Dynamic behavior of graphene-origami-based meta-auxetic doublet nanobeam with memory-dependent effect

This work explores the mechanical characteristics response electro-magneto-thermoelastic (EMT) nanobeams by simultaneously accounting for fractional viscoelasticity, nonlocal elastic interactions, doublet mechanics, and couple-stress effects. A meta-auxetic architecture is integrated into the nanobeam inspired by graphene-based origami structures, allowing its mechanical behavior to be tuned through geometric reconfiguration and engineered microstructural features. Time-dependent viscoelastic phenomena—such as nanoscale stress relaxation and strain evolution—are captured using the Caputo-form Atangana–Baleanu fractional operator representing the material’s memory characteristics. The governing relations are formulated through Hamilton’s principle under a nonlocal couple-stress formulation. Because these equations are nonlinear and fractional in nature, the Adomian decomposition technique (ADT) is applied to obtain analytical solution approximations. A comparative study with previously published results is carried out for model verification. The results demonstrate that couple-stress behavior, fractional-order memory effects, auxetic properties arising from graphene-origami structures, doublet mechanics, and nonlocal phenomena all strongly influence the stress–strain behavior and thermal response of the nanobeam. Overall, the study offers important guidelines for designing and optimizing next-generation nanoscale systems, including biomedical sensors, reconfigurable electronics, adaptive façade components, and intelligent infrastructural materials.