PSI - Issue 79

Domenico Ammendolea et al. / Procedia Structural Integrity 79 (2026) 467–474

470

Figure 1. A fractured body affected by dynamic crack propagation mechanisms.

Similarly, fracture functions are defined to manage the crack propagation process and the crack branching occurrence, which are: * 0 & 0 (propagation) 1 0 & 0 (arrest) P P F F P ID F f a K f K f a  = >  = − ⇒ = =    (10)

B f  =  < F B F f

0 (crack branching) 0 (no crack branching)

( )

a t 

(11)

, B v

1 = − ⇒

f

F

a

cr

( ) ID ID K K a =  is the dynamic crack growth toughness of the material, defined according to the

In Eq. (10),

empirical expression proposed by Kanninen and Popelar (Kanninen et al. (1988)): ( ) ( ) 1 IA ID m L K K a a V = −  

(12)

in which K IA and V L represent the crack arrest toughness and the limiting propagation velocity of the material, respectively. In addition, in Eq. (11), cr a is the critical propagation velocity of the material, that is, the velocity that marks the occurrence of crack branching. It is noted that , B v F f this is in accordance with the velocity criterion of crack branching. 3. Numerical implementation The proposed simulation framework is implemented within a customized environment that couples COMSOL Multiphysics, a powerful commercial FE software, with MATLAB via the LiveLink platform (COMSOL (2018)). This integration enables the definition of a homemade script to manage numerical simulation autonomously (De Maio et al. (2019), Pepe et al. (2019), De Maio et al. (2024b), De Maio et al. (2025a), De Maio et al. (2025b)). The procedure begins with a geometric definition that requires the input of a pre-cracked body (Figure 2-a). To facilitate propagation, an auxiliary node is introduced near the crack tip, dividing the pre-crack line into two parts: a static, longer segment and a short stretching segment (Figure 2-b). Only this stretching segment actively advances as the crack grows. Once the geometry is established, the domain is meshed, and boundary conditions are applied. After that, the analysis starts, and at each incremental step, the M -integral calculates the DSIFs and the kinking angle. Crack advance begins once the onset conditions are satisfied, with the crack tip moving in the direction calculated by the ALE mesh motion (Figure 2-c). A crucial feature of the model is its adaptive mesh control: element distortions, which inevitably occur due to mesh point movement, are quantified using the first invariant of the isochoric Green–Lagrange strain. Unlike traditional FEM, which remeshes after every crack advance, this method triggers remeshing only when the element distortion exceeds a user-defined threshold. This strategic remeshing significantly conserves computational resources and enhances numerical stability. Furthermore, the proposed strategy employs a mechanism to handle the continuous path of crack growth. Beyond element quality, the