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Decomposition of the displacement gradient into elastic and plastic parts
We know that total strain is the symmetric part of the displacement gradient. Total strain can be represented by the sum of the elastic and plastic (eigen) strains. Let consider a dislocation in an arbitrary solid. Suppose we computed the displacement filed, therefore the total strain can be obtained immediately. What are the criteria for the decomposition of the total strain into elastic and plastic parts? Maybe in classical continuum it is relatively easy to decompose the total strsain into elastic and plastic parts since the singular terms can be regarded as the plastic parts as deWit (1973) mentioned. However in some generalized theories of continuum mechanics that is not true. For example suppose a dislocation is located in an infinite medium. Consideting this case within strain gradient elasticity, it is well-known that the plastic strain exists everywhere as well as it is not singular. For more complicated problems what are the criteria for the decomposition?
- Kamyar M Davoudi's blog
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Dear Kamyar,
I think that if you want to see the plastic strain you must use a modified formulation in which some relative plastic constitutive laws are considered. For example you can see the problem of a cicular annulus which is subjected to internal pressure, details of this problem is disscussed inStructural plasticity Chen, you canuse same treatment.
decomposition into incompatible and compatible parts
Dear Kamyar,
Sec. 2 of the attachment at
http://www.imechanica.org/node/7342
has an answer to your question, especially related to questions of calculating the stress fields of nonsingular dislocations. In particular, the use of the theory (with the decomposition) there can be shown to calculate exactly the stress field of a (non)singular dislocation and the permanent deformation produced due to its motion (that is what the decomposition into incompatible and compatible parts was designed for).