SUMMARY
We consider an alternative way of obtaining the effective elastic properties of a cracked medium. Similarly, to the popular linear-slip model, we assume flat, parallel fractures, and long ...wavelengths. However, we do not treat fractures as weakness planes of displacement discontinuity. In contrast to the classical models, we represent fractures by a thin layer embedded in the background medium. In other words, we follow the Schoenberg–Douma matrix formalism for Backus averaging, but we relax the assumptions of infinite weakness and marginal thickness of a layer so that it does not correspond to the linear-slip plane. To represent the properties of a fracture, we need a fourth-order elasticity tensor and a thickness parameter. The effective tensor becomes more complicated, but it may describe a higher concentration of parallel cracks more accurately. Apart from the derivations of the effective elasticity tensors, we perform numerical experiments in which we compare the performance of our approach with a linear-slip model in the context of highly fractured media. Our model becomes pertinent if filled-in or empty cracks occupy more than one per cent of the effective medium.
ABSTRACT
We investigate the dependence of quasi P‐wave phase velocity propagating in orthotropic media on particular elasticity parameters. Specifically, due to mathematical facilitation, we consider ...the squared‐velocity difference, s2, resulted from propagation in two mutually perpendicular symmetry planes. In the context of the effective medium theory, s2 may be viewed as a parameter evaluating the influence of cracks – embedded in the background medium – parallel to one or both aforementioned planes. Our investigation is both theoretical and numerical. Based on Christoffel's equations, we propose two accurate approximations of s2. Due to them, we interpret the aforementioned squared‐velocity difference as being twice more dependent on C55−C44, than on C13−C23. To describe the magnitude of the dependence, we consider the proportions between the partial derivatives of s2. Further, it occurs that s2 is influenced by the ratio of vertically propagating quasi P‐wave to vertically propagating quasi S‐wave. Anomalously high s2 might be caused by the low P/S ratio, which in turn can be an indicator of the presence of gas in natural fractures or aligned porosity. Also, we carry out numerical sensitivity study, according to which s2 is approximately twice more dependent on C55 than on C13, twice more sensitive to C44 than to C23, and equally dependent on −C33 as on C13+C23. The dependence on C11 and C22 can be neglected, especially for small phase angles. We verify the approximations and perform the sensitivity study, using eight examples of the elasticity tensors.
Elastic anisotropy might be a combined effect of the intrinsic anisotropy and the anisotropy induced by thin-layering. The Backus average, a useful mathematical tool, allows us to describe such an ...effect quantitatively. The results are meaningful only if the underlying physical assumptions are obeyed, such as static equilibrium of the material. We focus on the only mathematical assumption of the Backus average, namely, product approximation. It states that the average of the product of a varying function with a nearly constant function is approximately equal to the product of the averages of those functions. We analyse particular problematic case for which the aforementioned assumption is inaccurate. Furthermore, we focus on the seismological context. We examine the inaccuracy’s effect on the wave propagation in a homogenous medium—obtained using the Backus average—equivalent to thin layers. Numerical simulations indicate clearly that the product approximation inaccuracy has negligible effect on wave propagation; irrespective of layers’ symmetries. To give the results a practical focus, we show that the problematic case of product approximation is strictly related to the negative Poisson’s ratio of constituents layers. We discuss the laboratory and well-log cases in which such a ratio has been noticed. Upon thorough literature review, it occurs that examples of so-called auxetic materials (media that have negative Poisson’s ratio) are not extremely rare exceptions as thought previously. The investigation and derivation of Poisson’s ratio for materials exhibiting symmetry classes up to monoclinic become a significant part of this paper. In addition to the main objectives, we also show that the averaging of cubic layers results in an equivalent medium with tetragonal (not cubic) symmetry. We present concise formulations of stability conditions for low symmetry classes, such as trigonal, orthotropic, and monoclinic.
ABSTRACT
We consider a transversely isotropic medium that is long‐wave equivalent to a stack of thin, parallel, isotropic layers and is obtained using the Backus average. In such media, we analyse ...the relations among anisotropy parameters; Thomsen parameters, ε and δ, and a new parameter ϕ. We discuss the last parameter and show its essential properties; it equals 0 in the case of isotropy of equivalent medium and/or constant Lamé coefficient λ in layers. The second property occurs to make ϕ sensitive to variations of λ in thin‐bedded sequences. According to Gassmann, in isotropic media the variation of fluid content affects only the Lamé coefficient λ, not μ; thus, the sensitivity to changes of λ is an essential property in the context of possible detection of fluids. We show algebraically and numerically that ϕ is more sensitive to these variations than ε or δ. Nevertheless, each of these parameters is dependent on the changes of μ; to understand this influence, we exhibit comprehensive tables that illustrate the behaviour of anisotropy parameters with respect to specific variations of λ and μ. The changes of μ in layers can be presented by the Thomsen parameter γ that depends on them solely. Hence, knowing the values of elasticity coefficients of equivalent transversely isotropic medium, we may compute ϕ and γ, and based on the aforementioned tables, we predict the expected variation of λ; in this way, we propose a new method of possible fluid detection. Also, we show that the prior approach of possible detection of fluids, proposed by Berryman et al., may be unreliable in specific cases. To establish our results, we use the Monte Carlo method; for the range and chosen variations of Lamé coefficients λ and μ – relevant to sandstones – we generate these coefficients in thin layers and, after the averaging process, we obtain an equivalent transversely isotropic medium. We repeat that process numerous times to get many equivalent transversely isotropic media, and – for each of them – we compute their anisotropy parameters. We illustrate ϕ, ε and δ in the form of cross‐plots that are relevant to the chosen variations of λ and μ. Additionally, we present a table with the computed ranges of anisotropy parameters that correspond to different variations of Lamé coefficients.
