Large bending behavior of creased paperboard. II. Structural analysis

• Finite rotation general kinematics of a typical creased carton in closed form.
• Configuration manifold.
• Statics derived by the Virtual Works Equation.
• Driving and reactive moment computation for erection paths.
• Bending constitutive equations with unstable branches and unloading.

The mechanics of a paradigmatic typical carton corner with five creases is analyzed theoretically, in closed form. A general kinematical analysis of the mechanism (in finite rotation) is presented, assuming the versor of the intermediate crease, s, as a 2-degree-of-freedom Lagrangian parameter. The rotation θc of the cth crease is derived, together with the existence domain and a discussion of the singular configurations.The actions, driving the carton during a prescribed quasi-static erection program, are derived in a very efficient manner using the Virtual Works Equation, taking into account a non-linear anholonomic bending constitutive law of the creased paperboard. In particular, the active and reactive components of the moment ϕ, driving s along its path, are identified. No resort to the tangent stiffness computation is required. Some numerical examples illustrate the rotation and the driving forces obtained for both monotone-loading and complex loading–unloading erection paths.The presented results, “exact” within the scope of the restrictive hypotheses assumed, may be used in a preliminary design approach as well as a benchmark for more realistic FEM or CAE simulators.

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