Multiscale analysis for the prediction of the full field in electromagnetoelastic composites with semi-infinite cracks

Abstract

The full field distributions in loaded electromagnetoelastic composites with semi-infinite cracks and other localized defects are predicted by employing micro-to-macroscale analyses. At the micro level, the effective properties of the electromagnetoelastic composite, which consists of piezoelectric and piezomagnetic constituents, are determined by employing a micromechanical analysis which takes into account the detailed interaction between the phases. The subsequent macroscale analysis employs the jumps of the K-field of a crack embedded within a homogeneous electromagnetoelastic medium, computed at the boundaries of a rectangular domain that is sufficiently far away from the localized effects. Then, the double finite Fourier transform is applied and the solution of the problem in the transform domain is derived. Inversion of the Fourier transform provides, in conjunction with an iterative procedure, the resulting electromagnetoelastic field distributions. Both crack fronts perpendicular and parallel to the poling (the axis of symmetry of the composite) are considered. After the verification of the offered approach, results are presented for piezoelectric/piezomagnetic composites with a semi-infinite crack which is interacting with a cavity. In addition, the field distributions in cracked porous electromagnetoelastic materials are presented. A particular emphasis is given to the induced magnetic field caused by the application of electromechanical loading, and to the induced electric field caused by the application of magnetomechanical loading.

Finite element implementation of a multi-scale dynamic piezomagnetic continuum model

“…One approach to modelling is to incorporate the heterogeneity of the material within a multi-scale piezomagnetic framework. The different phases at the lower level of observation are modelled explicitly and homogenisation principles may be applied to derive effective properties [1,2,18,27,28]. This requires the identification of a suitable Representative Volume Element at the lower scale of observation, after which Fourier transforms [1,2] or Eshelby solutions [18,27,28] may be used to quantify the relevant effective properties.…”

Micromechanical analysis of hyperelastic composites with localized damage using a new low-memory Broyden-step-based algorithm

“…Extensions of the multiscale analysis for composites with localized damage have been performed by [9] and [23]. The effects of various types of localized damage in 'smart' composites (piezoelectric, electromagneto-elastic and thermo-electro-magneto-elastic) have been investigated by [1], [3], [4], [5] and [6]. Thus far, the described multiscale analysis has been applied to composites with linear constituents, to predict the behavior of linear composites with various types of localized damage.…”

“…Extensions of the multiscale analysis for composites with localized damage have been performed by [9] and [23]. The effects of various types of localized damage in 'smart' composites (piezoelectric, electromagneto-elastic and thermo-electro-magneto-elastic) have been investigated by [1], [3], [4], [5] and [6].…”