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Homogenization of magneto-electro-elastic multilaminated materials. (English) Zbl 1147.74040

Summary: Based on periodic unfolding homogenization technique, we rigorously derive the limiting equations modelling the behaviour of three-dimensional magneto-electro-elastic periodic structures. The local problems and the corresponding homogenized coefficients of elastic, dielectric, magnetic permittivity, piezoelectric, piezomagnetic and magneto-electric (ME) tensors are explicitly described. The homogenization model is exemplified for laminated composites, and a unified general formula for all effective properties of periodic multilaminated magneto-electro-elastic composites is obtained. This formula is applied to investigate the global behaviour for the important case of transversely isotropic constituents and any finite number of layers in each periodic cell. Examples that provide theoretical evidence of the presence of both a product property and the ME effect are given.

MSC:

74Q15 Effective constitutive equations in solid mechanics
74Q05 Homogenization in equilibrium problems of solid mechanics
74E30 Composite and mixture properties
74F15 Electromagnetic effects in solid mechanics
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