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Tissue strain-rate independence

I have two basic questions for the experts in the soft tissue biomechanics community. 

a) I am interested in the biomechanics of a specific tendon in a specific high-speed deformation. How plausible is it for me to assume strain-rate independence, and therefore, the existence of a strain energy function? In other words, how accurate is the assumption of pseudoelasticity for tendons under high strain-rate? I feel comfortable with the assumption (evidence would help a lot, however) for tissues such as mesentery, skin and, I guess, even muscle. 

b) Has anyone experimentally tested the compressibility characteristics of soft tissues? In other words, how incompressible are, often explicitly or implicitly assumed, soft tissues like tendons?

c) Finally, in impacts/crashes etc., people may not have their soft tissues preconditioned. How tenable does this non-preconditioned state leave the pseduoelastic assumption? 


Hi Dear

I am also working in this area (constitutive equation of skeletal muscle particularly in finite element approach) . I am eagerly ready to share our knowledge in this field if you agree and even work together to get better result in reduced time.

Could I have your idea?

All The Best

I have seen quite a few variations of muscle models. Stojanovic (modified by Tang, Y. T. Lu), Weiss (modified by Blemker), Odegard and others have developed variations of muscle models. Which one are you most interested in? 

I have studed models based on Hill type which is the most popular among models of skeletal muscle. I will be so delighted if you accept me to be integrated in your research so that we can come up with a constitutive model with each other.

Could I have your e-mail to contact you more easily?

Thank you

It does not seem like our areas of interest overlap. However, if there is something you need help with, I'd strongly recommend posting your questions on imechanica, eng-tips, abaqus yahoo group and polymerFEM. That being said, if you could talk more about which FE package you are using, the application, your material model subroutine, etc., perhaps I could point you to helpful resources.  

To Ice 

Here are some comments that might be helpful for you:

 a)the strain-rate dependency of soft tissues is dependent on what
tissue you are considering. According to Fung (Biomechanics: Mechanical
Properties of Living Tissues, 1993),  some biological tissues as you
mentioned are said no to show considerably different instantaneous
responses under various frequencies. But, this I believe cannot be
generalized for all tissues. For example the ACL experimental data by
Pioletti (1998) shows a strain-rate dependent viscoelastic response or
cartilage is not very sensitive to strain-rate in a range of
strain-rates (10%/s to 30%/s) but shows a considerably higher dynamic
modulus under 70%/s.  Different ligaments and tendons may have different
viscoelastic properties as I believe they are optimized for their tasks
according to the range of forces, strains and strain-rates
experiencing. But put these all aside, I suggest you choose your
constitutive equation based on your needs and purpose of the
study. The only difference that I see between psuedoelastic and
viscoelastic constitutive models (as a mathematical representation or
model for a phenomena) is that the psuedoelastic model predict the
instantaneous response only at the specified strain-rate (and obviously
cannot predict stress relaxation).So, if you are doing
experiments/modeling under different strain-rates and your
material is strain-rate sensitive, then your model may not be accurate
enought, otherwise the psuedoelastic model will work for you. My
experience says it is better to avoid viscoelasticity due to some
possible numerical difficulties and go for the more straightforward
elastic model. 

 b)Ligaments are usually considered to be nearly incompressible
(although water exudes from them during experiment). Pioletti (1998)
suggested that it is not possible to fit the model to the experimental
data without considering the incompressibility.  

c) I think preconditioning the tissue is not related to whether you
consider the tissues as psuedoelastic or viscoelastic. In most of regular (not
very high strain-rates) tensile studies, the tissues are preconditioned.
I have not read much about impact testing, but I assume that the effect
of preconditioning may be more important for higher strain-rates as the
fibers have less time to align in the direction of loading. Someone
more experienced in experiments can comment on this issue more
accurately though.

Hi Sahand,

Thanks for your input. Your comments were helpful. 

As per my understand, I must disagree with your opinion on preconditioning. A non-preconditioned specimen will NOT possess a repeatable mechanical behavior which precludes assignment of a strain energy function, at least, when it comes to pseduoelasticity. 

 I am open to further discussion on this. 

I did some research on preconditioning and this what Fung, Fronek, and Patitucci had to say about a "pseduo strain energy function":

".. Strictly speaking, it can be defined only for a specific cyclic loading at a specific frequency after preconditioning."

Of course, if the tissue under consideration is not very sensisitive to strain-rate effects, some generality is allowed in the definition.

Maybe my third comment was a bit confusing. I meant that if you do the experiments without preconditioning and you get the results (which might not be favourable) and use it for characterizing your constitutive equation, you get inaccurate parameters in your equation irrespective of using viscoelastic or psuedoelastic model. The repeatibility of the response should also be true for voscoelastic model. If you need the data during ramp loading only, you may use psuedoelastic model. for characterizing the viscoelastic model you will also need the equilibrium (elastic) parameters which can be taken from literature I think.

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