Auxetic viscoelastic curved sandwich panels with designer functionally graded materials tailored to minimize creep buckling failure probabilities

Optimum designer materials, particularly auxetic viscoelastic functionally graded ones (i.e. non-homogeneous materials), are studied to minimize shear and bending stresses, and creep deflections while concurrently lowering failure probabilities and extending survival times of curved sandwich plates. Elastic auxetic materials are defined as those with negative Poisson ratios (PRs). However, for viscoelastic auxetic materials, any PR characterization is meaningless, but since elastic PRs form the initial conditions, large viscoelastic shear moduli are inherently possible and represent the stiffest and therefore possibly the lightest cores. Viscoelastic materials are known for their ability to dissipate energy. This property has been successfully used by the author and his colleagues to produce effective passive structural control for column and plate creep buckling, various vibratory modes, and aero-viscoelastic phenomena, such as torsional divergence, lifting surface and panel flutter, and attenuation of aerodynamic noise in panels. In self-excited systems the application of increased dissipation may stabilize or destabilize such systems depending on the influence of damping and all other forces on phase relations. Conventional design and analysis formulations call for use of the best off the shelf material. In this paper, relaxation modulus functions are tailored through prescriptions of appropriate functionally graded viscoelastic materials to produce the desired designer material performance. Relaxation moduli are, of course, highly temperature sensitive and performances are evaluated relative to operational demands. Sandwich plates generally have a cross section consisting of two metal, polymer or composite faceplates separated by foam, honeycomb or similar material cores. The primary function of the core is to carry shear loads while the faceplates resist bending stresses and moments. Therefore, it is desirable to have large shear moduli in order to maximize core rigidity and minimize deflections. Negative PR produce elastic shear moduli larger than Youngs moduli. However, while elastic PRs values may serve as a limited initial guide, the subsequent time behavior is no indicator of viscoelastic behavior, since viscoelastic PRs are not unique mechanical properties because they depend on loading paths and on material time histories. Consequently, detailed analyses and simulations are performed to establish the efficacy of viscoelastic shear modulus increases in the presence of different relaxation functions and loading conditions. The ultimate proof of the pudding is found in the selection of optimal designer material properties and their spatial distributions (FGM) that lead to low failure probabilities and long survival times.