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Dielectric materials,such as carbon fibre,glass reinforced plastic,polymers and ceramics,can be found in many engineering structures due to their various attractive features.However,its fracture features have not been fully investigated and understood.In this paper,an exact crack model for dielectric material is proposed to investigate the effect of the electrical boundary condition along the crack surface on the fracture-related parameters.We achieve our solutions by combining a sub-region boundary element formulation with the crack cavity being one of the sub-regions governed by the Poisson equation for the electric potential.