Análisis experimental y por el método de los elementos finitos del estado de tensiones en uniones carpinteras de empalme de llave

In this research, the halved and tabled traditional timber scarf joint is analyzed. This joint consists in two end joint pieces usually subjected to tension. Initially, the study is discussed from an experimental point of view. In this way, 3 critical cross-sections are established (section of the notch, section of the horizontal plane and reduced section) and mechanical tests are performed to achieve the failure on each of critical sections by changing the geometry of the joint. The study is completed by developing a finite element model which allows verify experimental results and extend the analysis to other geometries. This model has to simulate the real behavior of the material which is being studied, so mechanical tests are performed to obtain the elastic constants and the coefficients of friction of the material. In the reduced section, an abrupt decrease of the effective cross-section takes place, and this effect is also experimentally analyzed. These tests indicate that a crack is initiated before the bending-tension failure occurs in the reduced section. The test material consists of wood of Pinus sylvestris L. coming from the “Valsaín´s Sawmill” (Segovia) with “premium quality” according to the nonstructural wood visual classification of sawmill. It is observed that initiation of a crack, in the mortise (bottom of reduced section), and shear stress concentration, at the initial part of the heel (beginning of horizontal plane), completely determine the mechanical behaviour of the joint, resulting in 3 failure modes: local compression failure in the section of the notch, shear failure in the horizontal plane, and failure of stresses concentration, mainly perpendicular to the grain tension, at the bottom of reduced section. The geometric optimization is obtained for halved and tabled traditional scarf joint, when the joint has made with similar properties of wood than tested specimens, for any height and width of the cross-section. It is considered the failure due to the initiation of a crack in reduced section, by applying a correction coefficient into the usual equation used to design the members subjected to both tension and bending. Therefore, it is possible to obtain, analytically, the design conditions to be met of the 3 critical cross-sections. According to the theoretical optimization, the tension strength of complete cross-section is reduced until 14%, when using this type of joint. The experimental optimization indicates even a greater reduction, until 6%. En el presente trabajo de investigación se analiza el comportamiento mecánico de las uniones tradicionales de empalme de llave, que consisten en dos piezas unidas por sus testas transmitiéndose entre ellas principalmente un esfuerzo de tracción. Inicialmente, el estudio se aborda desde un punto de vista experimental. De este modo, se establecen las 3 secciones críticas o de estudio (sección del encaje, sección rasante del cogote y sección reducida) y se realizan ensayos mecánicos, variando la geometría de la unión, para alcanzar la rotura en cada una de ellas. Se completa el estudio mediante la elaboración de un modelo por elementos finitos que permite verificar los resultados experimentales y ampliar el análisis a otras geometrías. Este modelo debe simular el comportamiento real del material objeto de estudio, por lo que se realizan ensayos para obtener las constantes elásticas y los coeficientes de rozamiento del mismo. También se analiza, experimentalmente, el efecto entalladura que reduce bruscamente la sección completa del tirante, estableciendo que el fallo por flexotracción en la sección reducida de la pieza, no llega a producirse por el inicio previo de una grieta. El material de ensayo consiste en madera de Pinus sylvestris L. (pino silvestre) procedente del Aserradero de Valsaín (Segovia) y de calidad “Extra” o “Primera” según la clasificación visual no estructural del aserradero. Se observa que el inicio de una grieta en la mortaja del rediente y la concentración de tensiones tangenciales en la parte inicial del cogote, determinan completamente el comportamiento mecánico de la unión, dando lugar a 3 modos distintos de rotura: fallo por compresión en la sección del encaje, fallo por cortante en la sección rasante y fallo por concentración de tensiones, principalmente tracciones perpendiculares, en el rebaje de la sección reducida. Se consigue optimizar geométricamente cualquier empalme de llave confeccionado con madera de características similares a la ensayada, para cualquier valor de la altura y de la anchura de la sección. Se considera el agotamiento en la sección reducida causado por el inicio de grieta, mediante la aplicación de un coeficiente corrector en la expresión habitual de agotamiento por flexotracción, en consecuencia, finalmente es posible obtener, de modo analítico, un valor del índice de agotamiento en cada una de las 3 secciones de estudio. La optimización teórica del empalme de llave indica que la capacidad resistente del tirante bruto se reduce al 14%, cuando se coloca este tipo de unión tradicional. Experimentalmente se obtiene, que, para la sección ensayada, la capacidad resistente del tirante bruto se reduce todavía más, llegando al 6%.

