Edge wrinkling in elastically supported pre-stressed incompressible isotropic plates

Harnessing Gravity‐Induced Instability of Soft Materials: Mechanics and Application

This work offers a comprehensive overview of how gravity affects soft materials, with a particular emphasis on gravity‐induced instability. Soft materials, including biological tissues, elastomers, and gels, are characterized by low elastic moduli and the ability to undergo significant deformations. These large deformations can lead to instabilities and the emergence of distinctive surface patterns when even small perturbations are introduced. An in‐depth understanding of these gravity‐induced instabilities in soft materials is of paramount importance for both fundamental scientific research and practical applications across diverse domains. The underlying mechanisms governing these instabilities are delved in and elucidate the techniques employed to study and manipulate them. Further, the gravity‐induced wrinkling and the Rayleigh‐Taylor (RT) instability in soft materials are zoomed in, highlighting how altered gravity environments impact natural and synthetic systems. Lastly, current and potential applications are underscored where gravity‐induced instabilities are already making an impact or may hold promise in the near future. In sum, the exploration of gravity‐induced instabilities in soft materials paves the way for innovative applications and advancements in a wide range of fields.

Wrinkling and restabilization of a hyperelastic PDMS membrane at finite strain

Wrinkles are commonly observed in uniaxially stretched hyperelastic membranes and eventually disappear with the increase of stretching. The widely used scheme at present assumes the material parameters to be empirical values and straightforwardly considers some constitutive models to explore the wrinkling and restabilization behavior. However, this simple treatment may cause deviation from experiment by ignoring the applicability of the models and the authenticity of the input parameters, prompting us to report based on realistic material parameters. This paper presents an experimental, theoretical and numerical investigation on the wrinkling and restabilization behavior of hyperelastic materials. By fitting experimental stress-strain curves of PDMS films, we confirm that the 3-term Ogden model bears a closer resemblance to the experimental data than the widely used neo-Hookean, Mooney-Rivlin, and Arruda-Boyce models under certain circumstances. The simulation results indicate that different constitutive models quantitatively affect the critical buckling strain, wrinkling amplitudes, and restabilization points. Furthermore, the isolated central bifurcation point solved by Koiter stability theory agrees well with the simulation and experimental results. A 3D phase diagram of stability boundaries was established to gain a comprehensive insight into the effects of geometric parameters (length, width, and thickness) on wrinkling.

Mechanics of tension-induced film wrinkling and restabilization: a review

Wrinkling of thin films under tension is omnipresent in nature and modern industry, a phenomenon which has aroused considerable attention during the past two decades because of its intricate nonlinear behaviours and intriguing morphology changes. Here, we review recent advancements in the mechanics of tension-induced film wrinkling and restabilization, by identifying three major stages of its progress: small-strain (less than 5 % ) wrinkling of stiff sheets, finite-strain (up to 30 % ) wrinkling and restabilization (isola-centre bifurcation) of soft films, and the effects of curved configurations and material properties on pattern formation. Growing demand for fundamental understanding, quantitative prediction and precise tracking of secondary bifurcation transitions in morphological evolution of thin films helps to advance finite-strain plate/shell theories and sophisticated modelling methods. This progress not only promotes our insightful understanding of complex instability behaviour but also reveals novel phenomena and sheds light on developing wrinkle-tunable membrane structures and functional surfaces.

Bifurcation of elastic solids with sliding interfaces

Lubricated sliding contact between soft solids is an interesting topic in biomechanics and for the design of small-scale engineering devices. As a model of this mechanical set-up, two elastic nonlinear solids are considered jointed through a frictionless and bilateral surface, so that continuity of the normal component of the Cauchy traction holds across the surface, but the tangential component is null. Moreover, the displacement can develop only in a way that the bodies in contact do neither detach, nor overlap. Surprisingly, this finite strain problem has not been correctly formulated until now, so this formulation is the objective of the present paper. The incremental equations are shown to be non-trivial and different from previously (and erroneously) employed conditions. In particular, an exclusion condition for bifurcation is derived to show that previous formulations based on frictionless contact or 'spring-type' interfacial conditions are not able to predict bifurcations in tension, while experiments-one of which, ad hoc designed, is reported-show that these bifurcations are a reality and become possible when the correct sliding interface model is used. The presented results introduce a methodology for the determination of bifurcations and instabilities occurring during lubricated sliding between soft bodies in contact.

Flexural edge waves generated by steady-state propagation of a loaded rectilinear crack in an elastically supported thin plate

The problem of a rectilinear crack propagating at constant speed in an elastically supported thin plate and acted upon by an equally moving load is considered. The full-field solution is obtained and the spotlight is set on flexural edge wave generation. Below the critical speed for the appearance of travelling waves, a threshold speed is met which marks the transformation of decaying edge waves into edge waves propagating along the crack and dying away from it. Yet, besides these, and for any propagation speed, a pair of localized edge waves, which rapidly decay behind the crack tip, is also shown to exist. These waves are characterized by a novel dispersion relation and fade off from the crack line in an oscillatory manner, whence they play an important role in the far field behaviour. Dynamic stress intensity factors are obtained and, for speed close to the critical speed, they show a resonant behaviour which expresses the most efficient way to channel external work into the crack. Indeed, this behaviour is justified through energy considerations regarding the work of the applied load and the energy release rate. Results might be useful in a wide array of applications, ranging from fracturing and machining to acoustic emission and defect detection.