PSI - Issue 72

Thomas Steffen Methfessel et al. / Procedia Structural Integrity 72 (2025) 105–112

108

With the identified solution, eventually, all deformations, strains and stresses are available everywhere in the considered sandwich-type model configuration. The described approach has been implemented in MATLAB and can be run on a standard personal computer. A single static analysis then takes about 1 second which means that the required field quantities are practically instantaneously available. 3. Comparative numerical analyses For comparison and validation purposes a finite element model has been generated by means of the finite element software ABAQUS for a configuration of two steel adherends with a thickness of 2mm each, a standard epoxy adhesive of 0.5mm thickness and an overlap length of 25mm. Eight-node biquadratic plane strain continuum elements have been employed with a well-adjusted mesh refinement near the edges where the stress concentrations are expected. In total this involves about 1 300 000 degrees of freedom and on a standard personal computer requires a CPU time of about 130 seconds. 4. Stress results The analysis of a single-lap joint under simple mechanical tensile load shown in Fig. 1 with the described sandwich type model leads to the shear stress results shown in Fig. 3 and the peeling stress results shown in Fig. 4.

Fig. 3. Shear stresses along the x-axis starting at the left edge at x=-12.5mm.

Fig. 4. Peeling stresses along the x-axis starting at the left edge at x=-12.5mm.

In these diagrams the stresses are given at the upper and lower position of the adhesive (at the interfaces to the adherends) and in the midplane. The results of the sandwich-type model are presented as solid line curves whereas the finite element results are given by dotted markers. Near the left edge of the sandwich-type model high stress concentrations occur. As can be seen, in all cases there is a good agreement between the sandwich-type model results and the comparative numerical finite element results.