arXiv subjects

Yibin Fu

Publications and source records attributed to Yibin Fu.

At least 19 recordsLinked to original sources

arXiv2026

Inhomogeneous thinning of dielectric membranes under uniaxial tension and electric fields

Dielectric elastomers exhibit rich electromechanical instabilities arising from the coupling between mechanical deformations and electric fields. A widely used approach for analyzing instabilities in dielectric elastomers is the Hessian stability criterion proposed by Zhao and Suo (2007), which identifies the onset of instability of a homogeneous deformation but does not determine how the deformation develops beyond the instability threshold. To address this problem, we investigate dielectric membranes subjected to uniaxial tension and an electric field. Starting from a three-dimensional nonlinear electroelastic formulation, we derive asymptotically consistent reduced models, including a membrane model and a plate model, using the variational--asymptotic method. A linear bifurcation analysis first shows that the Hessian stability criterion is equivalent to a zero-wavenumber bifurcation condition, thereby establishing a direct connection between energy-based stability analysis and bifurcation theory. A subsequent weakly nonlinear analysis demonstrates that the zero-wavenumber bifurcation gives rise to localized necking, manifested as inhomogeneous thinning of the membrane. Furthermore, for the plane-stress configuration considered here, the membrane model accurately captures both the onset of instability and the associated localization behavior, while bending effects remain small. These results provide a physical interpretation of the Hessian instability and offer a framework for analyzing instabilities in dielectric membranes.

cond-mat.soft↗

arXiv2024

Analysis of axisymmetric necking of a circular dielectric membrane based on a one-dimensional model

To facilitate the understanding of the mechanisms underlying the electric breakdown of dielectric elastomers, we derive a one-dimensional (1d) model for axisymmetric necking in a dielectric membrane subjected to equibiaxial stretching and an electric field, starting from the three-dimensional (3d) nonlinear electroelasticity theory. Our reduction is built on the variational asymptotic method, so that the resulting 1d model is asymptotically self-consistent. The 1d model offers an easier and more efficient way to analyze axisymmetric necking in a dielectric membrane in the linear, weakly nonlinear and fully nonlinear regimes. It delivers results identical to the 3d theory in the linear and weakly nonlinear regimes, and near-identical results in the fully nonlinear regime due to its asymptotic self-consistency. We demonstrate the straightforward implementation of this 1d model by solving it using the Rayleigh--Ritz method and validate it by comparison with finite-element simulations. The 1d model enables a precise calculation of the minimum thickness that a dielectric membrane can reach when necking instability occurs and quantitative assessment of the effects of imperfections so that the integrity of a dielectric elastomer actuator can be evaluated with respect to electric breakdown. The developed methodology is not problem-specific and can also be applied to analyze similar phenomena in other soft materials subjected to any fields (e.g., the axisymmetric necking of stretched plastic membranes).

cond-mat.soft↗

arXiv2024

Wrinkling of differentially growing bilayers with similar film and substrate moduli

The study of growth-induced surface wrinkling in constrained bilayers comprising a thin film attached to a thick substrate is a canonical model for understanding pattern formation in many biological systems. While the bilayer model has received much prior attention, the nonlinear behaviour for arrangements with similar film and substrate properties, or substrate growth that outpaces film growth, remains poorly understood. This paper therefore focuses on these cases in which the substrate's elasticity dominates surface wrinkling. We study the critical states, and the initial and advanced post-critical behaviour of growing bilayers with film-to-substrate modulus ratios in the region of $2.5$--$50$, and cases where the substrate grows faster than the film. Based on nonlinear elasticity, we formulate analytical models for linear buckling analyses and asymptotic projections around the critical point, and use finite element (FE) models coupled to continuation and branch-switching algorithms to uncover the deep post-critical regime. It is shown that a rapidly growing substrate may change the critical mode from film-governed sinusoidal wrinkling to substrate-governed Biot wrinkling depending on the stiffness ratio and growth ratio. We present a phase change diagram of the post-critical modal landscape split into sinusoidal wrinkling, period doubling, period quadrupling, and creasing regimes in terms of the stiffness ratio and growth ratio. While the post-critical regime of film- and substrate-dominated bilayers (either in terms of dominant elasticity or growth rate) is governed by sinusoidal wrinkling and Biot creasing, respectively, the intermediate regions allow for period doubling and quadrupling bifurcations. Finally, we demonstrate the existence of multi-stability in the advanced post-buckling regimes for growing bilayers where growth in the substrate surpasses that of the film.

