Spontaneous bi-stability of liquid crystalline solid beams and state transitions via snap-through buckling

Liquid crystalline (LC) solids, as a type of soft active material, are capable of undergoing reversible spontaneous deformation in response to various external stimuli. This paper investigates the spontaneous bending of LC solid beams and the bistability of this phenomenon from a mechanics perspective, with general applicability to various external stimuli modeled as equivalent spontaneous strains. The spontaneous strain in the LC solid beam typically involves both axial normal strain and transverse shear strain. Therefore, we incorporate von Kármán geometric nonlinearity into an LC solid beam model that includes the effects of the spontaneous transverse shear strain to derive the governing equation and relevant bending solution. The results demonstrate that the bistability arises from the compressive axial force within the beam, which is generated by the constraint on its spontaneous elongation. When the beam exhibits bistability, the two stable bending states are oppositely directed, and the transitions between them can be achieved by applying a reversed transverse mechanical load that causes snap-through buckling. Furthermore, the critical conditions for the beam to exhibit the spontaneous bistability and to undergo the mechanical snap-through buckling are obtained through several distinct approaches. Our results are expected to offer valuable insights and theoretical guidance for the application of LC solids and a broad class of materials exhibiting similar spontaneous stain responses in sensing, actuation, and energy absorption in scenarios involving diverse external stimuli.