 successfully to model cartilage

behavior, using both the linear elastic approach, and the non-linear

hypoelastic model, as well as a transverse isotropy implemented with the

hypoelastic subroutine. When I say "successfully", I mean that we have

been able to validate our results against others' numerical and

analytical solutions for some standard problems of creep or stress

relaxation. (Prendergast et al, Proc Inst Mech Eng [H],1996 and

Wu et al, J. Biomechanics 1998, for example) Whether it truly captures

the cartilage behavior accurately is for another debate. I will

caution

you that in order to achieve this validation, we needed to obtain a

subroutine from MARC which was not part of the standard code (This was

after contacting Prendergast who had the same experience). It's

possible

that this is now included with whatever version of the code you have,

but

it was not for us. Thus - before considering any complicated problems

with

your code, I would take the time to do some validation tests.

Obviously,

this is always a good idea, but I would say it is particularly important

here... If you test it out and believe that you do need the subroutine,

I'd suggest you contact MARC yourself, so we can perhaps convince them

that enough people are interested so they will modify the code. If you

have trouble obtaining it, let me know, and I can provide a contact.

I don't see any reason that you couldn't implement a

hyperelastic model with a subroutine in MARC. The structure of the

program

allows quite a bit of access to the needed variables.

Another option that others have used is ABAQUS. I don't know if

it

has a hyperelastic model, but it does have at least a linear elastic

poroelastic model.

Best of luck with your analyses.

Amy

Amy L. Lerner

Asst. Professor

Mechanical and Biomedical Engineering

215 Hopeman Building

University of Rochester

Box Number 270132

Rochester, NY 14627-0132

Phone: 716-275-7847

Fax: 716-256-2509

e-mail: amlerner@me.rochester.edu

>>>>

Dear Gangming,

Your e-mail was particularly of a great interest to me. Since I have

been working on the FEA biphasic modeling for the past ten years, I feel

that I can answer some of your questions.

1) The Poisson's ratio of the solid component is defined in an apparent

geometric aspect, not a material aspect. In other words, the solid

material is incompressible. However, in the case of porous material,

the whole structure can be compressible even if the material

constituting

the structure is incompressible. One example is a porous sponge. Even

if

we make this porous sponge with an incompressible rubber, the porous

rubbery sponge is compressible since we can collapse the pores within

the porous sponge.

2) There are several other commercial FE packages which can handle the

biphasic modeling. Both ANSYS and ABAQUS have the capability. I have

developed my own FE formulation of the biphasic modeling back in 1989.

The FE biphasic model was not commercially available at that time.

You can easily incorporate the strain energy function into other

program.

3) If you need further information, please check the following articles:

R.L. Spilker and J-K. Suh, (1990) Formulation and evaluation of a finite

element model for the biphasic model of hydrated soft tissues, Computers

and Structures, 35:425-439.

J-K. Suh, R.L. Spilker, and M.H. Holmes, (1991) A penalty finite element

analysis for nonlinear mechanics of biphasic hydrated soft tissue under

large deformation, Int. J. Numerical Method in Engineering,

32:1411-1439.

Good luck,

J-K. Francis Suh, Ph.D.

Associate Professor

Dept. of Biomedical Engineering

Tulane University

>>>>

To Arik, to Gangming Luo,

First , if MARC says the solid is incompressible, it means a block of

pure solid, without pores is incompressible. When Poisson's ratio is <

0.5,

it means that the POROUS solid with no pressurised water in it is

compressible, i.e. its pores change volume during deformation.

MARC is fine for biphasic soft tissue analysis although the hypoelastic

behaviour might in many cases be better to replace by hyperelastic

behaviour. Alternative packages are ABACUS and DIANA. I think at least

one of them offers porohyperelasticity , maybe even

poroviscohyperelasticity.

Jacques Huyghe, Eindhoven University of Technology.

Jacques M. Huyghe

Dr.ir.

