Series solutions to elastic opening of double cantilever beam for several traction–separation laws

The aim of this paper is to develop semi-analytical solutions for double cantilever beam (DCB) problems using eigenfunction series expansions. This approach provides explicit expressions for deflection as a function of the axial coordinate for various traction-separation laws (TSL) and different external loading conditions. For a given cohesive zone length, the solutions are presented in a closed analytical form. Once the deflection function is derived, the length of the interaction zone is related to TSL parameters, bending stiffness, and applied loads through transcendental equations, which are solved numerically. To validate the accuracy of the derived expressions, results are compared with numerical solutions obtained via finite element analysis. The good agreement observed between the analytical and numerical solutions confirms the robustness of the proposed method and its ability to accurately capture both global (deflection) and local (cohesive traction distribution) behavior. Compared to general solutions for semi-infinite beams found in the literature, eigenfunction series offer greater flexibility, accommodating a wider range of boundary conditions and loading types. • An approach to derive analytical solutions for a double cantilever beam using an eigenfunction series is presented. • Explicit solution examples are derived for various traction-separation laws and loading cases. • Results based on beam theory show good agreement with finite element solutions employing a plane stress model. • The solutions accurately reproduce both global behavior (arm deflection) and local behavior (cohesive traction distribution).