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Viscoelastic shells subjected to a pressure loading exhibit rich and complex time-dependent responses. Here we focus on the phenomenon of pseudo-bistability, i.e. a viscoelastic shell can stay inverted when pressure is removed, and snap to its natural shape after a delay time. We model and explain the mechanism of pseudo-bistability with a viscoelastic shell model. It combines the small strain, moderate rotation shell theory with the standard linear solid as the viscoelastic constitutive law, and is applicable to shells with arbitrary axisymmetric shapes. As a case study, we investigate the pseudo-bistable behaviour of viscoelastic ellipsoidal shells. Using the proposed model, we successfully predict buckling of a viscoelastic ellipsoidal shell into its inverted configuration when subjected to an instantaneous pressure, creeping when the pressure is held, staying inverted after the pressure is removed, and eventually snapping back after a delay time. The stability transition of the shell from a monostable, temporarily bistable and eventually back to the monostable state is captured by examining the evolution of the instantaneous pressure–volume change relation at different time of the holding and releasing process. A systematic parametric study is conducted to investigate the effect of geometry, viscoelastic properties and loading history on the pseudo-bistable behaviour. This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'. 

Abstract In response to external stimuli, such as heat, light, or magnetic fields, stimuli-responsive soft materials can change their current configuration to a new equilibrium state through non-equilibrium kinetic processes, including reaction, diffusion, and viscoelastic relaxation, which generates novel spatiotemporal shape-morphing behavior. Using a photothermal shape memory polymer (SMP) cantilever beam as a model system, this work analytically, numerically, and experimentally studies its non-equilibrium kinetic processes and spatiotemporal bending under light illumination. We establish a thermomechanical model for SMPs capturing the concurrent non-equilibrium processes of heat transfer and viscoelastic relaxation, which induces inhomogeneous temperature and strain distributions through the thickness of the beam, resulting in its bending and unbending. By varying the key dimensionless parameters, we theoretically and experimentally observe different types of bending dynamics. Moreover, our theory takes into consideration changes in the angles of incidence caused by extensive beam bending, and demonstrates that this effect can dramatically delay the bending due to reduction of the effective light intensity, which is further validated experimentally. This work demonstrates programmable and predictable spatiotemporal morphing of SMPs, and provides design guidelines for SMP morphing structures and robots. 

Formation of desired three-dimensional (3D) shapes from flat thin sheets with programmed non-uniform deformation profiles is an effective strategy to create functional 3D structures. Liquid crystal elastomers (LCEs) are of particular use in programmable shape morphing due to their ability to undergo large, reversible, and anisotropic deformation in response to a stimulus. Here we consider a rectangular monodomain LCE thin sheet divided into one high- and one low-temperature strip, which we dub a ‘bistrip’. Upon activation, a discontinuously patterned, anisotropic in-plane stretch profile is generated, and induces buckling of the bistrip into a rolled shape with a transitional bottle neck. Based on the non-Euclidean plate theory, we derive an analytical model to quantitatively capture the formation of the rolled shapes from a flat bistrip with finite thickness by minimizing the total elastic energy involving both stretching and bending energies. Using this analytical model, we identify the critical thickness at which the transition from the unbuckled to buckled configuration occurs. We further study the influence of the anisotropy of the stretch profile on the rolled shapes by first converting prescribed metric tensors with different anisotropy to a unified metric tensor embedded in a bistrip of modified geometry, and then investigating the effect of each parameter in this unified metric tensor on the rolled shapes. Our analysis sheds light on designing shape morphing of LCE thin sheets, and provides quantitative predictions on the 3D shapes that programmed LCE sheets can form upon activation for various applications. 

A stretchable pressure sensor is a necessary tool for perceiving physical interactions that take place on soft/deformable skins present in human bodies, prosthetic limbs, or soft robots. However, all existing types of stretchable pressure sensors have an inherent limitation, which is the interference of stretching with pressure sensing accuracy. Here, we present a design for a highly stretchable and highly sensitive pressure sensor that can provide unaltered sensing performance under stretching, which is realized through the synergistic creations of an ionic capacitive sensing mechanism and a mechanically hierarchical microstructure. Via this optimized structure, our sensor exhibits 98% strain insensitivity up to 50% strain and a low pressure detection limit of 0.2 Pa. With the capability to provide all the desired characteristics for quantitative pressure sensing on a deformable surface, this sensor has been used to realize the accurate sensation of physical interactions on human or soft robotic skin.