International audienceThe goal of this work is to prove that within the framework of fracture mechanics with Dugdale's model of cohesive forces, small defects (compared to the material characteristic length) have no influence on the limit load that a structure can sustain. For that, we treat two cases: first, we solve the case of a precracked plate in closed form, and then we compute the response of a plate with a circular hole using the finite element method

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The main objective of this work is the contribution to the study of the piezoelectric structures which contain preexisting defect (crack). For that, we consider a Griffith crack located at the interface of two piezoelectric materials in a semi-infinite plane structure. The structure is subjected to an anti-plane shearing combined with an in-plane electric displacement. Using integral Fourier transforms, the equations of piezoelectricity are converted analytically to a system of singular integral equations. The singular integral equations are further reduced to a system of algebraic equations and solved numerically by using Chebyshev polynomials. The stress intensity factor and the electric displacement intensity factor are calculated and used for the determination of the energy release rate which will be taken as fracture criterion. At the end, numerical results are presented for various parameters of the problem; they are also presented for an infinite plane structure.

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