Mechanical instabilities in soft active materials: Flutter in electroactive structures and surface instability in magnetoelastic solids

Soft active materials deform in response to external fields, a feature enabling their untethered actuation. Of particular interest in this context are actuation strategies that exploit mechanical instabilities, whereby the loss of stability of an equilibrium at a critical value of the external stimulus triggers large-amplitude deformations or motions. This thesis explores this opportunity through the analysis of three model systems, under a restriction maintained throughout the study: the applied stimulus, either electric or magnetic, is constant in time and uniform in space. Each system is investigated following a common methodology. Starting from structural or three-dimensional continuum models, the approach comprises linear stability analyses, nonlinear simulations of the post-critical regime and, for two of the systems considered, small-scale physical experiments. Within a morphoelastic framework, it is shown that thin rods and shells made of polyelectrolyte hydrogel exhibit a flutter instability when the applied electric field exceeds a critical value. For rods, the periodic motions emerging beyond the instability are either two- or three-dimensional, with the latter arising through a secondary bifurcation from the former. The influence of a natural curvature imprinted at the fabrication stage is also investigated. For shells, the spontaneous dynamics are inherently three-dimensional, with the competition between bending and stretching energies selecting the emergent shapes. In all cases, the periodic motions are nonreciprocal, thus allowing a clamped rod to generate a net flow in the surrounding fluid or a free shell to swim through it. A continuum model is developed to investigate the Rayleigh--Taylor instability in soft magnetoelastic solids under plane-strain conditions, accounting for gravity, magnetic loading and the hydrostatic pressure exerted by an external fluid. For a layer fixed at its upper surface, a static bifurcation occurs when the layer height exceeds a critical value. Such instability is characterised by spatially periodic undulations of the free surface. The same phenomenon is also shown to occur in a layer supported from below, provided that a denser fluid rests on its free surface. The application of a magnetic induction across the thickness of the layer lowers the instability threshold, thereby allowing for the controlled morphing of patterned surfaces. The results of this thesis suggest possible strategies for controlling soft active bodies. Notably, the applied stimulus carries neither an intrinsic frequency nor a characteristic length scale: the emergent functional responses are determined by the interaction among the actuated system, the operating environment, and a minimally structured external stimulus. These findings open perspectives ranging from small-scale soft robotics and fluid transport in microfluidic devices to the reversible patterning of surfaces.