cond-mat.soft↗

arXiv2024

Wrinkling instability of 3D auxetic bilayers in tension

Bilayers, soft substrates coated with stiff films, are commonly found in nature with examples including skin tissue, vesicles, and organ membranes. They exhibit different types of instabilities when subjected to compression, depending on the contrast in material properties between the two components. In this work, we unravel the mechanisms behind wrinkling instabilities in auxetic bilayer systems under uniaxial tension. We find that a soft bilayer in tension can experience significant lateral contraction, and with sufficient contrast in Poisson ratios, compressive stresses may induce wrinkles aligned with the tensile direction. We analytically model the onset of wrinkles and validate our predictions using Finite Element simulations in ABAQUS. Our findings reveal that wrinkles occur when the Poisson ratio of the substrate is greater than that of the film. As the two Poisson ratios converge to a common value, the critical stretch for instability shoots up rapidly and the wrinkles disappear. We also confirm these results through asymptotic analysis. Using inverse analysis, we design film microstructures to achieve desired effective Poisson ratios and further validate the effective properties with the Finite Element code FEAP. We show that the critical stretch ratio for buckling in auxetic structures with microstructural patterns is in strong agreement with the homogenized model predictions. The proposed method has significant potential for controlling surface patterns in auxetic skin grafts and hydrogel organ patches under mechanical loads. Moreover, the asymptotic expressions for compressible bilayers developed in this work can also be applied under finite strain for buckling-based metrology.

cond-mat.mtrl-sci↗

arXiv2023

On the incremental equations in surface elasticity

We derive the incremental equations for a hyperelastic solid that incorporate surface tension effect by assuming that the surface energy is a general function of the surface deformation gradient. The incremental equations take the same simple form as their purely mechanical counterparts and are valid for any geometry. In particular, for isotropic materials, the extra surface elastic moduli are expressed in terms of the surface energy function and the two surface principal stretches. The effectiveness of the resulting incremental theory is illustrated by applying it to study the Plateau--Rayleigh and Wilkes instabilities in a solid cylinder.

cond-mat.soft↗

arXiv2023

A one-dimensional model for axisymmetric deformations of an inflated hyperelastic tube of finite wall thickness

We derive a one-dimensional (1d) model for the analysis of bulging or necking in an inflated hyperelastic tube of {\it finite wall thickness} from the three-dimensional finite elasticity theory by applying the dimension reduction methodology proposed by Audoly and Hutchinson (J. Mech. Phys. Solids, 97, 2016). The 1d model makes it much easier to characterize fully nonlinear axisymmetric deformations of a thick-walled tube using simple numerical schemes such as the finite difference method. The new model recovers the diffuse interface model for analyzing bulging in a membrane tube and the 1d model for investigating necking in a stretched solid cylinder as two limiting cases. It is consistent with, but significantly refines, the exact linear and weakly nonlinear bifurcation analyses. Comparisons with finite element simulations show that for the bulging problem, the 1d model is capable of describing the entire bulging process accurately, from initiation, growth, to propagation. The 1d model provides a stepping stone from which similar 1d models can be derived and used to study other effects such as anisotropy and electric loading, and other phenomena such as rupture.

cond-mat.soft↗

arXiv2023

Axisymmetric necking of a circular electrodes-coated dielectric membrane

We investigate the stability of a circular electrodes-coated dielectric membrane under the combined action of an electric field and all-round in-plane tension. It is known that such a membrane is susceptible to the limiting point instability (also known as pull-in instability) which is widely believed to be a precursor to electric breakdown. However, there is experimental evidence showing that the limiting point instability may not necessarily be responsible for rapid thinning and electric breakdown. We explore the possibility that the latter is due to a new instability mechanism, namely localised axisymmetric necking. The bifurcation condition for axisymmetric necking is first derived and used to show that this instability may occur before the Treloar-Kearsley instability or the limiting point instability for a class of free energy functions. A weakly nonlinear analysis is then conducted and it is shown that the near-critical behavior is described by a fourth order nonlinear ODE with variable coefficients. This amplitude equation is solved using the finite difference method and it is demonstrated that a localised solution does indeed bifurcate from the homogeneous solution. Based on this analysis and what is already known for the purely mechanical case, we may deduce that the necking evolution follows the same three stages of initiation, growth and propagation as other similar localisation problems. The insight provided by the current study is expected to be relevant in assessing the integrity of dielectric elastomer actuators.

