Counterintuitive Dynamic Behavior in Elastic-Plastic Structures
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The counterintuitive phenomena of elastic, perfectly plastic beam, circular plate and square plate are investigated numerically and experimentally. A new unstable slot and asymmetry of dynamic response of beam are revealed. The unsteady areas and uncertainty of response are observed numerically. At the end, the law of thermodynamics and the theorem of Lyapunov instability are employed to state the formation mechanism of counterintuitive behavior.Keywords:
Counterintuitive
Square (algebra)
Elastic instability
We study the undulatory instability of a straight crack front generated by peeling a flexible elastic plate from a thin elastomeric adhesive film. We show that there is a threshold for the onset of the instability that is dependent on the ratio of two length-scales that arise naturally in the problem: the thickness of the film and an elastic length defined by the stiffness of the plate and that of the film. A linear stability analysis predicts that the wavelength of the instability scales linearly with the film thickness. Our results are qualitatively and quantitatively consistent with recent experiments, and show how crack fronts may lose stability due to a competition between bulk and surface effects in the presence of multiple length scales.
Elastic instability
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The linear analysis of incompressible Rayleigh–Taylor instability is carried out for thick solid plates accelerated uniformly by a constant pressure. The instability threshold is found and the boundary for the elastic to plastic transition is also determined. It is demonstrated that transition from the elastic to the plastic regime is a necessary condition for the onset of instability but not a sufficient one. The theory is in excellent quantitative agreement with the results of two-dimensional numerical simulations and reveals the main physical mechanisms that control the instability.
Rayleigh–Taylor instability
Elastic instability
Constant (computer programming)
Richtmyer–Meshkov instability
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Soft elastic layers with top and bottom surfaces adhered to rigid bodies are abundant in biological organisms and engineering applications. As the rigid bodies are pulled apart, the stressed layer can exhibit various modes of mechanical instabilities. In cases where the layer's thickness is much smaller than its length and width, the dominant modes that have been studied are the cavitation, interfacial and fingering instabilities. Here we report a new mode of instability which emerges if the thickness of the constrained elastic layer is comparable to or smaller than its width. In this case, the middle portion along the layer's thickness elongates nearly uniformly while the constrained fringe portions of the layer deform nonuniformly. When the applied stretch reaches a critical value, the exposed free surfaces of the fringe portions begin to undulate periodically without debonding from the rigid bodies, giving the fringe instability. We use experiments, theory and numerical simulations to quantitatively explain the fringe instability and derive scaling laws for its critical stress, critical strain and wavelength. We show that in a force controlled setting the elastic fingering instability is associated with a snap-through buckling that does not exist for the fringe instability. The discovery of the fringe instability will not only advance the understanding of mechanical instabilities in soft materials but also have implications for biological and engineered adhesives and joints.
Elastic instability
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A new kind of meniscus instability leading to the formation of stationary fingers with a well-defined spacing has been observed in experiments with elastomeric films confined between a plane rigid glass and a thin curved glass plate. The wavelength of the instability increases linearly with the thickness of the confined film, but it is remarkably insensitive to the compliance and the energetics of the system. However, lateral amplitude (length) of the fingers depends on the compliance of the system and on the radius of curvature of the glass plate. A simple linear stability analysis is used to explain the underlying physics and the key observed features of the instability.
Meniscus
Radius of curvature
Elastic instability
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Elastic instability
Bending of plates
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Fluid-elastic instability is widely recognized as a mechanism which can cause rapid failure of tubes in shell and tube heat exchangers. The shellside flow velocity for the onset of the fluid-elastic whirling is commonly calculated from Connors’ formula provided that the instability factor is known. The literature contains several reported values of the instability factor for different tube bundles but these have been obtained from a variety of test configurations and this has led to some large discrepancies. This paper describes a systematic study of the effect of tube layout on the instability factor for sixteen tube bundles. The results presented show that the instability factor varies by a factor of 3 over the range of tube layouts tested. This paper concludes with a comparison of the results of the present study with values taken from the open literature.
Elastic instability
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The instability characteristic of a viscoelastic jet in a co-flowing gas stream is studied comprehensively. The important role of the non-uniform basic velocity in the instability analysis of viscoelastic jets is clarified, which first induces an unrelaxed elastic tension, and then produces a coupling term between the elastic tension and perturbation velocity. The elastic tension promotes the instability of the jet, while the coupling term exhibits a stabilizing effect, which is essentially related to the nonlinear constitutive relation of viscoelastic fluids and the non-uniform basic velocity. The competition between these two factors leads to the non-monotonic effect of fluid elasticity on the disturbance growth rate, which can be divided into two different regimes characterized by the Weissenberg number with values smaller or larger than unity. In different regimes, the structure of the eigenspectrum is also significantly different. Furthermore, three instability mechanisms are identified using the energy budget analysis, corresponding to the predominance of the surface tension, elastic tension and shear and pressure of the external gas, respectively. By analysing the variations of the growth rate and phase speed of the disturbances, the general features of viscoelastic jet instability are obtained. Finally, the transitions of instability modes in parameter spaces are investigated theoretically and the transition boundaries among them are provided. This study provides guidance for understanding the underlying mechanism of instability of a viscoelastic jet surrounded by a co-flowing gas stream and the transition criterion of different instability modes.
Elastic instability
Elasticity
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The counterintuitive phenomena of elastic, perfectly plastic beam, circular plate and square plate are investigated numerically and experimentally. The unsteady areas and uncertainty of response are observed numerically. At the end, the law of thermodynamics and the theorem of Lyapunov instability are employed to state the formation mechanism of counterintuitive behavior.
Counterintuitive
Square (algebra)
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Citations (2)
We report the observation of a Plateau instability in a thin filament of solid gel with a very small elastic modulus. A longitudinal undulation of the surface of the cylinder reduces its area thereby triggering capillary instability, but is counterbalanced by elastic forces following the deformation. This competition leads to a nontrivial instability threshold for a solid cylinder. The ratio of surface tension to elastic modulus defines a characteristic length scale. The onset of linear instability is when the radius of the cylinder is one-sixth of this length scale, in agreement with theory presented here.
Elastic instability
Length scale
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Citations (213)
The incompressible Rayleigh – Taylor instability of elastic-plastic solid plates accelerated uniformly by a constant pressure is studied in the linear regime. The instability threshold is found and the boundary for the elastic to plastic transition is also determined. It is demonstrated that transition from the elastic to the plastic regime is a necessary condition for the onset of instability but not a sufficient one. The theory is in excellent quantitative agreement with the results of two-dimensional numerical simulations and reveals the main physical mechanisms that control the instability.
Rayleigh–Taylor instability
Elastic instability
Constant (computer programming)
Richtmyer–Meshkov instability
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Citations (2)