Programmed buckling by controlled lateral swelling in a thin elastic sheet

Recent experiments have imposed controlled swelling patterns on thin polymer films, which subsequently buckle into three-dimensional shapes. We develop a solution to the design problem suggested by such systems, namely, if and how one can generate particular three-dimensional shapes from thin elastic sheets by mere imposition of a two-dimensional pattern of locally isotropic growth. Not every shape is possible. Several types of obstruction can arise, some of which depend on the sheet thickness. We provide some examples using the axisymmetric form of the problem, which is analytically tractable.Comment: 11 pages, 9 figure

Cellular buckling from mode interaction in I-beams under uniform bending

Beams made from thin-walled elements, whilst very efficient in terms of the structural strength and stiffness to weight ratios, can be susceptible to highly complex instability phenomena. A nonlinear analytical formulation based on variational principles for the ubiquitous I-beam with thin flanges under uniform bending is presented. The resulting system of differential and integral equations are solved using numerical continuation techniques such that the response far into the post-buckling range can be portrayed. The interaction between global lateral-torsional buckling of the beam and local buckling of the flange plate is found to oblige the buckling deformation to localize initially at the beam midspan with subsequent cellular buckling (snaking) being predicted theoretically for the first time. Solutions from the model compare very favourably with a series of classic experiments and some newly conducted tests which also exhibit the predicted sequence of localized followed by cellular buckling.Comment: 23 pages, 15 figures and 6 table

Ultra-light hierarchical meta-materials on a body-centred cubic lattice

Modern fabrication techniques offer the freedom to design and manufacture structures with complex geometry on many lengthscales, offering many potential advantages. For example, fractal/hierarchical struts have been shown to be exceptionally strong and yet light (Rayneau-Kirkhope D. et al., Phys. Rev. Lett., 109 (2012) 204301). In this letter, we propose a new class of meta-material, constructed from fractal or hierarchical struts linking a specific set of lattice points. We present a mechanical analysis of this meta-material resulting from a body-centred cubic (BCC) lattice. We show that, through the use of hierarchy, the material usage follows an enhanced scaling relation, and both material property and overall efficiency can be optimised for a specific applied stress. Such a design has the potential of providing the next generation of lightweight, buckling-resistant meta-materials

A variational approach to a circular hyperelastic membrane problem

The variational principles of nonlinear elasticity are applied to a problem of axially symmetric deformation of a uniform circular hyperelastic membrane. The supported edge of the membrane is in a horizontal plane and its radius is equal to that of the undeformed plane reference configuration, so that an initially plane unstretched membrane is subjected to a dead load due to its weight.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41727/1/707_2005_Article_BF01177244.pd

A review of source tracking techniques for fine sediment within a catchment

Excessive transport of fine sediment, and its associated pollutants, can cause detrimental impacts in aquatic environments. It is therefore important to perform accurate sediment source apportionment to identify hot spots of soil erosion. Various tracers have been adopted, often in combination, to identify sediment source type and its spatial origin; these include fallout radionuclides, geochemical tracers, mineral magnetic properties and bulk and compound-specific stable isotopes. In this review, the applicability of these techniques to particular settings and their advantages and limitations are reviewed. By synthesizing existing approaches, that make use of multiple tracers in combination with measured changes of channel geomorphological attributes, an integrated analysis of tracer profiles in deposited sediments in lakes and reservoirs can be made. Through a multi-scale approach for fine sediment tracking, temporal changes in soil erosion and sediment load can be reconstructed and the consequences of changing catchment practices evaluated. We recommend that long-term, as well as short-term, monitoring of riverine fine sediment and corresponding surface and subsurface sources at nested sites within a catchment are essential. Such monitoring will inform the development and validation of models for predicting dynamics of fine sediment transport as a function of hydro-climatic and geomorphological controls. We highlight that the need for monitoring is particularly important for hilly catchments with complex and changing land use. We recommend that research should be prioritized for sloping farmland-dominated catchments