A nonlinear modeling approach for corrugated sandwich beams

Enhancements in structural efficiency are central in reducing the carbon footprint of the transport industry. With recent manufacturing advances, sandwich panels became viable to reduce the structural weight in large plated structures. Methodologies for their structural modeling and optimization have, however, limitations, as simplified models cannot predict scale interactions that arise in lightweight settings. This dissertation proposes a scale-dependent modeling approach to predict the geometrically nonlinear response of elastic sandwich beams. The approach can predict size effects and the influence of local elastic buckling in the global beam response. In this work, a computationally efficient multiscale approach is defined. A couple stress-based beam model is employed to describe the global behavior, with constitutive relations that represent unit-cell deformation modes. Scale transitions are embedded in the beam constitutive matrix. Terms associated with the axial behavior of the sandwich face sheets are progressively adapted according to the global strain-state and an associated local model. Stress recovery is pursued consistently with the averaging rules, including recovery of periodic terms. A finite element based on previous works is presented along with adapted nonlinear root-finding schemes to solve the equilibrium equations. Stiffness properties of selected sandwich cells are derived and presented in closed form. The results reveal that the modeling approach succeeds in predicting the nonlinear response of elastic sandwich panels under quasi-static loads. Accurate stress distributions were obtained for linear and moderately nonlinear responses. Bending and progressive buckling geometric failure paths were successfully traced, including the effect of progressive local face sheet buckling. The approach was tested against different combinations of structural parameters, revealing a wide applicability range. With the present approach, accurate elastic response predictions result with low modeling and computational costs. Reliable output is obtained, from beams with lightweight local-buckling-prone to denser size-effect-sensitive unit cell setups. The approach offers substantial improvements in relation to other low-complexity models available in the literature. Unlike Cauchy-based models, it is able to describe size-dependent behavior through the couple stress-related parameters. In relation to conventional single-layer models, it incorporates nonlinear local scale information to the average global continuum. In the linear scale-independent case and for an antiplane core, the model reduces to the textbook thick-face sandwich theory.