PSI - Issue 77

D.C. Gonçalves et al. / Procedia Structural Integrity 77 (2026) 79–86 Gonçalves et al./ Structural Integrity Procedia 00 (2026) 000 – 000

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(FEM). This is the case of adhesively bonded joints applications. However, the complexity of the thin adhesive layer, or the use of high ductility adhesives, can hinder the use of classic FEM. Structural adhesive bonding is a widely used technology in leading automotive and aircraft industries, being a significant part of the production process of safe and optimized components the accurate and efficient computational simulation. Improved approaches such as cohesive zone modelling (CZM) and the extended FEM (XFEM) have been developed in order to overcome classic FEM drawbacks. More recently, meshless methods have been applied to several computational modelling fields. Problems involving crack propagation and large deformation represent applications where meshless techniques can overcome classic mesh- based approaches’ limitations. Neverteless, its extension to adhesive joints simulation is still underdeveloped. Meshless techniques can be traced back to the Smoothed Particle Hydrodynamics (SPH) method [1], [2], originally developed to model astrophysical events. Subsequently, several meshless methods employing approximating shape functions were developed. The Diffuse Element Method (DEM) [3] was the first documented method to use the Moving Least Squares (MLS) [4] to build the shape functions over scattered nodes, forming the basis of the Element Free Galerkin Method (EFGM) [5]. The EFGM is one of the most popular meshless methods within structural mechanics and is widely consolidated in the literature. Due to the lack of the Kronecker delta property, hindering the enforcement of boundary conditions, meshless methods based on interpolating shape functions were later developed. The Point Interpolation Method (PIM) [6], [7] was presented, yet singularity problems in the PIM shape functions quickly led to its improvement by adding radial basis functions (RBF) to the original PIM shape functions, hence giving birth to the Radial Point Interpolation Method (RPIM) [8] – [10]. In this work, we present the results of the application of the RPIM to predict fracture propagation in adhesive joints subjected to mode I and mode II loading. The previous determination of pure mode I and mode II parameters can then be considered in future applications to implement mixed-mode energy criteria in adhesive joint applications. Hence, Double Cantilever Beam (DCB) and End-Notched Flexure (ENF) tests were performed experimentally to compare and assess the numerical accuracy of the proposed fracture propagation algorithm. 2. Methods 2.1. Radial Point Interpolation Method The first procedure is to discretize the problem domain into a set of field nodes. Then, integration points must be collocated to numerically integrate the differential equations governing the solid mechanics problem. In meshless methods, a background integration mesh that is completely independent of the field nodes can be constructed. Nevertheless, integration meshes connected to the field nodes, usually originated from commercial finite element method software, can be used. Fig. 1 shows an example of this type of mesh. Triangular integration cells were used in this work. Each triangular subcell is then divided into smaller quadrilateral subcells [11], as shown, and integration points are collocated at the barycentre of the subcell, with the integration weight being the respective area. Finally, the problem domain is completely discretized in a ser of field nodes and integration points as shown in Fig. 1. Nodal connectivity is imposed by the overlap of influence domains. The influence domain of an integration point is defined as the set of nodes contributing to the shape function construction at that integration point. Influence nodes are found by radially searching the closest nodes to the integration point of interest as Fig. 2 shows for distinct integration points. The sharing of influence nodes between distinct influence domains enforces nodal connectivity, leading to a banded global stiffness matrix, usually wider than in classic FEM. Depending on , deeper nodal connectivity can be achieved, although at the cost of increased computational time.