Summary
This paper deals with the calculation of the J-integral for electrically limited permeable cracks in piezoelectrics. The electromechanical J-integral is extended to account for electrical crack surface charge densities representing electric fields inside the crack. To avoid the costly implementation of the line integral along the crack faces, an alternative is proposed replacing the line integral by a simple jump term across the crack faces. Previous work by other authors related to the same subject is critically illuminated. The derivation was inspired by the Dugdale- Barenblatt cohesive zone model and yields an expression containing solely the local jump of displacements and electric potentials across the crack faces. This approach is shown to be exact for the Griffth crack.Numerical examples give evidence that the simplified approach works well for arbitrary crack configurations too.
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Ricoeur, A., Enderlein, M. & Kuna, M. Calculation of the J-integral for limited permeable cracks in piezoelectrics. Archive of Applied Mechanics 74, 536–549 (2005). https://doi.org/10.1007/s00419-004-0370-5
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DOI: https://doi.org/10.1007/s00419-004-0370-5