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Contour integral evaluation for thermal stresses in Abaqus

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The way that Abaqus evaluates the J contour integral has been updated in v6.12 to account for thermal and residual stresses in the manner described by Shih et al. (1986) and later by Lei et al. (2000) - see the Abaqus theory manual section 2.16.1.

Ive been trying out J-integral evaluation for various different thermal fields. Starting with the supplied benchmark example (see Abaqus Benchmarks Manual sect. 1.16.8: Single-edged notched specimen under a thermal load), I defined various smooth thermal fields based on analytical functions (node-wise using *TEMPERATURE, rather than taking the thermal field from a .odb file as in the benchmark example) and checked the path-independence of the resulting J values. So far, so good: the results were realistic and contour-independent.

However, when I define a non-smooth thermal field, for example by raising all the nodes of a single element by 100 degrees with the rest of the nodes left at zero, the J-integral becomes strongly path-dependant. This is a bit surprising, because mathematically, the form of the underlying thermal field should not affect the path-independence (modified form of the) J-integral. Presumably, by defining a non-smooth thermal field I must be violating some assumption made by the solver, although I cant find anything which would affect this mentioned in the documentation.

Has anyone else come across this problem, or have any tips on evaluating contour integrals in the presence of thermal/residual stress fields using Abaqus?