Dynamic non-local theory analysis of multiple cracks in a FGPM under anti-plane shear waves

Article type: Research Article

Authors: Liu, Hai-Tao^a; | Li, Tie-Jun^a; | Wu, Jian-Guo^a

Affiliations: [a] School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, P. R. China

Correspondence: [*] Corresponding authors: Hai-Tao Liu and Tie-Jun Li. E-mails: [email protected], [email protected]

Abstract: This paper investigates the dynamic interaction of multiple cracks in a functionally graded piezoelectric material (FGPM) plane subject to an anti-plane shear stress wave. The non-local theory and Schmidt method are used. Employing the Fourier transform techniques, the problem is converted to dual integral equations, which the unknown variables are jumps of displacements across the crack surfaces. The present solution exhibits no stress and electric displacement singularities at the crack tips and the stress and electric displacement fields near the crack tips are obtained. The non-local elastic solutions yield a finite hoop stress and electric displacement at the crack tips. This research will give us ideas on material selection for evaluating strength and preventing material failure of FGPM with multiple cracks.

Keywords: Anti-plane shear waves, functionally graded piezoelectric material, multiple cracks, non-local theory, solid mechanics

DOI: 10.3233/SFC-180209

Journal: Strength, Fracture and Complexity, vol. 11, no. 1, pp. 1-17, 2018