Sensing and modelling mechanical properties of fruits for quality.

Nondestructive techniques are extensively researched for the measurement of physical properties of fruits related to quality. Optical properties can be applied mainly in the detection of those quality features which are related to the chemical composition of the fruit, color (in the VIS region) or chemical constituents (sugar, in the MR region) being the most important. The most relevant mechanical property of fruits is consistency, generally called firmness, and to date only techniques which are able to measure the mechanical properties of the fruit bulk tissue are used for its prediction. Fruits can be modelled as elastic bodies, or at least as partially elastic. Therefore, the measurement of some elastic constants of the fruit can be used for the evaluation of its firmness. The differences in the response to loading are relevant in studying a) fruit firmness and b) bruising susceptibility. Both have been modelled for selected fruit species and varieties.

Calibration of calculation models of wooden guardrails with Operational Modal Analysis

This study analyses the differences between two calculation models for guardrails on building sites that use wooden boards and tubular steel posts. Wood was considered an isotropic material in one model and an orthotropic material in a second model. The elastic constants of the wood were obtained with ultrasound. Frequencies and vibration modes were obtained for both models through linear analysis using the finite element method. The two models were experimentally calibrated through operational modal analysis. The results obtained show that for the three types of wood under analysis, the model which considered them as an orthotropic material fitted the experimental results better than the model which considered them as an isotropic material.

A sulphonate based hydrogel for nucleus pulposus repair

Introduction: Lower back pain treatment and compensation costs >$80 billion overall in the US. 75% of back pain is due to disc degeneration in the lumbar region of the spine. Current treatment comprises of painkillers and bed rest or as a more radical solution – interbody cage fusion. In the early stages of disc degeneration the patient would benefit from addition of an injectable gel which polymerises in situ to support the degenerated nucleus pulposus. This involves a material which is an analogue of the natural tissue capable of restoring the biomechanical properties of the natural disc. The nucleus pulposus of the intervertebral disc is an example of a natural proteoglycan consisting of a protein core with negatively charged keratin and chondroitin sulphate attached. As a result of the high fixed charge density of the proteoglycan, the matrix exerts an osmotic swelling pressure drawing sufficient water into support the spinal system. Materials and Methods: NaAMPs (sodium 2- acrylamido 2-methyl propane sulphonic acid) and KSPA (potassium 3- sulphopropyl acrylate) were selected as monomers, the sulphonate group being used to mimic the natural sulphate group. These are used in dermal applications involving chronic wounds and have acceptably low cytotoxicity. Other hydrophilic carboxyl, amide and hydroxyl monomers such as 2-hydroxyethyl acrylamide, ß-carboxyethyl acrylate, acryloyl morpholine, and polyethylene glycol (meth)acrylate were used as diluents together with polyethyleneglycol di(meth)acrylate and hydrophilic multifunctional macromers as cross-linker. Redox was the chosen method of polymerisation and a range of initiators were investigated. Components were packaged in two solutions each containing a redox pair. A dual syringe method of injection into the cavity was used, the required time for polymerisation is circa 3-7 minutes. The final materials were tested using a Bohlin CVO Rheometer cycling from 0.5-25Hz at 37oC to measure the modulus. An in-house compression testing method was developed, using dialysis tubing to mimic the cavity, the gels were swelled in solutions of various osmolarity and compressed to ~ 20%. The pre-gel has also been injected into sheep spinal segments for mechanical compression testing to demonstrate the restoration of properties upon use of the gel. Results and Discussion: Two systems resulted using similar monomer compositions but different initiation and crosslinking agents. NaAMPs and KSPA were used together at a ratio of ~1:1 in both systems with 0.25-2% crosslinking agent, diacrylate or methacrylate. The two initiation systems were ascorbic acid/oxone, and N,N,N,N - tetramethylethylenediamine (TEMED)/ potassium persulphate. These systems produced gelation within 3-7 and 3-5 minutes respectively. Storage of the two component systems was shown to be stable for approximately one month after mixing, in the dark, refrigerated at 1-4oC. The gelation was carried out at 37oC. Literature values for the natural disc give elastic constants ranging from 3-8kPa. The properties of the polymer can be tailored by altering crosslink density and monomer composition and are able to match those of the natural disc. It is possible to incorporate a radio-opaque (histodenz) to enable x-ray luminescence during and after injection. At an inclusion level of 5% the gel is clearly visible and polymerisation and mechanical properties are not altered. Conclusion: A two-pac injection system which will polymerise in situ, that can incorporate a radio-opaque, has been developed. This will reinforce the damaged nucleus pulposus in degenerative disc disease restoring adequate hydration and thus biomechanical properties. Tests on sheep spine segments are currently being carried out to demonstrate that a disc containing the gel has similar properties to an intact disc in comparison to one with a damaged nucleus.

