ON THE ANALOGY BETWEEN THE CURRENT DENSITY DISTRIBUTION IN A THIN CONDUCTIVE PLATE AND THE ANTI-PLANE SHEAR PROBLEM

Qualitative analysis of current density distribution in athin conductive plate containing cracks is the first problem to besolved forthe crack-preventing technology based on the electromagnetic heating effect.To investigate the singular distribution of the current density at the cracktips, most of the existing solutions are complicated or are only validfor a specificarrangement of the cracks. In this paper it is found that there exists aclose analogy between the current density distribution and the anti-planeshear problem. Hence the solution to the current density distribution in acracked conductive plate can be deduced by considering a corresponding modeIII crack problem. The current density factor is defined in a similar way asthe stress intensity factor, as its counterpart in the mode III crackproblem. The consequent crack problem can be solved efficiently by thedistributed dislocation technique, which is a widely applied tool infracture mechanics. A numerical example is provided to demonstrate that theproposed numerical method is convenient and accurate and also helpsto the understanding of the singularity of the current density distributionat the crack tip.