how to write stress-dependent model

[snowden]

Dear Jorgen:

I am developing one stress-dependent model, which means stiffness moduli is a function of stress. It needs stress tensor in last n step if stresses at n+1 step are to be obtained I am confused about how to express stress at last step.
can you tell me?

thank you very much.

[Jorgen]

Hi Snowden,

Can you explain some more details of your model. It sounds like a history integral-type of model. If the stiffness only depdends on stress, why do you need the stresses for the last steps?

In this case, it might be possible to reformulate the implementation of your theory such that it only needs the information from the previous step.

Jorgen

[snowden]

many thanks for you reply.

now I explained my model and my algorithm. In reality, my model belongs to viscoplastiv model.
the basic formula is
dsigma=D*(dstrain-dt*strainrvp)

dsigma--increment in stress; dstrain--increment in strain; strainrvp-viscoplastic strain rate; dt--dtime,increment in time

also, stiffness martrix D is not constant but dependent on stress condition.
D=D(p),which means D is related to mean stress p, p=tra(stress).

Bulk modulus Ke=p/constant, from Ke we can obtain D

For simplicity, I want to use p in last step to update stress tensor.

I don't know if I am clear.

thanks.

[Jorgen]

It sounds like you can update the stress in your model if you know dstrain and dt at the current time. What you need to do is to write your equations and explicitly indicate if the different quantities are expressed at time t or at time t+dt.

If I understand your model correctly, you can create a very simple first-order forward integration scheme that will capture the essence of the response, assuming that the time increment size is small enough to assert stability. There is also possible to use a more sophisticated (higher order) integration scheme that is more robust. The most appropriate approach for you will depend on how much time and effort you are willing to spend on developing the implementation of the model.