AN APPROXIMATE ANALYTICAL MODEL FOR ADHESIVE-LAYER STRESSES IN ASYMMETRIC SINGLE-LAP JOINTS

Differences in thickness or material properties between the upper and lower adherends produce asymmetric shear and peel stress distributions in the adhesive, complicating rapid assessment of single-lap joints. To address this problem, an approximate analytical model is developed while retaining the principal load-transfer mechanisms. Elastic beam theory and a spring-layer model are used to derive coupled equations for the shear and transverse displacement differences, while eccentric-load boundary conditions are formulated using the Goland-Reissner end-moment theory. The nonhomogeneous coupling term in the shear displacement-difference equation is neglected, allowing the shear displacement difference to be solved first. The boundary-decay property of the transverse displacement-difference solution is then used to construct left- and right-end approximations and obtain explicit shear- and peel-stress expressions. The model is verified against the symmetric-joint limit and linear-elastic finite element results, and evaluated for changes in adhesive thickness, adherend thickness ratio, elastic-modulus mismatch, and overlap length. It captures the overall stress distributions and trends in end asymmetry. For shear stress, the relative errors in peak values at both ends are below 21%, and all normalized root-mean-square errors (NRMSE) over the interior overlap region are below 15%. For peel stress, the interior-region NRMSE is below 15% in most cases, whereas the relative error in a single-end peak exceeds 40% in some strongly mismatched or short-overlap cases. The model is therefore more accurate for thin adhesive layers, small adherend-stiffness mismatch, and long overlaps; critical end peel stresses should be checked by finite element analysis for strongly mismatched or short-overlap joints. Supplementary comparisons with an elastic-perfectly plastic finite element model show load-dependent yielding effects, which remain localized near the overlap ends at lower load but reduce end peaks and produce a shear-stress plateau and redistribution toward the overlap interior at higher load. The model is compact and efficient for rapid engineering analysis and preliminary design of asymmetric adhesively bonded single-lap joints.