Disappearance of stretch-induced wrinkles of thin sheets: a study of orthotropic films

A recent paper (Healey et al., J. Nonlin. Sci., 2013, 23:777-805.) predicted the disappearance of the stretch-induced wrinkled pattern of thin, clamped, elastic sheets by numerical simulation of the F\"oppl-von K\'arm\'an equations extended to the finite in-plane strain regime. It has also been revealed that for some aspect ratios of the rectangular domain wrinkles do not occur at all regardless of the applied extension. To verify these predictions we carried out experiments on thin 20 micrometer thick adhesive covered), previously prestressed elastomer sheets with different aspect ratios under displacement controlled pull tests. On one hand the the adjustment of the material properties during prestressing is highly advantageous as in targeted strain regime the film becomes substantially linearly elastic (which is far not the case without prestress). On the other hand a significant, non-ignorable orthotropy develops during this first extension. To enable quantitative comparisons we abandoned the assumption about material isotropy inherent in the original model and derived the governing equations for an orthotropic medium. In this way we found good agreement between numerical simulations and experimental data. Analysis of the negativity of the second Piola-Kirchhoff stress tensor revealed that the critical stretch for a bifurcation point at which the wrinkles disappear must be finite for any aspect ratio. On the contrary there is no such a bound for the aspect ratio as a bifurcation parameter. Physically this manifests as complicated wrinkled patterns with more than one highly wrinkled zones on the surface in case of elongated rectangles. These arrangements have been found both numerically and experimentally. These findings also support the new, finite strain model, since the F\"oppl-von K\'arm\'an equations based on infinitesimal strains do not exhibit such a behavior.Comment: 16 pages, 5 figure

On interpretations and constructions of classical dynamical r-matrices

In this note we complement recent results on the exchange $r$-matrices appearing in the chiral WZNW model by providing a direct, purely finite-dimensional description of the relationship between the monodromy dependent 2-form that enters the chiral WZNW symplectic form and the exchange $r$-matrix that governs the corresponding Poisson brackets. We also develop the special case in which the exchange $r$-matrix becomes the `canonical' solution of the classical dynamical Yang-Baxter equation on an arbitrary self-dual Lie algebra.Comment: 8 pages, LaTeX, based on a talk given by L.F. at the QTS2 symposium, 18-21 July 2001, Krakow, Poland. References are updated, and a typo is removed in v2; a misprint in equation (A.13) is corrected in v

The Mullins effect in the wrinkling behavior of highly stretched thin films

Recent work demonstrates that finite-deformation nonlinear elasticity is essential in the accurate modeling of wrinkling in highly stretched thin films. Geometrically exact models predict an isola-center bifurcation, indicating that for a bounded interval of aspect ratios only, stable wrinkles appear and then disappear as the macroscopic strain is increased. This phenomenon has been verified in experiments. In addition, recent experiments revealed the following striking phenomenon: For certain aspect ratios for which no wrinkling occurred upon the first loading, wrinkles appeared during the first unloading and again during all subsequent cyclic loading. Our goal here is to present a simple pseudo-elastic model, capturing the stress softening and residual strain observed in the experiments, that accurately predicts wrinkling behavior on the first loading that differs from that under subsequent cyclic loading. In particular for specific aspect ratios, the model correctly predicts the scenario of no wrinkling during first loading with wrinkling occurring during unloading and for all subsequent cyclic loading.Comment: 15 pages, 9 figure

Exchange bias in phase-segregated Nd2/3Ca1/3MnO3 as a function of temperature and cooling magnetic fields

Exchange bias (EB) phenomena have been observed in Nd2/3Ca1/3MnO3 colossal magnetoresistance perovskite below the Curie temperature $T_{C}$ = 70 K and attributed to an antiferromagnetic (AFM) - ferromagnetic (FM) spontaneous phase segregated state of this compound. Field cooled magnetic hysteresis loops exhibit shifts toward negative direction of the magnetic field axis. The values of exchange field $H_{EB}$ and coercivity $H_{C}$ are found to be strongly dependent of temperature and strength of the cooling magnetic field $H_{cool}$. These effects are attributed to evolution of the FM phase content and a size of FM clusters. A contribution to the total magnetization of the system due to the FM phase has been evaluated. The exchange bias effect decreases with increasing temperature up to $T_{C}$ and vanishes above this temperature with disappearance of FM phase. Relaxation of a non-equilibrium magnetic state of the compound manifests itself through a training effect also observed while studying EB in Nd2/3Ca1/3MnO3.Comment: 18 page

Interplay between mesoscopic phase separation and bulk magnetism in the layered NaxCoO2

Specific heat of the layered NaxCoO2 (x=0.65, 0.70 and 0.75) oxides has been measured in the temperature range of 3-360 K and magnetic field of 0 and 9 T. The analysis of data, assuming the combined effect of inter-layer superexchange and the phase separation into mesoscopic magnetic domains with localized spins embedded in a matrix with itinerant electronic character, suggests that the dominant contribution to the specific heat in the region of short-range ordering is mediated by quasi-2D antiferromagnetic clusters, perpendicular to the CoO2 layers