Fundamental solutions and numerical modeling of internal and interfacial defects in magneto-electro-elastic bi-materials.

摘要

Magneto-electro-elastic materials can convert energies from one form to the other among the mechanical, electric and magnetic ones, and thus they have potential applications in clean energy harvest, various sensors, actuators and other hi-tech areas.;Analytical solutions are of great importance to analyze behaviors of magneto-electro-elastic materials, especially for magneto-electro-elastic bi-materials whose interface could substantially influence behaviors of the whole material. The extended Stroh formalism and Fourier transformation are adopted to derive the fundamental solutions in a three-dimesional magneto-electro-elastic bi-material. The solutions are in a line integral form. Responses on the interface are investigated. In terms of geometric domains, the obtained analytical solutions can be reduced to the ones in half space and homogeneous full space. In terms of material properties, the obtained solutions can be reduced to the ones in decoupled cases such as piezoelectric, piezomagnetic or elastic materials.;Interfacial cracks with impermeable conditions on crack faces in three-dimensional magneto-electro-elastic as well as two-dimensional piezoelectric bi-materials are investigated. A numerical scheme based on the Crouch-type fundamental solutions and the extended displacement-discontinuity method is defined for analyzing interfacial cracks. The physically unreal oscillating singularity at the interfacial crack tip or front is avoided by replacing the delta expression with the distribution function in the solutions. The influence of this replacement and the effect of the Gaussian parameter on predicting fracture parameters are examined numerically. Electric and magnetic nonlinearities at interfacial crack fronts in a magneto-electro-elastic bi-material are considered by adopting the electric-magnetic polarization saturation model. In this model, the perfect electric displacement and magnetic induction saturations are assumed. Green's functions for the ring element of uniform extended displacement discontinuities are derived to form the system of equations in the extended displacement discontinuity method. The unknown sizes of the electric and magnetic saturation zones are determined by the vanishing of the electric displacement and magnetic induction intensity factors at corresponding crack fronts. An iteration approach is designed to solve for the two unknown sizes. The effect of the electric/magnetic field on the saturation zones as well as the influence of the saturation zones on the stress intensity factor is discussed.