PSI - Issue 80

4

Author name / Structural Integrity Procedia 00 (2019) 000–000

D.C. Gonçalves et al. / Procedia Structural Integrity 80 (2026) 443–450

446

= U . Ω

2 − U 2

. Ω

− U

. Γ 3 ! =0 .

(6)

Manipulation of equation (6) allows to establish a system of equations in the form (Belinha, 2014): = + , where the global stiffness matrix , and the natural force vector are defined as: = U . Ω 2 = ( ( ! ) . ( ) ( ! ) ∙ ! ( ! ) # " "$% , (9) being the deformability matrix containing the shape functions’ partial derivatives, the material constitutive matrix for plane strain conditions, the shape function interpolation matrix, 7 the total number of Gauss points, and ! the weight of integration point ! . (7) (8) = U . ̅ Γ 0 3 # = ( ( ! ) # " "$% . ̅ ∙ ! 0 ( ! ) ,

Fig. 1. NRPIM Procedure: nodal discretization (a), Voronoi diagram; (b), integration cells (c), and integration points (d)

Following linear analysis using the NNRPIM, fracture propagation is addressed using the critical energy release rate criterion, being the crack propagated when, ! = !8 , (10) being !8 =0.2 the critical energy release rate of the adhesive material, and ! the energy release rate at the crack tip in a given increment. Since the DCB test is a pure mode I application, = can be assumed, and ! is obtained by numerically integrating the J integral in a contour domain around the crack tip. For the denser nodal discretization, three radius were studied ( % =0.1875mm , ( =0.1875mm, and 9 = 0.1875mm), whilst for the coarser mesh only 9 was used