An extended isogeometric analysis approach via symplectic system for interface V-notched magneto-electro-elastic bimaterial

Abstract

Magneto-electro-elastic (MEE) materials play a crucial role in intelligent structural devices, where their structural integrity under coupled mechanical, electrical, and magnetic loading is critical for operational safety, particularly in regions containing stress-concentrating V-shaped notches introduced during design or service. Extended isogeometric analysis (XIGA) is proposed to investigate the fracture behavior of MEE bi-material structures with interfacial V-shaped notches under anti-plane loading. The symplectic analytical solutions for the anti-plane problem of a MEE bi-material structure with interfacial V-notch are derived and incorporated as enrichment functions for the notch-tip control points. The geometric model and multi-physics field interpolations are constructed directly using non-uniform rational B-splines. Material domains and control point positions are judged via level set functions, while the notch surfaces and material interface are enriched using Heaviside functions and level set-based enrichment, respectively. The derived XIGA formulation is transformed into a novel system of linear equations through the application of series-form symplectic analysis solutions. This approach enables direct computation of the field intensity factors and energy release rate at the notch tip. Numerical examples validate the accuracy of the proposed method and further analyzed the influence of structural parameters on fracture behavior.