Configurations of curves and geodesics on surfaces

We study configurations of immersed curves in surfaces and surfaces in 3-manifolds. Among other results, we show that primitive curves have only finitely many configurations which minimize the number of double points. We give examples of minimal configurations not realized by geodesics in any hyperbolic metric.Comment: 13 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon2/paper11.abs.htm

Simple Closed Geodesics in Hyperbolic 3-Manifolds

This paper determines which orientable hyperbolic 3-manifolds contain simple closed geodesics. The Fuchsian group corresponding to the thrice-punctured sphere generates the only example of a complete non-elementary orientable hyperbolic 3-manifold that does not contain a simple closed geodesic. We do not assume that the manifold is geometrically finite or that it has finitely generated fundamental group.Comment: 7 pages, to appear in the Bulletin of the London Mathematical Societ

Moisture-induced stresses and distortions in spruce cross-laminates and composite laminates

The crosswise gluing of cross-laminated panels made of solid wood can cause problems when exposed to moisture variations. In the present study, the substitution of the spruce middle layer by a wood composite is tested for its influence on moisture-induced stresses and deformations in laboratory tests and numerical simulations. Furthermore, slits in the spruce middle layer were investigated. The hygroscopic warping due to a moisture gradient, stresses caused by moistening and cracks due to drying were studied. The results show larger warping in composite laminates compared to the spruce cross-laminate, which is governed by the modulus of elasticity of the middle layer. The in-plane swelling was found to be larger in composite laminates, while stresses were lower. The drying test discovered that cracks develop in the middle layer of spruce-medium density fiberboard laminates due to shear stresses and tensile stresses in the thickness direction. It was concluded that slits can be applied in the middle layer, as they have no significant influence on moisture-induced stresses but increase the thermal insulation. If the substitution of the spruce layer is required, the application of oriented strand board in the middle layer is recommende

Generic failure mechanisms in adhesive bonds

The failure of adhesive bondlines has been studied at the microscopic level via tensile tests. Stable crack propagation could be generated by means of samples with improved geometry, which made in situ observations possible. The interaction of cracks with adhesive bondlines under various angles to the crack propagation was the focus of this study, as well as the respective loading situations for the adhesives urea formaldehyde (UF), polyurethane (PUR), and polyvinyl acetate (PVAc), which have distinctly different mechanical behaviors. It has been shown how adhesive properties influence the occurrence of certain failure mechanisms and determine their appearance and order of magnitude. With the observed failure mechanisms, it becomes possible to predict the propagation path of a crack through the specime