Numerical method of crack analysis in 2D finite magnetoelectroelastic media

Abstract

The present paper extends the hybrid extended displacement discontinuity fundamental solution method (HEDD-FSM) (Eng Anal Bound Elem 33:592-600, 2009) to analysis of cracks in 2D finite magnetoelectroelastic media. The solution of the crack is expressed approximately by a linear combination of fundamental solutions of the governing equations, which includes the extended point force fundamental solutions with sources placed at chosen points outside the domain of the problem under consideration, and the extended Crouch fundamental solutions with extended displacement discontinuities placed on the crack. The coefficients of the fundamental solutions are determined by letting the approximated solution satisfy the prescribed boundary conditions on the boundary of the domain and on the crack face. The Crouch fundamental solution for a parabolic element at the crack tip is derived to model the square root variations of near tip fields. The extended stress intensity factors are calculated under different electric and magnetic boundary conditions.

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

“…Extending the well known Crouch fundamental solution (Crouch, 1976), Zhao et al (2010) derived the extended Crouch fundamental solutions for magnetoelectroelastic medium, which correspond to the extended displacement discontinuities on an element. Using the extended Crouch fundamental solutions and the extended point force fundamental solutions, and the method of superposition, we can express the extended displacement and extended stress at any field point X for an impermeable crack…”

“…In the numerical analysis, a total of 200 collocation points are chosen on the boundary and, thus 200 corresponding source points are taken. Based on the numerical results of NLHEDD-FS method in piezoelectric media (Zhao et al, 2008;Fan et al, 2009) and the linear elastic MEE media (Zhao et al, 2010), the parameter a is very critical in the NLEDD-FS method…”

“…This method was successfully applied to the study of the linear fracture of piezoelectric media and MEE media (Zhao et al, 2010). This paper is organized as follows: In Section 2, the basic equations are presented.…”

An iterative approach for analysis of cracks with exact boundary conditions in finite magnetoelectroelastic solids

“…Hence, in figures 8−13, only three crack BCs are adopted. The results of the central crack in a 2D magnetoelectroelastic solid under two simplified BCs are calculated with a hybrid extended displacement discontinuity-fundamental solution method [28].…”

Three-dimensional vertical cracks in magnetoelectroelastic media via the extended displacement discontinuity boundary integral equation method

“…In applications, however, unavoidable defects (e.g. cracks) in these materials exist, which requires us to analyze the fracture behavior of cracks in MEE media (Chen, 2009;Feng et al, 2010;Gao and Noda, 2004;Li et al, 2009;Rojas-Dı´az et al, 2010;Wang, 2012;Zhao et al, 2010;Zhong, 2009;Gao et al, 2003aGao et al, , 2003bJiang and Pan, 2004;Liu et al, 2001).…”