Dynamic Instability of Viscoelastic Plate in Supersonic Flow

The present work is investigating the aero-elastic instability of a viscoelastic plates under compressive forces. The Bubnov-Galerkin method used to solve the governing equations. The quasi-steady aerodynamic loadings are determined using linear piston theory. The nonlinear integro-differential equation of the plate is transformed into a set of nonlinear algebraic equations through a Galerkin approach. The resulting system of the equations is analytically solved. The influence of elastic and viscoelastic properties and the compressive load characteristicsof the plate material on the value of critical parameters are discussed

The behavior of elastic anisotropic laminated composite flat structures subjected to deterministic and random loadings

Within this research project, the following topics were studied: (1) foundation of the refined theory of flat cross-ply laminated composite flat and curved panels as well as their static and dynamic response analysis; (2) foundation of a geometrically-nonlinear shear-deformable theory of composite laminated flat panels including the effect of initial geometric imperfections and its application in the postbuckling analysis; (3) the study of the dynamic response of shear deformable elastic laminated composite panels to deterministic time-dependent external excitations as the sonic boom and explosive blast type-loadings; (4) the study of the dynamic response of shear deformable elastic laminated composite panels to random excitation as e.g. the one produced by a jet noise or by any time-dependent external excitation whose characteristics are expressed in a statistical sense; and (5) the dynamic stability of fiber-reinforced composite flat panels whose materials (due to e.g. an ambient high temperature field) exhibit a time-dependent physical behavior

Wrinkles Riding Waves in Soft Layered Materials

The formation of periodic wrinkles in soft layered materials due to mechanical instabilities is prevalent in nature and has been proposed for use in multiple applications. However, such phenomena have been explored predominantly in quasi-static settings. In this work, we measure the dynamics of soft elastomeric blocks with stiff surface films subjected to high-speed impact, and observe wrinkles forming along with, and riding upon, waves propagating through the system. We analyze our measurements with large-deformation, nonlinear visco-hyperelastic Finite Element simulations coupled to an analytical wrinkling model. The comparison between the measured and simulated dynamics shows good agreement, and suggests that inertia and viscoelasticity play an important role. This work encourages future studies of the dynamics of surface instabilities in soft materials, including large-deformation, highly nonlinear morphologies, and may have applications to areas including impact mitigation, soft electronics, and the dynamics of soft sandwich composites

Linear and nonlinear rheology of wormlike micelles

Several surfactant molecules self-assemble in solution to form long, cylindrical, flexible wormlike micelles. These micelles can be entangled with each other leading to viscoelastic phases. The rheological properties of such phases are very interesting and have been the subject of a large number of experimental and theoretical studies in recent years. We shall report on our recent work on the macrorheology, microrheology and nonlinear flow behaviour of dilute aqueous solutions of a surfactant CTAT (Cetyltrimethylammonium Tosilate). This system forms elongated micelles and exhibits strong viscoelasticity at low concentrations ($\sim$ 0.9 wt%) without the addition of electrolytes. Microrheology measurements of $G(\omega)$ have been done using diffusing wave spectroscopy which will be compared with the conventional frequency sweep measurements done using a cone and plate rheometer. The second part of the paper deals with the nonlinear rheology where the measured shear stress $\sigma$ is a nonmonotonic function of the shear rate $\dot{\gamma}$. In stress-controlled experiments, the shear stress shows a plateau for $\dot{\gamma}$ larger than some critical strain rate, similar to the earlier reports on CPyCl/NaSal system. Cates et al have proposed that the plateau is a signature of mechanical instability in the form of shear bands. We have carried out extensive experiments under controlled strain rate conditions, to study the time-dependence of shear stress. The measured time series of shear stress has been analysed in terms of correlation integrals and Lyapunov exponents to show unambiguously that the behaviour is typical of low dimensional dynamical systems.Comment: 15 pages, 10 eps figure

Unfolding the Sulcus

Sulci are localized furrows on the surface of soft materials that form by a compression-induced instability. We unfold this instability by breaking its natural scale and translation invariance, and compute a limiting bifurcation diagram for sulcfication showing that it is a scale-free, sub-critical {\em nonlinear} instability. In contrast with classical nucleation, sulcification is {\em continuous}, occurs in purely elastic continua and is structurally stable in the limit of vanishing surface energy. During loading, a sulcus nucleates at a point with an upper critical strain and an essential singularity in the linearized spectrum. On unloading, it quasi-statically shrinks to a point with a lower critical strain, explained by breaking of scale symmetry. At intermediate strains the system is linearly stable but nonlinearly unstable with {\em no} energy barrier. Simple experiments confirm the existence of these two critical strains.Comment: Main text with supporting appendix. Revised to agree with published version. New result in the Supplementary Informatio