Supposed we are working with elastic damage model. In that case, after exceeding a stress threshold, the damage will occur and localization problem occurs. The problem is then become ill-posed and there is non-uniqueness of the solution (i.e. solution is infinite).
What people do usually in cohesive element or damage mechanics is by using viscous regularization. Normally, we need to use a small value of viscous regularization so that convergence to a unique solution can be obtained.
My question is, how do we know if the solution with the that viscous value is the right solution? why not any other solutions using with different viscous value?
Hi Ditho,
If the material is really strain rate dependent, then use the actual viscosity of the material. It might help reducing the mesh dependence. But not always. Most of the time you have to exaggerate the viscosity to obtain mesh independent results.
see the following article, which explains, how localization of strain proceeds and how viscoplasticity works to overcome it. It also shows that there is a limit up to which the viscoplasticity will work.
Niazi, M.S. and Wisselink, H.H. and Meinders, V.T. (2012) Viscoplastic regularization of local damage models: revisited. Computational mechanics, 51 (2). 203 - 216. ISSN 0178-7675
The point is that both viscous regularization and nonlocal formulations are mostly used as a numerical techniques in which we introduce a length scale to make the results mesh independent.. This length scale, directly or indirectly, defines a region over which we average out the strain/damage. Generally, it is taken such that we fit the experimental results. However, there is some work in which the length scale is defined based on real physics. see the thread below
https://www.researchgate.net/post/What_is_the_physical_interpretation_of_length_scale_in_a_nonlocal_damage_model
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