Anisotropic properties of human tibial cortical bone as measured by nanoindentation

The purpose of this study was to investigate the effects of elastic anisotropy on nanoindentation measurements in human tibial cortical bone. Nanoindentation was conducted in 12 different directions in three principal planes for both osteonic and interstitial lamellae. The experimental indentation modulus was found to vary with indentation direction and showed obvious anisotropy (oneway analysis of variance test, P < 0.0001). Because experimental indentation modulus in a specific direction is determined by all of the elastic constants of cortical bone, a complex theoretical model is required to analyze the experimental results. A recently developed analysis of indentation for the properties of anisotropic materials was used to quantitatively predict indentation modulus by using the stiffness matrix of human tibial cortical bone, which was obtained from previous ultrasound studies. After allowing for the effects of specimen preparation (dehydrated specimens in nanoindentation tests vs. moist specimens in ultrasound tests) and the structural properties of bone (different microcomponents with different mechanical properties), there were no statistically significant differences between the corrected experimental indentation modulus (Mexp) values and corresponding predicted indentation modulus (Mpre) values (two-tailed unpaired t-test, P < 0.5). The variation of Mpre values was found to exhibit the same trends as the corrected Mexp data. These results show that the effects of anisotropy on nanoindentation measurements can be quantitatively evaluated. © 2002 Orthopaedic Research Society. Published by Elsevier Science Ltd. All rights reserved.

Phase coexistence of cluster crystals: beyond the Gibbs phase rule

We report a study of the phase behavior of multiple-occupancy crystals through simulation. We argue that in order to reproduce the equilibrium behavior of such crystals it is essential to treat the number of lattice sites as a constraining thermodynamic variable. The resulting free-energy calculations thus differ considerably from schemes used for single-occupancy lattices. Using our approach, we obtain the phase diagram and the bulk modulus for a generalized exponential model that forms cluster crystals at high densities. We compare the simulation results with existing theoretical predictions. We also identify two types of density fluctuations that can lead to two sound modes and evaluate the corresponding elastic constants.

Numerical Simulation Of Ultrasonic Wave Propagation In Elastically Anisotropic Media

The ultrasonic non-destructive testing of components may encounter considerable difficulties to interpret some inspections results mainly in anisotropic crystalline structures. A numerical method for the simulation of elastic wave propagation in homogeneous elastically anisotropic media, based on the general finite element approach, is used to help this interpretation. The successful modeling of elastic field associated with NDE is based on the generation of a realistic pulsed ultrasonic wave, which is launched from a piezoelectric transducer into the material under inspection. The values of elastic constants are great interest information that provide the application of equations analytical models, until small and medium complexity problems through programs of numerical analysis as finite elements and/or boundary elements. The aim of this work is the comparison between the results of numerical solution of an ultrasonic wave, which is obtained from transient excitation pulse that can be specified by either force or displacement variation across the aperture of the transducer, and the results obtained from a experiment that was realized in an aluminum block in the IEN Ultrasonic Laboratory. The wave propagation can be simulated using all the characteristics of the material used in the experiment evaluation associated to boundary conditions and from these results, the comparison can be made.

