Flow-induced buckling of a viscoelastic bistable structure in time varying flow

This study investigates the influence of linear viscoelasticity on the snap-through dynamics of bistable structures subjected to fluid flows with changing speed. The viscoelastic behavior is modeled using a Prony series, capturing the time-dependent relaxation modulus. Numerical simulations based on the Arbitrary Lagrangian–Eulerian framework are conducted to analyze the structural response under changing flow speeds. Key parameters, including relaxation times and Prony coefficients, are systematically evaluated to elucidate their roles in governing dynamic stability and energy transfer between the fluid and structure systems. Two critical dimensionless parameters are identified: a Cauchy number modified by viscoelastic stiffness and the Deborah number. The modified Cauchy number quantifies the interaction between fluid forces and effective structural stiffness, while the Deborah number captures the transition between viscous-dominated and elastic-dominated regimes. Structures with significant viscous effects exhibit delayed buckling and increased strain energy under faster inlet flow acceleration, indicating a stiffness amplification effect. These findings provide insight into the interplay between viscoelastic material response and flow conditions and inform the design of adaptive bistable structures for applications in soft robotics, morphing surfaces, and energy-harvesting technologies.