Abstract. 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 Föppl-von Kármán 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 µm 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 Föppl-von Kármán equations based on infinitesimal strains do not exhibit such a behavior.
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.
Shape properties of rocks carry important geological information about their origin, and they may also provide a window to study the abrasion processes forming their geometry. The number of mechanical equilibria is a significant property with a profound mathematical background that could reveal the secrets hidden in the artifacts of Nature. Although it is easy to count by hand, the automation of its measurement is not a straightforward task. A new workflow is introduced for the fast and efficient measurement of geometrical properties, including the number and location of stable and unstable equilibrium points 5 of rocks based on a portable 3D scanner combined with computer software that can analyze the resulting point cloud. The technique allows for the fast examination of statistically sufficient sample sizes without the need for transportation or storage of the specimens. A previously hand-measured set of pebbles and fragments was used as a reference for the validation of the method, and its effectiveness is demonstrated through the examination of beach pebbles carried out in Kawakawa Bay, New Zealand. 1 IntroductionMeasuring shape characteristics of sedimentary particles is an effective way to formulate hypotheses about their history based on the mathematical models of abrasion processes. Theoretical results show that analysis of the shape of rocks may answer questions related to their place of origin, travel distance, and it can also reveal details of the abrasive forces that contributed 15 to the final geometry. The most general shape descriptors are the axis ratios (c/a, b/a for a > b > c) (Zingg, 1935) and the roundness or isoperimetric ratio (I) that expresses how close a shape is to a sphere. Traditional measurement techniques often incorporate personal factors or rely on the verbal characterization of the shape (Wentworth, 1923;Boggs, 2001) to approximate these values. The number of stable (S) and unstable (U ) mechanical equilibria of a particle as a shape descriptor gained significant attention recently (Domokos et al., 2009; Miller et al., 2014;Domokos et al., 2015;Novák-Szabó et al., 2018) and it is not only insensitive for small measurement errors, but it also has a rich mathematical literature (Grayson, 1987;Domokos et al., 2015;Domokos and Lángi, 2019).It is beneficial to switch from the traditional hand-measurements to automated shape analysis of the particles to avoid personal bias. Recently, several works appeared aiming to reduce subjectivity by automatically calculating shape properties from 2D digital images of the particles (Roussillon et al., 2009;Durian et al., 2007;Cassel et al., 2018;Cheng et al., 2018), 25 3D laser scanning (Hayakawa and Oguchi, 2005; Anochie-Boateng et al., 2013) or X-ray CT (Deiros Quintanilla et al., 2019). Development in sensors and 3D cameras induced a technological revolution in shape detection in many fields from the poultry industry (Chan et al., 2018) to ballast in railway track structures (Anochie-Boateng et al., 2013). 3D scanning was successfully applied i...
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