PSI - Issue 41

Fabrizio Greco et al. / Procedia Structural Integrity 41 (2022) 576–588 Author name / Structural Integrity Procedia 00 (2019) 000–000

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tips. More interestingly, XFEMs permit properly replicating the initiation and propagation of arbitrary growing cracks without requiring re-meshing actions. Indeed, the discontinuous displacement fields allow crack propagation within the finite elements. However, using enriched shape functions adds extra degrees of freedom to the governing equations of the problem. This aspect may lead to numerical difficulties in simulating the propagation of multiple cracks, as often occurs in quasi-brittle materials. Besides, XFEMs typically require highly refined meshes to reproduce arbitrarily growing cracks accurately, thus being inconvenient to use with extensive and articulated computational domains. In recent years, great efforts have been made to develop novel modeling approaches to alleviate the major drawbacks of traditional methods. Among these, several hybrid procedures have been proposed. Such methods merge the strengths of classic approaches while reducing their weaknesses (see, for instance, the SB-FEM proposed by Ooi et al. in (Ooi et al. (2013))). In addition, many enhanced methods based on the combination of traditional approaches and innovative numerical techniques have been proposed. In this framework, the present authors have developed a suitable modeling approach for simulating crack propagation processes based on a standard FEM code enhanced by the Moving Mesh technique consistent with the ALE formulation (Ammendolea et al. (2021), Greco et al. (2021a)). According to this approach, the nodes of computational mesh are moved consistently with the crack path evolution, thereby involving remeshing actions only when finite elements distort considerably because of the node motions. The motion of the mesh nodes is governed by provisions dictated by standard fracture criteria, which define crack onset conditions and the direction of propagation. To this end, the developed method utilized the interaction method (Yu and Kuna (2021)), which is probably one of the widely used procedures because of its simplicity and accuracy. In particular, the ALE formulation of the M -integral is implemented in the numerical model, which permits extracting the leading fracture variables ( i.e. , Stress Intensity Factors (SIFs)) on deforming elements. However, the modeling strategy developed by the present authors in (Ammendolea et al. (2021), Greco et al. (2021a)) has been utilized to simulate crack propagation processes in quasi-brittle materials under quasi-static conditions. Therefore, further improvements are necessary to simulate dynamic crack propagation phenomena. To this end, this work aims to extend the above-mentioned modeling approach to simulate more complex fracture problems involving dynamic crack propagation phenomena in quasi-brittle materials. In particular, the present work proposes a novel ALE formulation of the M -integral capable of extracting Dynamic Stress Intensity Factors (DSIFs) at the crack front during the motion of mesh nodes. Besides, novel fracture functions are introduced to describe the fracture processes associated with dynamic crack propagation and crack arrest events. After the introduction, an overview of the theoretical concepts at the base of the proposed modeling approach is reported in Section 2. Subsequently, an exhaustive description of the numerical implementation is presented in Section 3. Finally, Section 4 deals with numerical results aimed at assessing the reliability and accuracy of the proposed modeling strategy. 2 Theoretical Background This section summarizes the key theoretical concepts at the base of the proposed modeling approach. At first, an exhaustive overview of the Arbitrary Lagrangian-Eulerian (ALE) formulation is introduced. Next, the main governing equations of the solid and fracture mechanics are presented. Finally, a description of the Interaction Integral method (M-Integral) for the analysis of dynamic fracture problems is reported. The strategy is presented concerning two-dimensional fracture problems. However, the discussion is quite general to be easily extended to three-dimensional cases. 2.1 The ALE formulation Classical continuum mechanics theories are usually formulated using two reference frames: the spatial domain x R (consisting of spatial points fixed in space identified by spatial coordinates x ) and the material domain X R (formed by material particles identified by spatial coordinates X at time t =0). The former is generally referred to as a Eulerian approach, whereas the latter is a Lagrangian approach.