Nonlinear fracture of 2D magnetoelectroelastic media: Analytical and numerical solutions

Abstract

Keywords:Crack Magnetoelectroelastic (MEE) medium Electric and magnetic yielding Strip electric-magnetic polarization saturation (SEMPS) model Non-linear hybrid extended displacement discontinuity-fundamental solution (NLHEDD-FS) method a b s t r a c t A strip electric-magnetic polarization saturation (SEMPS) model is developed to study the electric and magnetic yielding effects on a crack in magnetoelectroelastic (MEE) media. In this model, the MEE medium is treated as being mechanically brittle, and electrically and magnetically ductile. Analogously to the classic Dugdale model, the electric and magnetic yielding zones in front of the crack are represented for simplicity by two strips. In the electric yielding strip the electric displacement equals the electric displacement saturation and meanwhile in the magnetic yielding zone the magnetic induction equals the magnetic induction saturation. The nonlinear analytical solution of this SEMPS model of crack in an infinite MEE medium is obtained using an integral equation approach. The equivalence between the proposed SEMPS model and the existing strip electric-magnetic breakdown (SEMB) model is demonstrated.To analyze the nonlinear fracture problem in the corresponding finite MEE media, the non-linear hybrid extended displacement discontinuity-fundamental solution (NLHEDD-FS) method is modified, and a multiple iteration approach is adapted to determine the electric and magnetic yielding zones. Comparing with the analytical solution, the applicability and effectiveness of the NLHEDD-FS method is verified. Numerical results based on the SEMPS model for a center crack in infinite and finite MEE strip are presented.

A Modified Strip-Yield-Saturation-Induction Model Solution for Cracked Piezoelectromagnetic Plate

“…The boundary conditions (iv) to (vi) together with continuity of traction condition on -axis lead to 1 ( ) = 0 for | | > , 2 ( ) = 0 for | | > , and 3 ( ) = 0 for | | > . Equations to determine the desired potentials ( ) ( = 1, 2, 3) may be written using (16) as…”

“…Zhao and Fan [15] proposed a strip electric-magnetic breakdown model for an electrically and magnetically impermeable crack in MEE media using extended Stroh formalism and the extended dislocation modelling of a crack. They have also proposed [16] a strip electric-magnetic polarization saturation model for an infinite and finite MEE strip. Using finite element method Krahulec et al [17] discussed a crack problem for MEE solid under various electromagnetic boundary conditions on the crack rims.…”

Electric and magnetic polarization saturations for a thermally loaded penny-shaped crack in a magneto-electro-thermo-elastic medium

“…By extending the DB model, Zhao and Fan [19] proposed a strip electricmagnetic breakdown model to investigate the electric and magnetic yielding behaviors in magneto-electro-elastic crack problems. It should be noted that the strip PS and DB models are built on different physical mechanisms, and some analytical and numerical comparisons between these two models have been made [12,13,20]. As pointed out by Zhao et al [13], the nonlinear fracture behaviors could be predicted equivalently by the PS and DB models, expect for a little difference of J-integral values.…”

“…In view of the similarities between the electric and magnetic fields, a strip electric and magnetic PS model was developed by Fan and Zhao [12], to study the electric and magnetic yielding effect at the front of a crack in a 2D magneto-electro-elastic medium. The electric and magnetic PS model for penny-shaped cracks in 3D magneto-electroelastic media was investigated by Zhao et al [13], the field intensity factors and the sizes of electric and magnetic yielding zones were explicitly obtained.…”

A mode III moving interfacial crack based on strip magneto-electric polarization saturation model

“…In the case of permeable electric boundary conditions, Hu and Yang [26] discussed the moving Dugdale type crack along the interface of dissimilar ferroelectric materials, and determined the crack sliding displacement and yield zone size. For nonlinear MEE materials, Zhao and Fan [27] and Fan and Zhao [28] proposed the static strip magneto-electric breakdown and saturation models respectively in the MEE homogeneous medium, with the assumptions of mechanical brittleness and magneto-electric ductility. However, to the best of the authors' knowledge, studies on the nonlinear magneto-electric behaviors of the moving MEE interfacial crack have not yet been addressed.…”