X-FEM in isogeometric analysis for linear fracture mechanics

Emmanuel de Luycker (1, 2) , David J. Benson (1) , Ted Belytschko (2) , Yuri Bazilevs (1) , Ming Chen Hsu (1)

1 UC San Diego - University of California [San Diego]
2 Northwestern University [Evanston]

The extended finite element method (X-FEM) has proven to be an accurate, robust method for solving problems in fracture mechanics. X-FEM has typically been used with elements using linear basis functions, although some work has been performed using quadratics. In the current work, the X-FEM formulation is incorporated into isogeometric analysis to obtain solutions with higher order convergence rates for problems in linear fracture mechanics. In comparison with X-FEM with conventional finite elements of equal degree, the NURBS-based isogeometric analysis gives equal asymptotic convergence rates and equal accuracy with fewer degrees of freedom (DOF). Results for linear through quartic NURBS basis functions are presented for a multiplicity of one or a multiplicity equal the degree.

Mots clés: Isogeometric analysis; Linear fracture mechanics; NURBS; X-FEM

Domaines: Mécanique des matériaux [physics.class-ph]

Emmanuel de Luycker, David J. Benson, Ted Belytschko, Yuri Bazilevs, Ming Chen Hsu. X-FEM in isogeometric analysis for linear fracture mechanics. International Journal for Numerical Methods in Engineering, 2011, 87 (6), pp.541-565. ⟨10.1002/nme.3121⟩. ⟨hal-01657905⟩