Anharmonicity in NaCl and beta brass

U of I Only

MEASUREMENT OF ELASTIC PROPERTIES OF MATERIALS BY THE ULTRASONIC THROUGH-TRANSMISSION TECHNIQUE

The elastic mechanical behavior of elastic materials is modeled by a pair of independent constants (Young`s modulus and Poisson`s coefficient). A precise measurement for both constants is necessary in some applications, such as the quality control of mechanical elements and standard materials used for the calibration of some equipment. Ultrasonic techniques have been used because wave velocity depends on the elastic properties of the propagation medium. The ultrasonic test shows better repeatability and accuracy than the tensile and indentation test. In this work, the theoretical and experimental aspects related to the ultrasonic through-transmission technique for the characterization of elastic solids is presented. Furthermore, an amorphous material and some polycrystalline materials were tested. Results have shown an excellent repeatability and numerical errors that are less than 3% in high-purity samples.

Anisotropy in elastic properties of lithium sodium sulphate hexahydrate single crystal—An ultrasonic study

The double sulfate family (ABSO4), where A and B are alkali metal cations, is the object of great interest owing to the complexity and richness of its sequence of phase transition induced by temperature variation. A new sulfate salt characterized by the presence of water molecule in the unit cell with the chemical formula, Li2Na3(SO4)2⋅6H2O (LSSW), was obtained. The ultrasonic velocity measurement was done with pulse echo overlap technique [PEO]. All the six second order elastic stiffness constants, C11 = C22, C33, C44 = C55, C12, C14 and C13 = C23 are reported for the first time. The anisotropy in the elastic properties of the crystal are well explained by the pictorial representation of the polar plots of phase velocity, slowness, Young’s modulus and linear compressibility in a–b and a–c planes.

The Inertio-Elastic Planar Entry Flow of Low-Viscosity Elastic Fluids in Micro-fabricated Geometries

The non-Newtonian flow of dilute aqueous polyethylene oxide (PEO) solutions through microfabricated planar abrupt contraction-expansions is investigated. The contraction geometries are fabricated from a high-resolution chrome mask and cross-linked PDMS gels using the tools of soft-lithography. The small length scales and high deformation rates in the contraction throat lead to significant extensional flow effects even with dilute polymer solutions having time constants on the order of milliseconds. The dimensionless extra pressure drop across the contraction increases by more than 200% and is accompanied by significant upstream vortex growth. Streak photography and videomicroscopy using epifluorescent particles shows that the flow ultimately becomes unstable and three-dimensional. The moderate Reynolds numbers (0.03 ≤ Re ≤ 44) associated with these high Deborah number (0 ≤ De ≤ 600) microfluidic flows results in the exploration of new regions of the Re-De parameter space in which the effects of both elasticity and inertia can be observed. Understanding such interactions will be increasingly important in microfluidic applications involving complex fluids and can best be interpreted in terms of the elasticity number, El = De/Re, which is independent of the flow kinematics and depends only on the fluid rheology and the characteristic size of the device.

Inferring a weighted elastic network from partial unfolding with coarse-grained simulations

A number of studies have demonstrated that simple elastic network models can reproduce experimental B-factors, providing insights into the structure-function properties of proteins. Here, we report a study on how to improve an elastic network model and explore its performance by predicting the experimental B-factors. Elastic network models are built on the experimental C coordinates, and they only take the pairs of C atoms within a given cutoff distance r(c) into account. These models describe the interactions by elastic springs with the same force constant. We have developed a method based on numerical simulations with a simple coarse-grained force field, to attribute weights to these spring constants. This method considers the time that two C atoms remain connected in the network during partial unfolding, establishing a means of measuring the strength of each link. We examined two different coarse-grained force fields and explored the computation of these weights by unfolding the native structures. Proteins 2014; 82:119-129. (c) 2013 Wiley Periodicals, Inc.

On the nucleation and growth of amyloid beta-protein fibrils: detection of nuclei and quantitation of rate constants.

