Localized contacts, stress concentrations and transient states in bent-lamination with viscoelastic adhesion. An analytical study

• Bent-lamination of layered beams consists in gluing the plies while curved bent.
• Stress/curvature vary in time due to the viscoelasticity of the adhesive interface.
• Stress localization in the interface depends upon the constraining mould shape.
• Gradual release from the mould is studied as a contact problem.
• Optimal mould shapes and gradual release procedures are proposed.

An analytical study is presented for the bent-lamination of curved layered beams, a process consisting in gluing the constituent plies together after they have been elastically bent against a constraining negative mould. Possible applications range from glued laminated timber manufacturing, to cold-lamination-bending of structural glass. After removal of the constraint, the shear coupling through the glue maintains the curvature only partially, because the laminate suffers an initial spring-back followed by a long-term relaxation. The model problem considered here is that of two Euler–Bernoulli beams coupled by a thin viscoelastic adhesive layer. Within a variational approach, we analytically describe the relationship between the mould shape and the shape of the curved beam, which is time-dependent due to the viscosity of the adhesive layer. Localized contacts with the mould and stress concentrations may occur, depending upon the type of profile that is initially imposed. Comparison of the cases of instantaneous or gradual release of the contact with the mould, evidences a remarkable reduction of the transient state of stress in the second case.