<p>Many engineering applications require structures that are strategically designed, highly durable, and possess excellent energy absorption capabilities. To address this need, various structural configurations inspired by biological systems have been developed. These bio-inspired structures have demonstrated superior performance in terms of energy absorption and durability compared to conventional designs. Consequently, biomimetic strategies are increasingly employed in engineering to develop advanced structures with enhanced mechanical characteristics. This study presents the first investigation into the static bending behavior of a two-curvature nanoshell resting on a viscoelastic substrate. The outer layers are composed of piezoelectric materials, while the core layer is a composite made of nanoscale sublayers arranged according to biomimetic principles. A finite element-based approach, incorporating nonlocal elasticity theory, refined shear deformation theory, and the principle of virtual work, is employed to derive the governing equilibrium equations. Additionally, the flexoelectric effect is taken into account. The numerical results highlight the influence of the viscous drag coefficient of the substrate, showing that its presence leads to a noticeable reduction in the shell’s displacement.</p>