Hard magnetic materials belong to a novel class of soft active materials with the capability of quick, large, and complex deformation via applying an external actuation. They have an extensive range of potential applications in soft robots, biomedical devices, and stretchable electronics, etc. Recently, investigation on the experimental and theoretical nonlinear mechanics of hard magnetic soft cantilevers has received notable considerations. In the available analyses, the most attention was paid to the non-bifurcation-type nonlinear mechanics of the system, and bifurcation was considered for a specific case. In the current study, the general trend of bifurcation-type nonlinear mechanics of hard magnetic soft cantilevers is introduced and the effective parameters on the occurrence of bifurcation are identified. Additionally, new trajectories due to the bifurcation and the corresponding workspace are presented. Eventually, a comprehensive comparative study between the new trajectories and workspace with those reported in the prior studies is carried out.
It is generally acknowledged that a hanging cantilevered pipe conveying fluid becomes unstable by flutter-type instability at a critical flow velocity; moreover, the pipe undergoes periodic self-excited oscillations in the post-flutter region. Additionally, the critical flow velocity increases when the magnetized pipe is exposed to an actuating parallel magnetic field. The question arises as to whether the actuating magnetic field leads to lessening the oscillation amplitude of the system in the post-flutter region. To answer the question, the nonlinear responses of a fluid-conveying cantileve…
We present here a novel cantilever based apparatus to perform translational stress or strain controlled rheology in very soft solids, and obtain simultaneous confocal imaging of the 3 dimensional microstructure. The stress is measured using eddy based sensors. Both the stress and strain are controlled by applying PID control loops on measured quantities and changing position using a micromanipulator. To get rid of surface tension forces, the sample and cantilever are immersed. This enables stress measurement and control down to 3mPa. With this apparatus, we can independently apply shear and no…
In this work, we discuss and numerically validate a strategy to attain reversible macroscopic changes in the wave propagation characteristics of cellular metamaterials with soft microstructures. The proposed cellular architecture is characterized by unit cells featuring auxiliary populations of symmetrically-distributed smart cantilevers stemming from the nodal locations. Through an external stimulus (the application of an electric field), we induce extreme, localized, reversible curling deformation of the cantilevers---a shape modification which does not affect the overall shape, stiffness an…
Soft elastomers that can exhibit extremely large deformations under the action of an electric field are essential for applications such as soft robotics, stretchable and flexible electronics, energy harvesting among others. The critical limiting factor in conventional electro-actuation of such materials is the occurrence of the so-called pull-in instability. In this work, we demonstrate an extraordinarily simple way to coax a dielectric thin film towards a symmetry-breaking pitchfork bifurcation state while avoiding pull-in instability. Through the nonlinear interplay between the two bifurcati…
We investigate localised bulging or necking in an incompressible, hyperelastic cylindrical tube under axial stretching and surface tension. Three cases are considered in which the tube is subjected to different constraints. In case 1 the inner and outer surfaces are traction-free and under surface tension, whilst in cases 2 and 3 the inner and outer surfaces (respectively) are fixed to prevent radial displacement and surface tension. However, each free surface in these latter two cases is still under surface tension. We first state the analytical bifurcation conditions for localisation and the…
Soft materials, such as liquids, polymers, foams, gels, colloids, granular materials, and most soft biological materials, play an important role in our daily lives. From a mechanical viewpoint, soft materials can easily achieve large deformations due to their low elastic moduli; meanwhile, surface instabilities, including wrinkles, creases, folds, and ridges, among others, are often observed. In particular, soft dielectrics subject to electrical stimuli can achieve significantly large deformations that are often accompanied by instabilities. While instabilities are often thought to cause failu…
Matrix stiffness expressions are derived for the particle movements in an assembly of rigid granules having compliant contacts. The derivations include stiffness terms that arise from the particle shapes at their contacts. These geometric stiffness terms may become significant during granular failure. The geometric stiffness must be added to the mechanical stiffnesses of the contacts to produce the complete stiffness. With frictional contacts, this stiffness expression is incrementally nonlinear, having multiple loading branches. To aid the study of material behavior, a modified stiffness is d…
