PSI - Issue 52

Made Wiragunarsa et al. / Procedia Structural Integrity 52 (2024) 583–593 Wiragunarsa et al. / Structural Integrity Procedia 00 (2023) 000–000

586

4

x

2

x

1

Γ

Fig. 1. A contour to calculate the J -integral

Based on the illustration in Figure 1, the J 1 will be used to calculate the stress intensity factor. The decomposition of the J 1 in Equation 7 to obtain the stress intensity factor K I is discussed in Rigby and Aliabadi [1998], Dirgantara and Aliabadi [2000].

3. Smoothed particle hydrodynamics

3.1. Spatial discretisation

The SPH method calculates the value of an arbitrary function using the summation of neighbour particle’s proper ties. In Figure 2, the area of influence or support domain ( Ω ) of particle i is bounded by a radius equal to κ h . κ is a parameter depending on the kernel type used, and h is the particle spacing. The SPH discretisation of Equation 1 is

κh

r

Ω

i

ij

j

Fig. 2. Neighbour particles within the support domain of particle i

represented by Equation 8. Parameter N is the total number of particles within the support domain of particle i , and ˜ ∇ W j ( x i ) is the corrected kernel gradient, as reported by Bonet and Lok [1998].

N j = 1

V j σ j ˜ ∇ W j ( x i ) + σ i ˜ ∇ W i ( x j ) + D

d p i dt

= s i +

(8)