Dear Aamir,

As pointed out by Mikael, the m4 model implementation only supports the elastic stiffness, as the tangent one is not so easy to obtain due to the formulation of the model. Perhaps, the numerical differentiation could be used to construct the tangent matrix, but this could be relatively costly. Due to lack of tangent stiffness, the model is typically used in explicit solution schemes (explicit  dynamics, or explicit dynamic relaxation for statics), however, it can be used in implicit simulations as well. The convergence is slow, of course, but it should be stable. I don't remember any problems with convergence.
Another problem of the model is that it does not includes any regularization, so it must be used carefully in problems with strain softening to ensure proper energy dissipation.
The convergence problems usually do not depend on stiffness type. For example, when constructing tangent one, you assume the future behavior (loading or unloading, for example) which may not be always correct. Usually the problem is due to incorrect control on the global level (load vs displacement control, etc). With elastic stiffness I would expect slow, but stable convergence.

Hello,
it's me again,
I have two more questions,
1-in your code I can't see any part regarding the Unloading and stiffness Degradation regarding Microplane Tangential (Shear) Components, I mean CT for Unloading case, is it always a proportional of CD, (CT=mu*CD)? but if this the case it doesn't make a sense, since the damage and loading and unloading criteria should be independently for all microplanes Components (The Volumetric,  Deviatoric and Tangential),
or simply consider no Degradation and take CT=ET, (ET=Virgin Tangential (Shear) Stiffness)??

2-The previous values,
I mean let us assume we're at  the END of time step= time3,
and Now I should Store Some Quantities for Next time Step for Example Microplane Volumetric Stress Sigv, Previous_Sigv=Sigv,
and Now we Started the  time step= time4,

and Now is my question, is this Previous_Sigv should be updated during the inner Newton Iterations?? or remains constant and just be updated at the End of the Iteration (Means End of  time4) only and hence,  at  the END of time step= time4 =>Previous_Sigv=Sigv??
I'm really confused regarding this part, and I'm really looking forward for your reply,
All the best

Unfortunately, the documentation doesn't reveal the original author, nor refer to any research paper (both are things that I strongly encourage new contributions to include).

I'll give you the answers I can, but I know absolutely nothing on the theory.

2- Material routines with state variables keep track of in respective MaterialStatus class.
The MaterialStatus class also stores temporary values, which contains the values rom the last iteration.
When a timestep is finalized, i.e. convergence have been reached, we know we have the right values stored in the temporary fields, the temporary variables are copied over (MaterialStatus::updateYourself), and the next time step can begin.

M4Material::updateVolumetricStressTo is called every newton iteration, and stores the temp value o the volumetric stress, which is copied over from temp to real stress at the end of each time step.

I should mention that the object oriented design of OOFEM allows similar classes of material routines to share common code, and in this case, not everything about the M4 material is actually located in m4.c.
You should look at the class M4Material inherits from, and in particular, look for the main entry-point for all constitutive drivers, which is the "giveRealStressVector" function. For the M4 material, this is located in
microplanematerial_bazant.C
where this is what you are probably looking for;
MicroplaneMaterial_Bazant :: giveRealStressVector

I don't know the theory here at all, but at least this function has a conditional statement, perhaps this is the unloading part you are looking for?

In this case, the MaterialStatus stores the stress, and the strain (of the last equilibrated state), and the temporary values (which comes from guess of the displacements in the last newton iteration).
When convergence have been reached, the time step is finalized, and the temporary stress and strain are copied over to the equilibrated values.
So, yes. They are stored, and copied over when the new time step starts.

We don't want to have to call the material routine an extra time to get the final values at the end of the time step.

I'm not sure what you mean by the variables being "called". When you ask for the tangents, the temp* values are read (you always get the tangent corresponding to the last call to "giveRealStressVector"), other than that, they are not read, just written to.

Generally, temp values can be read, and are typically done so when computing the tangent.
In this case, since M4 only computes the elastic tangent, it doesn't need to read the temporary values.