cond-mat.soft↗

arXiv2022

A refined model for the buckling of film/substrate bilayers

The classical reduced model for a film/substrate bilayer is one in which the film is governed by the Euler-Bernoulli beam equation and the substrate is replaced by an array of springs (the so-called Winkler foundation assumption). We derive a refined model in which the normal and shear tractions at the bottom of the film are expressed in terms of the corresponding horizontal and vertical displacements, and the response of the half-space is described by the exact theory. The self-consistency of the refined model is confirmed by showing that it yields a four-term (in the incompressible case) or six-term (in the compressible case) expansion for the critical strain that agrees with the expansion given by the exact theory.

cond-mat.soft↗

arXiv2022

Localised bulging of an inflated rubber tube with fixed ends

When a rubber tube with free ends is inflated under volume control, the pressure will first reach a maximum and then decrease monotonically to approach a constant asymptote. The pressure maximum corresponds to the initiation of a localised bulge and is predicted by a bifurcation condition, whereas the asymptote is the Maxwell pressure corresponding to a "two-phase" propagation state. In contrast, when the tube is first pre-stretched and then has its ends fixed during subsequent inflation, the pressure versus bulge amplitude has both a maximum and a minimum, and the behaviour on the right ascending branch has previously not been fully understood. We show that for all values of pre-stretch and tube length, the ascending branches all converge to a single curve that is only dependent on the ratio of tube thickness to the outer radius. This curve represents the Maxwell state to be approached in each case (if Euler buckling or axisymmetric wrinkling does not occur first), but this state is pressure-dependent in contrast with the free-ends case. We also demonstrate experimentally that localized bulging cannot occur when the pre-stretch is sufficiently large and investigate what strain-energy functions can predict this observed phenomenon.

cond-mat.soft↗

arXiv2021

Axisymmetric necking versus Treloar-Kearsley instability in a hyperelastic sheet under equibiaxial stretching

We consider bifurcations from the homogeneous solution of a circular or square hyperelastic sheet that is subjected to equibiaxial stretching under either force- or displacement-controlled edge conditions. We derive the condition for axisymmetric necking and show, for the class of strain-energy functions considered, that the critical stretch for necking is greater than the critical stretch for the Treloar-Kearsley (TK) instability and less than the critical stretch for the limiting-point instability. An amplitude equation for the bifurcated necking solution is derived through a weakly nonlinear analysis and is used to show that necking initiation is generally sub-critical. Abaqus simulations are conducted to verify the bifurcation conditions and the expectation that the TK instability should occur first under force control, but when the edge displacement is controlled the TK instability is suppressed, and it is the necking instability that will be observed. It is also demonstrated that axisymmetric necking follows a growth/propagation process typical of all such localization problems.

cond-mat.soft↗

arXiv2021

An analytic derivation of the bifurcation conditions for localization in hyperelastic tubes and sheets

We provide an analytic derivation of the bifurcation conditions for localized bulging in an inflated hyperelastic tube of arbitrary wall thickness and axisymmetric necking in a hyperelastic sheet under equibiaxial stretching. It has previously been shown numerically that the bifurcation condition for the former problem is equivalent to the vanishing of the Jacobian determinant of the internal pressure $P$ and resultant axial force $N$, with each of them viewed as a function of the azimuthal stretch on the inner surface and the axial stretch. This equivalence is established here analytically. For the latter problem for which it has recently been shown that the bifurcation condition is not given by a Jacobian determinant equal to zero, we explain why this is the case and provide an alternative interpretation.