The bistability of embedded elements provides a natural route through which to introduce reprogrammability to elastic meta-materials. One example of this is the soft morphable sheet, in which bistable elements that can be snapped up or down, are embedded within a soft sheet. The state of the sheet can then be programmed by snapping particular elements up or down, resulting in different global shapes. However, attempts to leverage this programmability have been limited by the tendency for the deformations induced by multiple elastic elements to cause large global shape bifurcations. We study th…
Coupled magneto-mechanical wrinkling has appeared in many scenarios of engineering and biology. Hence, soft magneto-active (SMA) plates buckle when subject to critical uniform magnetic field normal to their wide surface. Here, we provide a systematic analysis of the wrinkling of SMA plates subject to an in-plane mechanical load and a transverse magnetic field?. We consider two loading modes: plane-strain loading and uni-axial loading, and two models of magneto-sensitive plates: the neo-Hookean ideal magneto-elastic model and the neo-Hookean magnetization saturation Langevin model. Our analysis…
Instability patterns of rolling up a sleeve appear more intricate than the ones of walking over a rug on floor, both characterized as uniaxially compressed soft-film/stiff-substrate systems. This can be explained by curvature effects. To investigate pattern transitions on a curved surface, we study a soft shell sliding on a rigid cylinder by experiments, computations and theoretical analyses. We reveal a novel post-buckling phenomenon involving multiple successive bifurcations: smooth-wrinkle-ridge-sagging transitions. The shell initially buckles into periodic axisymmetric wrinkles at the thre…
We derive a model for the finite motion of a magneto-elastic rod reinforced with isotropic (spherical) or anisotropic (ellipsoidal) inclusions. The particles are assumed weakly and uniformly magnetised, rigid and firmly embedded into the elastomeric matrix. We deduce closed form expressions of the quasi-static motion of the rod in terms of the external magnetic field and of the body forces. The dependences of the motion on the shape of the inclusions, their orientation, their anisotropic magnetic properties and the Young modulus of the matrix are analysed and discussed. Two case studies are pr…
Wrinkling of an inextensible elastic lining of an inner-lined tube under imposed pressure is considered. A simple equation modeling the elastic properties of the lining, the pressure, and the soft-substrate forces is derived. This equation aims to capture the wrinkling response of arterial endothelium to blood pressure changes. Numerical continuation is used to construct a bifurcation diagram as a function of the imposed pressure for in-plane deformations, in excellent agreement with weakly nonlinear theory, which we also develop. Our approach explains how the wavelength and amplitude of the w…
The necking instability is a precursor to tensile failure and rupture of materials. A quasistatically loaded free-standing uniaxial specimen typically exhibits necking at a single location, corresponding to a long wavelength bifurcation mode. If confined to a substrate or embedded in a matrix, the same filament can exhibit periodic necking thus creating segments of finite length. While periodic instabilities have been extensively studied in ductile metal filaments and thin sheets, less is known about necking in hyperelastic materials. There is a renewed interest in the role of necking in novel…
Pressurised cylindrical channels made of soft materials are ubiquitous in biological systems, soft robotics, and metamaterial designs. In this paper, we study large deformation of a long, thick-walled, and compressible hyperelastic cylindrical channel under internal pressure. The applied pressure can lead to elastic bifurcations along the axial or circumferential direction. Incremental theory is used to derive the partial differential equations that govern the bifurcation behaviour of the cylindrical channel. Two cases of boundary conditions on the outer surface of the cylinder, namely, free a…
Ferromagnetic particles are incorporated in a thin soft elastic matrix. A lamella, made of this smart material, is studied experimentally and modeled. We show herein that thin films can be actuated using an external magnetic field applied through the system. The system is found to be switchable since subcritical pitchfork bifurcation is discovered in the beam shape when the magnetic field orientation is modified. Strong magnetoelastic effects can be obtained depending on both field strength and orientation. Our results provide versatile ways to contribute to many applications from the microfab…
Weakly nonlinear dynamics of follower-force-induced oscillations in Cosserat rods
Cavendish Laboratory, University of Cambridge（剑桥大学卡文迪许实验室）；Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge（剑桥大学数学科学中心应用数学与理论物理系）
