Bayesian Optimization of Equilibrium States in Architected Elastomers

Hyperelastic lattice-based architectures have demonstrated potential for energy absorption and vibration control due to their inherent buckling instabilities, which reconfigure the energy and stiffness distribution of the structure. Multi-resonant vibration isolation can possibly be achieved by tuning the local stiffness properties between the stable equilibrium states. In this study, we develop a design optimization framework to tune the local configuration of the stable equilibrium points and characterize the transition in stiffness through the bistability. We utilize Bayesian optimization to navigate the design space through a balanced approach of exploitation and exploration. The design architecture is parameterized with a Fourier series expansion of the beam geometry, which controls the periodicity and phase of the beam thickness as a function of length. The force-displacement relationship of each design candidate is calculated by the finite element method and segmentation of mono- and bi-stable designs is employed to retain the desired behavior of the response surface. The preliminary results suggest the periodicity of the beam thickness, parameterized by the 1st term in Fourier series, most critically affects the bistability mode.