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Combined analytical and numerical solution of 2D interface corner configurations between dissimilar piezoelectric materials

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Abstract

The failure assessment of smart composite structures requires efficient analytical and numerical techniques in order to tackle electrical and mechanical field concentrations. The present work is directed to the analysis of interface corner and crack configurations which occur in smart composite materials. It delivers a new technique to solve the corresponding piezoelectric boundary value problems. The purpose of the given paper is to describe exactly the asymptotic behaviour at piezoelectric interface corner configurations using the eigenfunction expansions on the one hand, and in the linking of these expansions to regular finite elements on the other. Specific singular eigenfunctions for homogeneous and interface crack configurations are discussed. For the considered cases, the classical crack modes (Mode I and Mode II) and a new Electric Mode are identified. The coupling of the full eigenfunction expansions to the finite elements surrounding the tip region is based on the principle of virtual work applied to the orthogonalised eigenfunctions. Finally, one gets an asymptotic stiffness matrix which does not depend on the distance to the tip. The coefficients of the eigenfunctions can be obtained efficiently from the generalised displacements of the global solution by means of the orthogonalised eigenfunctions. The technique allows to numerically bypass possible singular oscillatory terms in the weak sense, although they actually exist in the strong solution. The given approach is proven and verified in numerical test examples. Standard finite element methods encounter difficulties to give correct solutions at piezoelectric interface crack tips.

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  1. Institute of Mechanics and Fluiddynamics, Technische Universität, Bergakademie Freiberg, D-09596, Freiberg, Germany

    M. Scherzer & M. Kuna

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  1. M. Scherzer
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Scherzer, M., Kuna, M. Combined analytical and numerical solution of 2D interface corner configurations between dissimilar piezoelectric materials. International Journal of Fracture 127, 61–99 (2004). https://doi.org/10.1023/B:FRAC.0000035056.34258.4b

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