Abstract
Anti-plane shear of piezoelectric fibrous composites is theoretically investigated. The geometry of composites is described by the 2-dimensional geometry in a section perpendicular to the unidirectional fibers. The previous constructive results obtained for scalar conductivity problems are extended to piezoelectric anti-plane problems. First, the piezoelectric problem is written in the form of the vector-matrix \({\mathbb{R}}\) -linear problem in a class of double periodic functions. In particular, application of the zeroth-order solution to the \({\mathbb{R}}\) -linear problem yields a vector-matrix extension of the famous Clausius–Mossotti approximation. The vector-matrix problem is decomposed into two scalar \({\mathbb{R}}\) -linear problems. This reduction allows us to directly apply all the known exact and approximate analytical results for scalar problems to establish high-order formulae for the effective piezoelectric constants. Special attention is paid to non-overlapping disks embedded in a two-dimensional background.
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Rylko, N. Effective anti-plane properties of piezoelectric fibrous composites. Acta Mech 224, 2719–2734 (2013). https://doi.org/10.1007/s00707-013-0890-6
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DOI: https://doi.org/10.1007/s00707-013-0890-6