Instability-driven shape-shifting via active stiffness tailoring: A computational optimisation framework for energy landscape reprogramming

Shape-shifting structures that respond rapidly and efficiently to environmental stimuli are of growing interest for applications ranging from soft robotics to adaptive engineering systems. While structural instabilities are traditionally regarded as failure mechanisms, they can be harnessed in a controlled manner to enable fast, energy-efficient shape transformations. In this work, we propose a design strategy termed active stiffness tailoring , in which the spatial distribution of thermally responsive materials is optimised to reprogramme the underlying energy landscape of a structure. By exploiting temperature-induced phase changes in active polymers, a structure can be driven from bi-stability to mono-stability, triggering rapid shape-shifting through a snap-back instability without requiring continuous actuation. A bi-material shallow arch is used as a proof-of-concept system. A parametric nonlinear finite element (FE) model is developed and embedded within an optimisation framework to determine the optimal layout of active and passive materials that maximises the strain energy released at the instability limit point. Two independent designs are obtained to demonstrate shape-shifting induced by either monotonic cooling or heating, highlighting the generality of the proposed approach. Numerical results reveal how targeted stiffness modulation reshapes the energy landscape, governs stability transitions, and enables rapid shape transformation. Experimental validation is performed for a heating-induced case using multi-material PolyJet-fabricated specimens. Thermally triggered snap-back is observed in good qualitative agreement with numerical predictions. Discrepancies in the transition temperature are analysed and attributed primarily to viscoelastic prestress loss and uncertainties in temperature-dependent material properties. Overall, this study establishes active stiffness tailoring as a powerful and versatile strategy for designing reprogrammable, fast-response shape-shifting structures driven by environmental stimuli.