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Register a new userElasto-capillary circumferential buckling of soft tubes under axial loading: existence and competition with localised beading and periodic axial modes
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We provide an extension to previous analysis of the localised beading instability of soft slender tubes under surface tension and axial stretching. The primary questions pondered here are: under what loading conditions, if any, can bifurcation into circumferential buckling modes occur, and do such solutions dominate localisation and periodic axial modes? Three distinct boundary conditions are considered; in case 1 the tubes curved 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. A linear bifurcation analysis is conducted to determine numerically the existence of circumferential mode solutions. In case 1 we focus on the tensile stress regime given the preference of slender compressed tubes towards Euler buckling over axial wrinkling. We show that tubes under several loading paths are highly sensitive to circumferential modes; in contrast, localised and periodic axial modes are absent, suggesting that the circumferential buckling is dominant by default. In case 2, circumferential mode solutions are associated with negative surface tension values and thus are physically implausible. Circumferential buckling solutions are shown to exist in case 3 for tensile and compressive axial loads, and we demonstrate for multiple loading scenarios their dominance over localisation and periodic axial modes within specific parameter regimes.
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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 then validate them numerically whilst determining whether localisation is preferred over bifurcation into periodic modes. It is shown that bifurcation into a localised solution is unattainable in case 1 but possible and favourable in cases 2 and 3. In contrast, in case 1 any bifurcation must necessarily take the form of a periodic mode with a non-zero wave number. Our results are validated using Finite Element Method (FEM) simulations.
Previous linear bifurcation analyses have evidenced that an axially stretched soft cylindrical tube may develop an infinite-wavelength (localised) instability when one or both of its lateral surfaces are under sufficient surface tension. Phase transition interpretations have also highlighted that the tube admits a final evolved two-phase state. How the localised instability initiates and evolves into the final two-phase state is still a matter of contention, and this is the focus of the current study. Through a weakly non-linear analysis conducted for a general material model, the initial sub-critical bifurcation solution is found to be localised bulging or necking depending on whether the axial stretch is greater or less than a certain threshold value. At this threshold value, an exceptionally super-critical kink-wave solution arises in place of localisation. A thorough interpretation of the anticipated post-bifurcation behaviour based on our theoretical results is also given, and this is supported by Finite Element Method (FEM) simulations.
This article investigates the large deflection and post-buckling of composite plates by employing the Carrera Unified Formulation (CUF). As a consequence, the geometrically nonlinear governing equations and the relevant incremental equations are derived in terms of fundamental nuclei, which are invariant of the theory approximation order. By using the Lagrange expansion functions across the laminate thickness and the classical finite element (FE) approximation, layer-wise (LW) refined plate models are implemented. The Newton-Raphson linearization scheme with the path-following method based on the arc-length constraint is employed to solve geometrically non-linear composite plate problems. In this study, different composite plates subjected to large deflections/rotations and post-buckling are analyzed, and the corresponding equilibrium curves are compared with the results in the available literature or the traditional FEM-based solutions. The effects of various parameters, such as stacking sequence, number of layers, loading conditions, and edge conditions are demonstrated. The accuracy and reliability of the proposed method for solving the composite plates geometrically nonlinear problems are verified.
A liquid surface touching a solid usually deforms in a near-wall meniscus region. In this work, we replace part of the free surface with a soft polymer and examine the shape of this elasto-capillary meniscus, result of the interplay between elasticity, capillarity and hydrostatic pressure. We focus particularly on the extraction threshold for the soft object. Indeed, we demonstrate both experimentally and theoretically the existence of a limit height of liquid tenable before breakdown of the compound, and extraction of the object. Such an extraction force is known since Laplace and Gay-Lussac, but only in the context of rigid floating objects. We revisit this classical problem by adding the elastic ingredient and predict the extraction force in terms of the strip elastic properties. It is finally shown that the critical force can be increased with elasticity, as is commonplace in adhesion phenomena
In this paper, we present an analysis of the guided circumferential elastic waves in soft EA tube actuators, which has potential applications in the in-situ non-destructive evaluation or online structural health monitoring (SHM) to detect structural defects or fatigue cracks in soft EA tube actuators and in the self-sensing of soft EA tube actuators based on the concept of guided circumferential elastic waves. Both circumferential SH and Lamb-type waves in an incompressible soft EA cylindrical tube under inhomogeneous biasing fields are considered. The biasing fields, induced by the application of an electric voltage difference to the electrodes on the inner and outer cylindrical surfaces of the EA tube in addition to an axial pre-stretch, are inhomogeneous in the radial direction. Dorfmann and Ogdens theory of nonlinear electroelasticity and the associated linear theory for small incremental motion constitute the basis of our analysis. By means of the state-space formalism for the incremental wave motion along with the approximate laminate technique, dispersion relations are derived in a particularly efficient way. For a neo-Hookean ideal dielectric model, the proposed approach is first validated numerically. Numerical examples are then given to show that the guided circumferential wave propagation characteristics are significantly affected by the inhomogeneous biasing fields and the geometrical parameters. Some particular phenomena such as the frequency veering and the nonlinear dependence of the phase velocity on the radial electric voltage are discussed. Our numerical findings demonstrate that it is feasible to use guided circumferential elastic waves for the ultrasonic non-destructive online SHM to detect interior structural defects or fatigue cracks and for the self-sensing of the actual state of the soft EA tube actuator.
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