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A question about electric displacement intensity factor of interacting cracks in piezoelectric materials

I am working on the problem of interacting cracks in piezoelectric materials. Due to the interaction of cracks, I found a non-intuitive phenomenon that the electric displacement intensity factor of the crack for some interacting profiles may be negative under some loading conditions (a tensile stress and an applied electric displacement). However, under the same loading conditions, the electric displacement intensity factor can never be negative for a single crack problem. I think the negative electric displacement intensity factor may be caused by the change of the direction of electric field intensity in the piezoelectric medium due to the interacting crack effect. Am I right? Could anybody give me some suggestions about this phenomenon? Thank ou very much.

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