Eindhoven University of Technology

P.O. Box 513

Eindhoven

5645JN

The Netherlands

Work: +31-40-2473137

Fax: +31-40-2461418

Conference Software Address

Default Directory Server

>>>> End of Summary >>>>

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

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

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

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

Last week I posted a message about FEA biphasic model for soft

tissues. I have received a lot of feedback. Thank to all people for

their encouraging and helpful replies. The following is a summary of

responses starting with my original question.

>>>> Original Message: >>>>

I am trying to use biphasical model to simulate soft issues, e.g.

muscle, fat..., mechanical behavior. At this time, I am using MARC 7.2

(MARC Analysis Research Corporation). In the FEA package, there is a

soil model that allows a fully solid-fluid coupled approach with

following features and limits.

(1) The fluid behavior is modeled using Darcy's law and the fluid is

assumed to be slightly compressible.

(2) The solid behavior is defined by

(a) linear elasticity: the Young's moduli and the Poisson ratio;

(b) non-linear elasticity: hypoelastic model.

(In MARC 'User Information' book, it states the solid grains are assumed

to be incompressible. It seems conflicting with the solid behavior as

defined above, because if Poisson ratio < 0.5, solid is compressible. I

prefer a FEA package that allows to use hyperelastic model for solid,

i.e. use a user defined strain energy function.)

Here are my questions:

(1) Is the above MARC FEA soil model appropriate for biphasic model to

simulate soft tissues?

(2) Are there other commercial FEA packages that have a biphasic model

to simulate soft tissues?

Any comments are welcome. Thank you in advance.

>>>>Summary of Responses >>>>

>>>>

> In MARC 'User Information' book, it states the solid

> grains are assumed to be incompressible. It seems

> conflicting with the solid behavior as defined above,

> because if Poisson ratio < 0.5, solid is compressible.

I believe that in this formulation, the individual solid

constitutents are incompressible, but the poisson's ratio

refers to the poisson's ratio of the drained solid

continuum. These two conditions do not conflict.

> (1) Is the above MARC FEA soil model appropriate for

> biphasic model to simulate soft tissues?

Commercial FEA software with soil elements has been shown to

adequately model "biphasic" tissues. See papers by

Prendergast, P.J. in 1996 (Proc.Instn.Mech.Eng.) and Wu, J.Z.

in 1998 (J.Biomech.)

>(2) Are there other commercial FEA packages that have a

>biphasic model to simulate soft tissues?

ABAQUS and DIANA come to mind. ABAQUS has quite a nice

selection of elements, with the ability to model

poroelastic objects in 3D, and also to model contact

between two poroelastic objects.

regards

Stephen

Stephen Ferguson

AO ASIF Research Institute

Davos, Switzerland

>>>>

Hello Gangming,

you might get a lot of replies with this answer, but ABAQUS is a good

choice to model poroelastic materials. It uses a similar model as

MARC, but it is more flexible in the sense of user material definitions.

If you look in the literature under Articular Cartilage, you will find

a lot of work has been done to qualify ABAQUS as a solver for cartilage

problems.

I myself used it for my MS thesis to examine osteoporosis in the rabbit

knee with very good results.

Give it a try if you can and let me know what you came up with.

Cheers, Michael

Michael Nilsson

Senior Research Engineer

Cleveland Clinic Foundation

Biomedical Engineering Department

>>>>

For details of using the program FiDAP, see:

SL Butler, SS Kohles, RJ Thielke, CT Chen, R Vanderby Jr. "Interstitial

Fluid Flow in tendons or Ligaments: A Porous Medium Finite Element

Simulation," Medical & Biological Engineering & Computing,

35(6):742-746, 1997.

