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Finite element techniques for dynamic crack analysis in piezoelectrics. (English) Zbl 1196.74264

Summary: This paper deals with numerical methods, developed to analyze plane stationary cracks in piezoelectric structures under dynamic electromechanical loading conditions. In the first part an explicit finite element scheme is presented, which has been developed to solve the transient coupled electromechanical boundary value problem. A special technique is implemented in the algorithm, accounting for the limited electrical permeability of the crack. In contrast to well known algorithms for static calculations it does not require any iteration. In order to calculate dynamic stress and electric displacement intensity factors for arbitrary crack configurations, the interaction integral is generalized for electromechanical problems. The efficient applicability and the high accuracy of the implementations are demonstrated by numerical examples, giving insight into several effects occuring with dynamically loaded cracks in piezoelectrics.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74R10 Brittle fracture
74F15 Electromagnetic effects in solid mechanics

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References:

[5] Cui Y., Westram, I., Rödel, J. and Yang, W. (submitted) Electromechanical cracking in ferroelectrics driven by large scale domain switching. Journal of the Mechanics and Physics of Solids
[7] Dominguez J., Sáez A., Garcia-Sánchez F. (2004). Numerical approach for dynamic fracture in piezoelectric solids. Proceedings of the XXI International Congress of Theoretical and Applied Mechanics (XXI ICTAM), Warsaw, Poland
[10] Enderlein M., Ricoeur A., Kuna M. (2004). Theoretical investigations of fatigue crack growth in ferroelectrics under cyclic electromechanical loading. Final Report in the Sino-German Program ”Properties and Mechanics of Smart Materials” DFG Contract No. 050/9
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