physics.bio-ph↗

arXiv2021

Post-bifurcation behaviour of elasto-capillary necking and bulging in soft tubes

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.

nlin.PS↗

arXiv2021

On propagation of waves in pressurized fiber-reinforced hyperelastic tubes based on a reduced model

A refined dynamic finite-strain shell theory for incompressible hyperelastic materials was developed by the authors recently. In this paper, we first derive the associated linearized incremental theory, and then use it to investigate wave propagation in a fiber-reinforced hyperelastic tube that is subjected to an axial pre-stretch and internal pressure. We obtain the dispersion relations for both axisymmetric and non-axisymmetric waves and discuss their accuracy by comparing them with the exact dispersion relations. The bending effect is also examined by comparing the dispersion curves based on the present theory and membrane theory. It is shown that the present theory is more accurate than the membrane theory in studying wave propagation and the bending effect plays an important role in some wave modes for relatively large wavenumbers. The effects of the pressure, axial pre-stretch and fiber angle on the dispersion relations are displayed. These results provide the necessary validation for using the refined dynamic finite-strain shell theory and wave propagation to determine arterial properties.

physics.bio-ph↗

arXiv2021

Buckling and post-buckling of a compressed elastic half-space coated by double layers

We investigate the buckling and post-buckling properties of a hyperelastic half-space coated by two hyperelastic layers when the composite structure is subjected to a uniaxial compression. In the case of a half-space coated with a {\it single} layer, it is known that when the shear modulus $\mu_f$ of the layer is larger than the shear modulus $\mu_s$ of the half-space, a linear analysis predicts the existence of a critical stretch and wave number, whereas a weakly nonlinear analysis predicts the existence of a threshold value of the modulus ratio $\mu_s/\mu_f\approx 0.57$ below which the buckling is super-critical and above which the buckling is sub-critical. It is shown in this paper that when another layer is added, a larger variety of behaviour can be observed. For instance, buckling can occur at a preferred wavenumber super-critically even if both layers are softer than the half-space although the top layer would need to be harder than the bottom layer. When the shear modulus of the bottom layer lies in a certain interval, the super-critical to sub-critical transition can happen a number of times as the shear modulus of the top layer is increased gradually. Thus, an extra layer imparts more flexibility in producing wrinkling patterns with desired properties, and our weakly nonlinear analysis provides a road map on the parameter regimes where this can be achieved.

nlin.PS↗

arXiv2021

Localised bifurcation in soft cylindrical tubes under axial stretching and surface tension

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.

cond-mat.soft↗

arXiv2021

Elasto-capillary circumferential buckling of soft tubes under axial loading: existence and competition with localised beading and periodic axial modes

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 tube's 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.

cond-mat.soft↗

arXiv2020

A refined dynamic finite-strain shell theory for incompressible hyperelastic materials: equations and two-dimensional shell virtual work principle

Based on previous work for the static problem, in this paper we first derive one form of dynamic finite-strain shell equations for incompressible hyperelastic materials that involve three shell constitutive relations. In order to single out the bending effect as well as to reduce the number of shell constitutive relations, a further refinement is performed, which leads to a refined dynamic finite-strain shell theory with only two shell constitutive relations (deducible from the given three-dimensional (3D) strain energy function) and some new insights are also deduced. By using the weak formulation of the shell equations and the variation of the 3D Lagrange functional, boundary conditions and the two-dimensional (2D) shell virtual work principle are derived. As a benchmark problem, we consider the extension and inflation of an arterial segment. The good agreement between the asymptotic solution based on the shell equations and that from the 3D exact one gives verification of the former. The refined shell theory is also applied to study the plane-strain vibrations of a pressurized artery, and the effects of the axial pre-stretch, pressure and fibre angle on the vibration frequencies are investigated in detail.

cs.CE↗

arXiv2008

A wave near the edge of a circular disk

It is shown that in the Love-Kirchhoff plate theory, an edge wave can travel in a circular thin disk made of an isotropic elastic material. This disk edge wave turns out to be faster than the classic flexural acoustic wave in a straight-edged, semi-infinite, thin plate, a wave which it mimics when the curvature radius becomes very large compared to the wavelength.

physics.class-ph↗