On complex eigenvalues and eigenvectors of the velocity gradient

According to Bertrand’s Theorem [J. Bertrand, Théorème relatif au mouvement le plus général d’un fluide, Comptes Rendus de l’Académie des Sciences de Paris, 66, (1867) 1127-1230], at any point in a continuum, at any time, there exists at least one infinitesimal material line element whose direction does not change, instantaneously. This direction is along an eigenvector of the velocity gradient tensor corresponding to a real eigenvalue. Corresponding to this eigenvalue there is also an infinitesimal material area element whose direction does not change, instantaneously. The Theorem does not address the question as to properties associated with complex eigenvalues of the velocity gradient. This note fills the gap. It is shown that corresponding to a complex eigenvalue there are two invariant ellipses, one associated with material line elements and the other with material areal elements.     

Granular flows down inclined channels with a strain-rate dependent friction coefficient. Part I: Non-cohesive materials

The flow of a granular material down an incline of finite width with a strain-rate dependent coefficient of friction and a conical yield criterion is semi-analytically obtained using a characteristic method for flows on a deep layer of grains. This analysis leads to a flow field with three distinct zones: a Bagnold-flow zone below the free surface, a dead-zone and a matching zone between the two, linked to slippage at the wall. A good agreement between the computed flow field and experimental data is obtained.     

Exploration of trabecular bone nonlinear elasticity using time-of-flight modulation

Bone tissue contains microcracks that may affect its mechanical properties as well as the whole trabecular structure. The relationship between crack density and bone strength is nevertheless poorly understood. Linear ultrasound techniques being almost insensitive to the level of damage, we propose a method to measure acoustic non- linearity in trabecular bone using time-of-flight modulation (TOFM) measurements. Ultrasonic short bursts times-of- flight (TOF) are modulated as a result of nonlinear interaction with a low-frequency (LF) wave in the medium. TOF variations are directly related to elastic modulus variations. Classical and nonclassical nonlinear parameters beta, delta, and alpha can be derived from these measurements. The method was validated in materials with classical, quadratic, nonlinear elasticity. In dense trabecular bone region, TOFM related to classical, quadratic, nonlinear elasticity as a function of the LF pressure exhibits tension-compression asymmetry. The TOFM amplitude measured in dense areas of trabecular bone is almost one order of magnitude higher than in a low-density area, but the linear parameters show much smaller variations: 5% for ultrasound propagation velocity and 100% for broadband ultrasonic attenuation (BUA). In high-density trabecular bone regions, beta depends on the LF pressure amplitude and can reach 400 at 50 kPa.     

Understanding of Void Formation in Cu/Sn-Sn/Cu System During Transient Liquid Phase Bonding Process Through Diffusion Modeling

Metallurgical and Materials Transactions B - Transient Liquid Phase (TPL) bounding of Sn foil sandwiched between two Cu foils involves, in the temperature range above the melting point of Sn...     

Postshaking Shear Strain Localization in a Centrifuge Model of a Saturated Sand Slope

This paper presents analyses of a test conducted on a 9-m-radius centrifuge to study the redistribution of pore water during diffusion of earthquake-induced excess pore pressures in a sand slope with embedded silt layers. The centrifuge model developed large postshaking deformations associated with shear strain localization at the interface between the sand and silt layers. Dense arrays of pore pressure transducers provided detailed measurements of pore pressure variations in time and space within the slope. A new data analysis approach is presented in which measured pore-pressures are used to compute flow rates and volumetric strains as a function of time and position throughout the slope. Hydraulic gradients were calculated by numerical differentiation of measured pore-pressure distributions with respect to position. Flow rates that were based on Darcy’s law were then integrated with respect to time to obtain flow quantities, from which volumetric strains were computed. A second data analysis approach that computes volumetric strains on the basis of soil compressibility and changes in pore pressure provided an independent computation of strains in consolidating zones. Results using these data analysis procedures confirm that a dilating (loosening) zone of significant thickness developed in the sand immediately beneath an embedded silt layer that had impeded the drainage of high pore pressures. These results support the hypothesis that the dilating zone corresponds to regions where the mobilized friction angle exceeds the critical state friction angle and that the dilating zone can be initially relatively thick before its size diminishes to the thickness of a thin shear band after the peak friction angle is mobilized. Quantification of the evolution of the size of the dilating zone is a key to understanding the magnitude of deformations associated with void redistribution.     

