RESUMEN
Necking localization under quasi-static uniaxial tension is experimentally observed in ductile thin-walled cylindrical tubes, made of soft polypropylene. Necking nucleates at multiple locations along the tube and spreads throughout, involving the occurrence of higher-order modes, evidencing trefoil and fourth-foiled (but rarely even fifth-foiled) shaped cross-sections. No evidence of such a complicated necking occurrence and growth was found in other ductile materials for thin-walled cylinders under quasi-static loading. With the aim of modelling this phenomenon, as well as all other possible bifurcations, a two-dimensional formulation is introduced, in which only the mean surface of the tube is considered, paralleling the celebrated Flügge 's treatment of axially-compressed cylindrical shells. This treatment is extended to include tension and a broad class of nonlinear-hyperelastic constitutive law for the material, which is also assumed to be incompressible. The theoretical framework leads to a number of new results, not only for tensile axial force (where necking is modelled and, as a particular case, the classic Considère formula is shown to represent the limit of very thin tubes), but also for compressive force, providing closed-form formulae for wrinkling (showing that a direct application of the Flügge equation can be incorrect) and for Euler buckling. It is shown that the J2-deformation theory of plasticity (the simplest constitutive assumption to mimic through nonlinear elasticity the plastic branch of a material) captures multiple necking and occurrence of higher-order modes, so that experiments are explained. The presented results are important for several applications, ranging from aerospace and automotive engineering to the vascular mechanobiology, where a thin-walled tube (for instance an artery, or a catheter, or a stent) may become unstable not only in compression, but also in tension.
RESUMEN
The famous bifurcation analysis performed by Flügge on compressed thin-walled cylinders is based on a series of simplifying assumptions, which allow to obtain the bifurcation landscape, together with explicit expressions for limit behaviours: surface instability, wrinkling, and Euler rod buckling. The most severe assumption introduced by Flügge is the use of an incremental constitutive equation, which does not follow from any nonlinear hyperelastic constitutive law. This is a strong limitation for the applicability of the theory, which becomes questionable when is utilized for a material characterized by a different constitutive equation, such as for instance a Mooney-Rivlin material. We re-derive the entire Flügge's formulation, thus obtaining a framework where any constitutive equation fits. The use of two different nonlinear hyperelastic constitutive equations, referred to compressible materials, leads to incremental equations, which reduce to those derived by Flügge under suitable simplifications. His results are confirmed, together with all the limit equations, now rigorously obtained, and his theory is extended. This extension of the theory of buckling of thin shells allows for computationally efficient determination of bifurcation landscapes for nonlinear constitutive laws, which may for instance be used to model biomechanics of arteries, or soft pneumatic robot arms.
RESUMEN
Analysis of foods, which are typically highly complex mixtures, by 1H NMR can be difficult because the prevalence of signal overlap complicates characterization and quantification. The various components of a food sample may have a wide range of concentrations, leading to a high dynamic range NMR spectrum and complicating the analysis of less concentrated species. One source of this complication is the presence of 13C satellites, peaks that appear either side of a parent peak with â¼0.56% of its intensity. Satellites of concentrated species can easily be comparable in intensity to the signals of minor components, and can partly or wholly obscure them. This is commonly seen in olive oil samples, leading to inaccurate calculation of the fatty acid ester composition of the oil, used for determining the quality of edible oils and for detecting adulteration. Here, we show that the recently introduced Destruction of Interfering Satellites by Perfect Echo Low-pass filtration (DISPEL) experiment is able to suppress 13C satellites and can substantially improve the accuracy of integration of minor signals. The DISPEL experiment does not require any complicated optimization, working "out of the box" with standard parameters, and incurs no significant loss of sensitivity. It has the potential to become the default experiment, replacing conventional 1D 1H NMR, for quantitative analysis of olive oil.
RESUMEN
A generic approach is presented that allows high-resolution NMR spectroscopy of water/oil droplet emulsions in microfluidic devices. Microfluidic NMR spectroscopy has recently made significant advances due to the design of micro-detector systems and their successful integration with microfluidic devices. Obtaining NMR spectra of droplet suspensions, however, is complicated by the inevitable differences in magnetic susceptibility between the chip material, the continuous phase, and the droplet phases. This leads to broadening of the NMR resonance lines and results in loss of spectral resolution. We have mitigated the susceptibility difference between the continuous (oil) phase and the chip material by incorporating appropriately designed air-filled structures into the chip. The susceptibilities of the continuous and droplet (aqueous) phases have been matched by doping the droplet phase with a Eu3+ complex. Our results demonstrate that this leads to a proton line width in the droplet phase of about 3 Hz, enabling high-resolution NMR techniques.