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# Research on the plasticity/damage coupling model using continuum damage mechanics

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Currently, i am now attempting to establish a plasticity/damage coupling model using continuum damage mechanics for complex metal structures such as steel pressure vessel, which can be implemented using finite element analysis. The model can predict the progressive failure and damage evolution as well as the crack initiation and propogation due to large plastic deformation of metal structures. Who can give me some suggestion or idea?

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## Comments

## Pengfei, Reduced to its

Pengfei,

Reduced to its essentials, damage plasticity models include a damage evolution function, a conventional plasticity model for matrix for strain hardening, a damage-coupled yield condition and a flow rule.

Almost all damage models now a days use, at least in part, some sort of integral form of stress-state-weighted plastic strain. Some damage models consider void volume fraction due to plastic deformation, which can be computed from associated flow with pressure dependent yield surface. It depends on your application as for whether the void volume fracture is vital. In many cases, a von Mises type of yield condition is sufficient in generating some useful results for you as it is easy to write your own code for the radial return mapping.

I suggest you start with and test your damage/plasticity model with very simple geometry to predict the fracture path. When you gain enough confidence in your model then try it on more complex geometries and structures, otherwise, your effort may lose in vain due to other factors may come into play when geometry is complicated.

Liang

## Re: Damage-plasticcity

Dear Penfei,

In addition to Liang's comments, you have to keep in mind that when you have large plastic deformations the material becomes strongly anisotropic. That aspect has been studied by Miehe and others (probably Mark Geers too). You have to include elastic anisotropy, the effect of voids on the elastic properties (anisotropic elastic damage), and also anisotropic plasticity at the very least. Also, I you're doing a rate independent problem which can ignore inertia effects, the momentum equation will lose ellipticity when the material stiffness changes sign. You will need a nonlocal or gradient regularization of the problem to keep it well posed.

Also, and this is not directly related to the question, see Amit Acharya's

"Void expansion as wave phenomena - might damage evolution be mathematically related to fluid dynamics and turbulence? "

and

"Musings on continuum thermodynamic formalism and (yet another) damage model "

-- Biswajit

## Thank you for your kind

Thank you for your kind answers.

I have performed anisotropic stiffness degradation of cylindrical composite laminates under increasing internal pressure by carrying out the progressive failure analysis. However, the stiffness degradation properties of metal materials are not obvious from the macroscopic point of view compared with composites. Maybe, some microscopic changes for the mechanical performance due to excessive ductile plastic deformations of structures will occur. Therefore, i think if the popular damage plasticity models suggested by Dr. Liang can be combined with the nonlocal or gradient theories including the effect of voids suggested by Prof. Biswajit Banerjee, the problems of the damage evolution for simple structures can be solved. As for the complex structures such as the steel pressure vessels with nozzles, i will try to predict the crack initiation and failure pressure by extending the 3D anisotropic plastic/damage model. However, i believe that is a very challenging task.

Pengfei.