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Stress analysis and closed-form formulae for the ultimate axial lap-shear loads of an adhesively bonded double-lap joint, including strain-gradient effects: Elastic shear lag model
Journal article   Peer reviewed

Stress analysis and closed-form formulae for the ultimate axial lap-shear loads of an adhesively bonded double-lap joint, including strain-gradient effects: Elastic shear lag model

Stylianos Markolefas and Dimitrios Fafalis
International journal of adhesion and adhesives, v 150, 104396
Sep 2026
DOI: https://doi.org/10.1016/j.ijadhadh.2026.104396
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Abstract

Adhesive bonding Dipolar gradient elasticity Double-lap joint Elastic lap-shear load capacity Microstructural parameter Strain gradient effects
This study presents an elastic shear lag formulation for symmetric, stiffness-imbalanced, adhesively bonded double-lap joints, incorporating the influence of adhesive microstructure on the joint’s mechanical response. The model considers axial lap-shear loading — both tensile and compressive — and includes residual thermal strains due to mismatched axial thermal expansion between adherends. Load path eccentricities and bending of the outer adherends are neglected. Microstructural effects in the adhesive are modeled using a reduced one-dimensional strain gradient constitutive relation with two microstructural constants. However, the governing differential equations depend on a single microstructural parameter derived from one of these constants. Closed-form expressions for the elastic axial lap-shear load capacity are derived for sufficiently long overlaps. Parametric results are presented for various combinations of joint elasto-geometric properties and adhesive microstructural parameter values. Comparisons with classical shear lag models validate the proposed formulation. The results demonstrate that strain gradient effects become significant in micro- and nano-scale adhesive joints, where the microstructural parameter attains large values. An extended model is also developed, incorporating strain gradient effects in both the adhesive and the adherends. •Strain-gradient shear-lag models for double-lap joints: adhesive only, and with adherends.•Closed-form ultimate axial lap-shear load capacity including adhesive microstructure.•Comparison with classical Volkersen model via true and Cauchy shear stress profiles.

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