Abstract Modern transportation, medical, and leisure equipment are often manufactured with non-metallic and composite materials bonded with adhesives. Numerical analyses of these joints are commonly performed using the Finite Element Method (FEM). In adhesive joints, the bond line is small compared to the substrates requiring highly refined meshes to perform the analyses. Also, adhesives can reach higher strains compared to the substrates, and so causing mesh distortion and compromising the solution. Alternatively, meshless methods (MM) can be employed. Single-lap joints (SLJ), during loading, present tensile and compressive stresses along the adhesive layer. Commonly, in elastic-plastic analyses, equal adhesive's strength in tension and compression is considered (using von Mises (vM) yield criterion), but it has been reported that adhesives are stronger in compression. Thus, a yielding criterion such as the Exponent Drucker-Prager (EDP) can be used; however, no MM implementations are available in the literature. This work seeks to implement the EDP into a MM, the Natural Neighbour Radial Point Interpolation Method (NNRPIM). Then, using the NNRPIM elastic-plastic parametric analyses of SLJ with aluminium substrates were performed considering four overlap lengths ( L O ) and two different ductile adhesives. All the cases were also evaluated using MM and the vM yield criterion, as a benchmark. Stress and strain distributions along the bond-line were obtained; afterwards, joint strength ( P m a x ) was determined by using continuum mechanics failure criteria, and then, evaluated and compared. Then, the results were compared against experimental data. The cases solved using the EDP predicted P m a x closer to the experimental data; the joints with intermediate overlap lengths L O = 25.0 mm presented the closest values. In conclusion, the results' correlation with experimental data indicates the EDP is closer than vM to the actual adhesive behaviour in the joints. Also, the EDP was successfully implemented. Overall, the NNRPIM is a strong and accurate alternative for elastic-plastic analyses of adhesive joints.

中文翻译：

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用延展性粘合剂粘合的 SLJ 数值分析中的材料非线性：无网格方法

摘要 现代交通、医疗、休闲设备多采用非金属和复合材料用粘合剂粘合而成。这些接头的数值分析通常使用有限元方法 (FEM) 进行。在粘合接头中，与需要高度精细网格来执行分析的基材相比，粘合线很小。此外，与基材相比，粘合剂可以达到更高的应变，因此会导致网格变形并影响解决方案。或者，可以采用无网格方法 (MM)。单搭接接头 (SLJ) 在加载过程中会沿粘合剂层产生拉伸和压缩应力。通常，在弹塑性分析中，考虑相同的粘合剂在拉伸和压缩方面的强度（使用 von Mises (vM) 屈服准则），但据报道，粘合剂的抗压性更强。因此，可以使用屈服准则，例如指数 Drucker-Prager (EDP)；然而，文献中没有可用的 MM 实现。这项工作旨在将 EDP 实现为 MM，即自然邻域径向点插值法 (NNRPIM)。然后，使用 NNRPIM 弹塑性参数分析 SLJ 与铝基材，考虑四个重叠长度 (LO) 和两种不同的延展性粘合剂。还使用 MM 和 vM 屈服标准作为基准对所有案例进行了评估。获得沿粘合线的应力和应变分布；之后，采用连续介质力学破坏准则确定接头强度（P max ），然后进行评估和比较。然后，结果与实验数据进行了比较。使用 EDP 预测的 P max 解决的案例更接近实验数据；中间重叠长度 LO = 25.0 mm 的接头呈现最接近的值。总之，结果与实验数据的相关性表明 EDP 比 vM 更接近于接头中的实际粘合行为。此外，EDP 已成功实施。总体而言，NNRPIM 是粘合接头弹塑性分析的强大而准确的替代方案。EDP​​ 成功实施。总体而言，NNRPIM 是粘合接头弹塑性分析的强大而准确的替代方案。EDP​​ 成功实施。总体而言，NNRPIM 是粘合接头弹塑性分析的强大而准确的替代方案。