Analytical and numerical modeling of the mixed-mode delamination process for composite moment-loaded double cantilever beams

This work aims at studying the mixed-mode delamination process in Moment-Loaded Double Cantilever Beam (MLDCB) specimens. The delamination problem is addressed both analytically and numerically, while considering the interfaces as an assemblage of two sublaminates partly bonded together by an elastic interface. Such interface is modeled as a continuous distribution of elastic-brittle springs acting along the normal and/or tangential direction depending on the interfacial mixed-mode condition. The Timoshenko's beam theory is here applied to determine the governing equations of the differential problem and the associated boundary conditions, whose solution is not straightforward. The Generalized Differential Quadrature (GDQ) method is then applied as numerical tool to solve directly the differential equations of the problem in a strong form. The capability of the proposed numerical approach is first exploited through a comparative evaluation of the results with the analytical predictions resting on a suitable change of variables for delamination test specimens. The local and global response is determined, in terms of interfacial stresses, internal forces and displacements, as well as in terms of compliance, energy release rate, mode mixity angle, and moment-rotation curves. A further check of the proposed numerical method is performed with respect to a Finite Fracture Mechanics (FFM) criterion, which is able to join both stress-and energy-based approaches. A good agreement between results confirms the good feasibility of the GDQ method when studying delamination phenomena occurring within composite materials or laminated joints, usually subjected to mixed-mode conditions.