Hi,
How to calculate 3 components of j integral using domain integral method.
Silvio Rabbolini
You may find some useful tips here:
http://www.tf.uni-kiel.de/matwis/brocks/report_brocks-rabbolini.pdf
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Matthew Robert Molteno
It is the Eshelby tensor: Hij and a chosen crack extension function qi,j integrated with whatever method you choose (e.g. sum(:)).
Start with the tensor you get from summing over i,j, for Hij x qj,k for every material point around the crack tip, then dot multiply the tensor with ni (the normal or q-vector to the crack tip). Then divide the result by the same thing but omitting Hij and only along the crack front (i.e. the projected area). The eshelby tensor for elastic problems is pretty simple - just stresses, strains and displacement gradients.
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