Good luck,

Sean S. Kohles, PhD

Assistant Professor of Biomedical and

Mechanical Engineering

Dept. of Biomedical Engineering

Worcester Polytechnic Institute

100 Institute Road

Worcester, MA 01609-2280 USA

Ph1: 508-831-5384 (Office 414 Salisbury Labs)

Ph2: 508-831-5097 (Lab 306B SL)

Ph3: 508-831-5424 (Lab 124 Higgins Labs)

FAX: 508-831-5541

email: kohles@wpi.edu

http://www.wpi.edu/~kohles

>>>>

Gangming,

I use COSMOS/M for modelling bone tissue using my own constitutive

model. The package allows you to write your own fortran subroutines

for linking

with the solver module to define the stress and stress/strain matrices

given the current strain vector during the analysis (non-linear or say

pseudo-linear: ie. very few iterations to converge). A fellow student

here has used this approach to model bone as a biphasic material.

regards,

Dean

Dean Inglis, B. Eng., PhD candidate

Department of Civil Engineering \ Email: dean@numog.eng.mcmaster.ca

BSB B101A \ Voice: (905) 525-9140 x23167

McMaster University \ Fax: (905) 524-2121

Hamilton, Ontario, Canada L8S 4M1 \

>>>>

Dr Luo,

I am not familiar with MARC - but I use ABAQUS to do biphasic modelling

of articular cartilage.

In abaqus, a mixture theory is used - a typical example being a mixture

of a porous solid like sand and a fluid, like water. There can be two

types of fluid - a highly compressible and and an almost incompressible

type - there are also provisions of dealing with absorption/trapping of

some of the fluid by the solid particles.

The behaviour of the mixture is described by an effective stress

principle, where total stress at a point is the sum of the solid and

fluid stresses. The effective stress of the solid phase has regular

terms that can be derived from principles of elasticity, for example,

and an interaction term with fluid pressure components. You might be

able to implement a user defined strain energy function - but I have

never tried it.

For fluid flow Forchheimers's Law is used, which accounts for changes in

permeability as a function of fluid flow velocity - and reduces to

Darcy's law as fluid velocity reduces.

Equilibrium is expressed from virtual work principles.

A continuity equation is also enforced.

The material properties input into the model are really partially

structural, because the equations consider the interaction between the

two phases. Thus, it is possible to have both phases as intrinsically

incompressible and still have the mixture behave as a compressible

substance. This also means that the solid phase could have a high

modulus, but the mixture could behave as something with a much lower

modulus.

The biphasic theory proposed by Mow et al, 1980, uses similar

constitutive equations. They have a tutorial web page where they

derive all their equations.... I don't remember the exact URL - but

if you go to the Columbia University website - You can look for it

as a link from Dr Mow's page.

Wu et al. J Biomech 31( 1998)165-169..... showed that the two theories

(biphasic and the one used by ABAQUS) predict similar results if the

fluid phase is inviscid.

Mostly, I have seen ABAQUS being used to model cartilage, because that

is what I was looking for - but I am sure, it could be and probably has

been used for other soft tissues as well. I have seen ABAQUS being used

to model whole joints - but the ones I have seen, cartilage and

ligaments

are often used as elastic components.

I have tried to test the ABAQUS output in a variety of ways - and so far

I am satisfied with my test results. The model shows characteristic

properties of creep and stress relaxation. There is a transfer of stress

from fluid to solid when a load is applied and held... with the fluid

taking all the stress in the beginning, then a stress transfer, then

equilibrium reached at which point all the stress is taken by the solid

and fluid pressures are zero . For cyclic loading,for the right

frequencies,

you can see a significant time lag between the applied force and the

fluid pressures .

Hope this helps

Nilay

Nilay Mukherjee, Ph. D.

