Hi, let me know what type of experiment you have performed. Did you used test machine which controls grips velocity? In such case you should know corresp strain rate for your test and taking the tests with diff strain rates you should evaluate strain rate sensitivity of the material. In positive case, you should select corresp constitutive equation of plasticity which reflects the dependence of stress on strain and also strain rate and find its coefficients. It is clear that the equation should be selected from Abaqus list. Alternative approach exists but it demands more qualified solution supported by optimization theory. Let cont discuss in necces.

Hi, Your model is very much experiment dependant. Size of RVE, trabecular, cortical, porosity, anisotropy, boundary conditions used, etc ... and this even before you start looking at strain rate dependency. So it's rather difficult to answer your question.

Dear Daniel, let me note that the lot of simplifying hypotheses are introduced into computer modeling of bone tissues. They are supported experimentally. It was multiple note that porous cancel bone may be assumed  as linearly elastic  with experimentally found modulus. Anizotropy of cort tissue is described, for example, in review of A. N. Natali and E.A. Meroi A review of the biomechanical properties of bone as a material. A few powerful  scientific groups make these problems not so terrible in practical applications and lot of studies support  now wide range of prosthetic  oral and orthopeadic applications. It will be pleasant for me to send you wide bibliography..

Dear Vladislav, Thanks for your answer.

I agree with you using these simplifying hypotheses. Viscoelasticity seems then appropriate. Either simplified visocelastic models available in Abaqus should do it. Else, you would have to code the specific behavior. In case of  available models, experimental tests to characterize bone viscosity parameters (although there exist also literature on it) would do and it is possible to implement it in the numerical model. On the other hand, if you want to model bone evolution, not just the mechanichal properties, Young's modulus is not enough, since all biological activities is completely forgotten. But this does not seem to be the question here.

Dear Vladislav and Daniel, Yes I performed this experiment by controlling the displacement rate, i.e with control grip velocity.  

Once I performed simulation by using young's modulus, yield stress and yield strain rate corresponding to different strain rate. But I think this is not an efficient way to simulation. Can I use Prony series for this type of experiment? 

Dear Daniel, it seems to me that modern strategy in simulating living tissue mechan behavior is in applying remodeling theories (Cowin, Huiskes at al ) which are developed to include strain rate into bone density and modulus relationships.

Dear Ram, The models you have done are correct in the hypotheses of the model you use. As long as bone has variable responses (as many biological tissues) there is no one "good" model. Using Prony series may improve but it is not like metals for example where you do a series of tests (relaxation or creep) and extract material parameters that are valid on all situations. Simulation of biologiocal tissues using standard literature model will give you "averaged" behavior. This is correct as long as you need an average response for your application but not if you want something more specific like "patient dependent". This is all the point of the argument. What is exactly the answer you want to extract. Is it an average behavior (for which averaged experimental values will suffice, being strain rate dependent or not) or is it something more specific (in this case, more detailed modeling is required) ?

Dear Prof. Daniel ,

We want to make patient specific model at different strain rate. I am looking to compare the simulation result with experimental result  and then I want to generalize the model.

When we use Young's modulus corresponding to different strain rate,then our concern is what ever the change in slope we got in stress strain curve, is due to using different modulus value. Is there any constitutive equation is available for Viscoelastic model of bone which is strain rate dependent? 

If you want to go to patient specific, this is rather a difficult task and as previously said, the best you can hope for in using a generic model is probably to target certain population but not all. This is just impossible with this kind of model. Accounting for true patient specific would require to integrate much more information in your model than we can extract experimentally. My belief is that you should target 3 objectives : (i) what population (average), (ii) what model parameters (biological, mechanical) and therefore the model that goes with them (for example building (for younger patient) and degrading (osteoporosis) for old ones), and (iii) the importance of the parameters (I believe macroscopic from your question) that trigger patient specific.

To my knowledge you can find quite a few viscoelastic model in the litterature for bone. See for example :

- TPM. Johnson et al., Acta Biomaterialia, 6 (2010) 4073-4080

But again, there is no one model for all unless you have some sort of average population to trigger

Regards