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A question about anisotropic plastic

I've got a question about anisotropic plastic. The anisotropic models like Hill or Barlat yield criteria are about anisotropic yielding. However, the hardening behaviors in different directions like rolling direction or transverse direction are still the same, i.e. they work harden in the same speed. My question is what if material in different directions work hardens in different speed? How can I deal with this in finite element simulation?

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I have god some clue about the strain hardening anisotropy. It is a phenomenon which is hard to simulate. See the work:

Effect of texture and microstructure on strain hardening anisotropy for aluminum deformed in uniaxial tension and simple shear.A novel approach for anisotropic hardening modeling. Part II: Anisotropic hardening in proportional and non-proportional loadings, application to initially isotropic material

I have god some clue about the strain hardening anisotropy. It is a phenomenon which is hard to simulate. See the work:

Effect of texture and microstructure on strain hardening anisotropy for aluminum deformed in uniaxial tension and simple shear.A novel approach for anisotropic hardening modeling. Part II: Anisotropic hardening in proportional and non-proportional loadings, application to initially isotropic material

Anisotropic hardening seems to be the subject of recent research. I cannot think of a completely general model that might suit you, but perhaps basic kinematic hardening might be applicable, as this is a (simplified) form of anistropic hardening. You could also look into distortional hardening models developed by Dafalias and others, though they are primarily concerned with special features  like the flattening of the yield-surface.

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