High Overburden Stress Effects in Liquefaction Analyses

A reevaluation is presented of two factors that can strongly affect the estimation of liquefaction resistance for clean sands under high effective overburden stresses (σv′): the relation used to normalize penetration resistances to a σv′ of 1 atm (i.e., CN), and the adjustment factor for the effects of σv′ on cyclic resistance ratio (i.e., Kσ). These two factors have been investigated in a number of ways and several relations exist for each of them. An improved CN relation is developed based on cone penetration theory and validation against calibration chamber test data for both cone penetration and standard penetration tests. A relative state parameter index (ξR) is shown to provide a consistent theoretical framework for interrelating the penetration and cyclic loading resistances. It is subsequently shown that the CN and Kσ relations are interrelated through the sand properties and relative density (DR) in ways that have compensating effects on the predicted cyclic resistance. The derived relations provide an improved representation of the effects of high σv′ levels, and reduce the conservatism that results when some established relations are extended to σv′ levels higher than they were calibrated for.     

Proteolytic degradation of rat growth hormone-releasing factor(1-29) amide in rat pituitary and hypothalamus

The identification of peptide bonds vulnerable to tissue peptidases is a valuable approach to design peptide agonists which exhibit a longer duration of action than the native molecules. Therefore, the kinetic of disappearance of rat growth hormone-releasing factor (rGRF(1-29)NH2) and the identification of its metabolites were studied in rat pituitary and hypothalamus. Synthetic rGRF(1-29)NH2 (10 microM) was incubated (0-120 min, 37 degrees C) in the presence of a pituitary (237 +/- 51 micrograms protein/ml) or hypothalamus homogenate (576 +/- 27 micrograms protein/ml). Using analytical high pressure liquid chromatography (HPLC), apparent half-lives of 22 +/- 3 min and 25 +/- 4 min were found in pituitary and hypothalamus, respectively. In both tissues, three degradation products, all less hydrophobic than the native peptide, were detected and isolated by preparative HPLC. The identification of the purified metabolites was ascertained by amino acid analysis, sequencing and chromatography with synthetic homologs. These results indicate that the main sites of cleavage in the pituitary and hypothalamus are Lys21-Leu22 (trypsin-like cleavage site), Leu14-Gly15 and Tyr10-Arg11 (chymotrypsin-like cleavage sites). TLCK and leupeptin did not affect the formation of fragment (1-21)OH while TPCK blocked the cleavage of Leu14-Gly15. The low affinity of fragment (1-21)NH2 for pituitary GRF binding sites suggests that hydrolysis of the Lys21-Leu22 bond inactivates rGRF(1-29)NH2 in this target tissue.     

Observed Seismic Lateral Resistance of Liquefying Sand

This paper presents results from a study of the dynamic response of pile foundations in liquefying sand during seismic loading. The study included a series of dynamic centrifuge tests of pile-supported structures and the back-calculation of time histories for the lateral resistance p and relative displacement y between a pile and the free-field soil. Details of the centrifuge experiments and the procedures used to back-calculate p and y time histories are described. The back-calculated p-y time histories provide a concise representation of the experimental results and can be compared to the equivalent p-y behavior predicted by soil-pile interaction analysis methods. The observed p-y behavior provides insight into the mechanisms of soil-pile interaction in liquefying sand, showing characteristics that are consistent with the undrained cyclic loading behavior of saturated sand, including the effects of relative density, cyclic degradation, pore-pressure generation, prior displacement (strain) history, and phase transformation behavior.     

A study using Monte Carlo Simulation for failure probability calculation in Reliability-Based Optimization

In this study, a Reliability-Based Optimization (RBO) methodology that uses Monte Carlo Simulation techniques, is presented. Typically, the First Order Reliability Method (FORM) is used in RBO for failure probability calculation and this is accurate enough for most practical cases. However, for highly nonlinear problems it can provide extremely inaccurate results and may lead to unreliable designs. Monte Carlo Simulation (MCS) is usually more accurate than FORM but very computationally intensive. In the RBO methodology presented in this paper, limit state approximations are used in conjunction with MCS techniques in an approximate MCS-based RBO that facilitates the efficient calculation of the probabilities of failure. A FORM-based RBO is first performed to obtain the initial limit state approximations. A Symmetric Rank-1 (SR1) variable metric algorithm is used to construct and update the quadratic limit state approximations. The approximate MCS-based RBO uses a conditional-expectation-based MCS, that was chosen over indicator-based MCS because of the smoothness of the probability of failure estimates and the availability of analytic sensitivities. The RBO methodology was implemented for an analytic test problem and a higher-dimensional, control-augmented-structure test problem. The results indicate that the SR1 algorithm provides accurate limit state approximations (and therefore accurate estimates of the probabilities of failure) for these test problems. It was also observed that the RBO methodology required two orders of magnitude fewer analysis calls than an approach that used exact limit state evaluations for both test problems.