We have studied the fibrillogenesis of synthetic amyloid beta-protein-(1-40) fragment (A beta) in 0.1 M HCl. At low pH, A beta formed fibrils at a rate amenable to detailed monitoring by quasi-elastic light-scattering spectroscopy. Examination of the fibrils with circular dichroism spectroscopy and electron microscopy showed them to be highly similar to those found in amyloid plaques. We determined the hydrodynamic radii of A beta aggregates during the entire process of fibril nucleation and growth. Above an A beta concentration of approximately 0.1 mM, the initial rate of elongation and the final size of fibrils were independent of A beta concentration. Below an A beta concentration of 0.1 mM, the initial elongation rate was proportional to the peptide concentration, and the resulting fibrils were significantly longer than those formed at higher concentration. We also found that the surfactant n-dodecylhexaoxyethylene glycol monoether (C12E6) slowed nucleation and elongation of fibrils in a concentration-dependent manner. Our observations are consistent with a model of A beta fibrillogenesis that includes the following key steps: (i) peptide micelles form above a certain critical A beta concentration, (ii) fibrils nucleate within these micelles or on heterogeneous nuclei (seeds), and (iii) fibrils grow by irreversible binding of monomers to fibril ends. Interpretation of our data enabled us to determine the sizes of fibril nuclei and A beta micelles and the rates of fibril nucleation (from micelles) and fibril elongation. Our approach provides a powerful means for the quantitative assay of A beta fibrillogenesis.

Small strain elastic behaviour of unsaturated soil investigated by bender/extender element testing

The aim of this project was to investigate very small strain elastic behaviour of soils under unsaturated conditions, using bender/extender element (BEE) testing. The behaviour of soils at very small strains has been widely studied under saturated conditions, whereas much less work has been performed on very small strain behaviour under unsaturated conditions. A suction-controlled double wall triaxial apparatus for unsaturated soil testing was modified to incorporate three pairs of BEEs transmitting both shear and compression waves with vertical and horizontal directions of wave transmission and wave polarisation. Various different techniques for measuring wave travel time were investigated in both the time domain and the frequency domain and it was concluded that, at least for the current experimental testing programme, peak-to-first-peak in the time domain was the most reliable technique for determining wave travel time. An experimental test programme was performed on samples of compacted speswhite kaolin clay. Two different forms of compaction were employed (i.e. isotropic and anisotropic). Compacted kaolin soil samples were subjected to constant suction loading and unloading stages at three different values of suction, covering both unsaturated conditions (s= 50kPa and s= 300kPa) and saturated conditions (s=0). Loading and unloading stages were performed at three different values of stress ratio (η=0, η=1 and η=-1 ). In some tests a wetting-drying cycle was performed before or within the loading stage, with the wetting-drying cycles including both wetting-induced swelling and wetting-induced collapse compression. BEE tests were performed at regular intervals throughout all test stages, to measure shear wave velocity Vs and compression wave velocity Vp and hence to determine values of shear modulus G and constrained modulus M. The experimental test programme was designed to investigate how very small strain shear modulus G and constrained modulus M varied with unsaturated state variables, including how anisotropy of these parameters developed either with stress state (stress-induced anisotropy) or with previous straining (strain-induced anisotropy). A new expression has been proposed for the very small strain shear modulus G of an isotropic soil under saturated and unsaturated conditions. This expression relates the variation of G to only mean Bishop’s stress p* and specific volume v, and it converges to a well-established expression for saturated soils as degree of saturation approaches 1. The proposed expression for G is able to predict the variation of G under saturated and unsaturated conditions at least as well as existing expressions from the literature and it is considerably simpler (employing fewer state variables and fewer soil constants). In addition, unlike existing expressions from the literature, the values of soil constants in the proposed new expression can be determined from a saturated test. It appeared that, in the current project at least, any strain-induced anisotropy of very small strain elastic behaviour was relatively modest, with the possible exception of loading in triaxial extension. It was therefore difficult to draw any firm conclusion about evolution of strain-induced anisotropy and whether it depended upon the same aspects of soil fabric as evolution of anisotropy of large strain plastic behaviour. Stress-induced anisotropy of very small strain elastic behaviour was apparent in the experimental test programme. An attempt was made to extend the proposed expression for G to include the effect of stress-induced anisotropy. Interpretation of the experimental results indicated that the value of shear modulus was affected by the values of all three principal Bishop’s stresses (in the direction of wave transmission, the direction of wave polarisation and the third mutually perpendicular direction). However, prediction of stress-induced anisotropy was only partially successful, and it was concluded that the effect of Lode angle was also significant.