Cartilage and Connective Tissue Research Lab

Room 3-31, Medical Sciences Building

Mayo Clinic

Rochester, MN 55905

Ph : (507) 280-7826 (h)

(507) 284-3484 (w)

Fax: (507) 284-5075 (w)

>>>>

Gangming,

We have been using MARC 7.2 successfully to model cartilage

behavior, using both the linear elastic approach, and the non-linear

hypoelastic model, as well as a transverse isotropy implemented with the

hypoelastic subroutine. When I say "successfully", I mean that we have

been able to validate our results against others' numerical and

analytical solutions for some standard problems of creep or stress

relaxation. (Prendergast et al, Proc Inst Mech Eng [H],1996 and

Wu et al, J. Biomechanics 1998, for example) Whether it truly captures

the cartilage behavior accurately is for another debate. I will

caution

you that in order to achieve this validation, we needed to obtain a

subroutine from MARC which was not part of the standard code (This was

after contacting Prendergast who had the same experience). It's

possible

that this is now included with whatever version of the code you have,

but

it was not for us. Thus - before considering any complicated problems

with

your code, I would take the time to do some validation tests.

Obviously,

this is always a good idea, but I would say it is particularly important

here... If you test it out and believe that you do need the subroutine,

I'd suggest you contact MARC yourself, so we can perhaps convince them

that enough people are interested so they will modify the code. If you

have trouble obtaining it, let me know, and I can provide a contact.

I don't see any reason that you couldn't implement a

hyperelastic model with a subroutine in MARC. The structure of the

program

allows quite a bit of access to the needed variables.

Another option that others have used is ABAQUS. I don't know if

it

has a hyperelastic model, but it does have at least a linear elastic

poroelastic model.

Best of luck with your analyses.

Amy

Amy L. Lerner

Asst. Professor

Mechanical and Biomedical Engineering

215 Hopeman Building

University of Rochester

Box Number 270132

Rochester, NY 14627-0132

Phone: 716-275-7847

Fax: 716-256-2509

e-mail: amlerner@me.rochester.edu

>>>>

Dear Gangming,

Your e-mail was particularly of a great interest to me. Since I have

been working on the FEA biphasic modeling for the past ten years, I feel

that I can answer some of your questions.

1) The Poisson's ratio of the solid component is defined in an apparent

geometric aspect, not a material aspect. In other words, the solid

material is incompressible. However, in the case of porous material,

the whole structure can be compressible even if the material

constituting

the structure is incompressible. One example is a porous sponge. Even

if

we make this porous sponge with an incompressible rubber, the porous

rubbery sponge is compressible since we can collapse the pores within

the porous sponge.

2) There are several other commercial FE packages which can handle the

biphasic modeling. Both ANSYS and ABAQUS have the capability. I have

developed my own FE formulation of the biphasic modeling back in 1989.

The FE biphasic model was not commercially available at that time.

You can easily incorporate the strain energy function into other

program.

3) If you need further information, please check the following articles:

R.L. Spilker and J-K. Suh, (1990) Formulation and evaluation of a finite

element model for the biphasic model of hydrated soft tissues, Computers

and Structures, 35:425-439.

J-K. Suh, R.L. Spilker, and M.H. Holmes, (1991) A penalty finite element

analysis for nonlinear mechanics of biphasic hydrated soft tissue under

large deformation, Int. J. Numerical Method in Engineering,

32:1411-1439.

Good luck,

J-K. Francis Suh, Ph.D.

Associate Professor

Dept. of Biomedical Engineering

Tulane University

>>>>

To Arik, to Gangming Luo,

First , if MARC says the solid is incompressible, it means a block of

pure solid, without pores is incompressible. When Poisson's ratio is <

0.5,

it means that the POROUS solid with no pressurised water in it is

compressible, i.e. its pores change volume during deformation.

MARC is fine for biphasic soft tissue analysis although the hypoelastic

behaviour might in many cases be better to replace by hyperelastic

behaviour. Alternative packages are ABACUS and DIANA. I think at least

one of them offers porohyperelasticity , maybe even

poroviscohyperelasticity.

Jacques Huyghe, Eindhoven University of Technology.

Jacques M. Huyghe

Dr.ir.

Eindhoven University of Technology

P.O. Box 513

Eindhoven

5645JN

The Netherlands

Work: +31-40-2473137

Fax: +31-40-2461418

Conference Software Address

Default Directory Server

>>>> End of Summary >>>>

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

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

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