Material non-linearity in the numerical analysis of SLJ bonded with ductile adhesives: A meshless approach

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 (LO) 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 (Pmax) 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 Pmax closer to the experimental data; the joints with intermediate overlap lengths LO=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.