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why the back stress is independent of stress

alpha_ij is the back stress. During the derivation of the consistent condition (please see attachment),

d(sigma_ij-alpha_ij)/d (alpha_ij)=-1.

The back stress is related to the plastic strain, why it is independent of the stress.

Thank you.




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Haoran Wang's picture

Hi Huadong, mu understanding is as follows.

the alpha_ij here shows the state at this moment. it's influenced by the loading history instead of the stress at this moment. It is dalpha_ij (the increment of backstress at this moment) that is influenced by the current stress state.

aslan mohammadpour's picture


This question is a very fundamental question and can be answered from many perspectives. I am not in the place to give an elaborative answer. However I could answer it from my points of view.

The stress is purely related to elastic deformation of the material which itself is related to macroscopic lattice deformation. Here, for instance, a macroscopic volume is the volume in which we assume that material is continuous. On the boundary of this macroscopic volume we can define stress fields and these stress fields should satisfy the balance of momentum. Although there are some internal microstructural interactions between the material crystals or atoms, they do not affect the stress directly.

The back-stress is an internal stress field which is responsible for motion of less stable dislocation [Yoshida et al 2002].  Back-stress or long range internal stresses happens in microstructural scale [Kassner et al 2009]. Unlike the stress which is purely depends on elastic deformation, the back stress depends solely on plastic deformation.


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