We attempt to formalise the relationship between the poroelasticity theory and the effective medium theory of micromechanics. The assumptions of these two approaches vary, but both can be linked by ...considering the undrained response of a material; and that is the main focus of the paper. To analyse the linkage between poroelasticity and micromechanics, we do not limit ourselves to the original theory of Biot. Instead, we consider a multi‐porous extension of anisotropic poroelasticity, where pore fluid pressure may vary within the bulk medium of interest. As a consequence, any inhomogeneities in the material are not necessarily interconnected; instead, they may form isolated pore sets that are described by different poroelastic parameters and fluid pressures. We attempt to incorporate the effective methods inside Biot‐like theory and investigate the poroelastic response of various microstructures. We show the cases where such implementation is valid and the others that appear to be questionable. During micromechanical analysis, we derive a particular case of cylindrical transverse isotropy—commonly assumed in conventional laboratory triaxial tests—where the symmetry is induced by sets of aligned cracks.
Objective
Evaluation of sensory attributes of cosmetic products is traditionally based on sensory panels. However, in some cases, a suitable candidate method that can reduce time and costs is the use ...of instrumental analysis that can detect relatively very small changes of entry ingredients. Such approach has been already applied for emollients, salt content, stabilizers, etc. The aim of this contribution is to apply the relations between sensory analysis and rheology to a series of body lotions differing in the contents of emulsifiers and viscosity regulators.
Methods
Sensory and rheological analyses are related. Rheological analysis can represent a good alternative to basic orientation in chosen customer's feelings. A rotational rheometer is the only instrumental device required for the measurements.
Results
An empirical rheological model was proposed by means of which the selected sensory attributes were evaluated using the numerical values of adjustable model parameters. This approach exhibited a very good agreement with the results obtained by the sensory panel.
Conclusion
It was shown that a description of chosen sensory attributes can be responsibly carried out by rheological measurements, that is through the attained numerical values of the parameters appearing in a proposed empirical model characterizing shear viscosity of body lotions.
Résumé
Objectif
L’évaluation des attributs sensoriels des produits cosmétiques est traditionnellement basée sur des panels sensoriels. Cependant, dans certains cas, l'utilisation d'une analyse instrumentale qui permet de détecter de très faibles variations relatives aux ingrédients d'entrée peut être une méthode appropriée et qui peut réduire le temps et les coûts. Cette approche a déjà été appliquée pour les émollients, la teneur en sel, les stabilisants, etc. Le but de cette contribution est d'appliquer les relations entre l'analyse sensorielle et la rhéologie à une série de lotions pour le corps qui diffèrent dans le contenu des émulsifiants et des régulateurs de viscosité.
Méthodes
Les analyses sensorielle et rhéologique sont liées. L'analyse rhéologique peut représenter une bonne alternative à l'orientation de base dans les sensations des utilisateurs. Un rhéomètre dà rotation est le seul dispositif instrumental requis pour les mesures.
Résultats
Un modèle rhéologique empirique a été proposé au moyen duquel les attributs sensoriels sélectionnés ont été évalués en utilisant les valeurs numériques des paramètres réglables du modèle. Cette approche a présenté un très bon accord avec les résultats obtenus par le panel sensoriel.
Conclusion
Il a été montré que la description des attributs sensoriels choisis peut être effectuée de façon raisonnable par des mesures rhéologiques, i. e. à travers les valeurs numériques atteints des paramètres apparaissant dans un modèle empirique proposé caractérisant la viscosité de cisaillement des lotions pour le corps.
An empirical rheological model was proposed by means of which the selected sensory attributes of body lotions were evaluated using the numerical values of adjustable model parameters. This relatively cheap and fast approach exhibited a very good agreement with the results obtained by the sensory panel.
Nanomaterials are being produced in large volumes for the development of advanced new materials. Composites can easily make use of the nanomaterials because of the small size of the particle. With ...the large surface area of nanomaterials very small quantities are needed to observe significant friction altering effects as observed by numerous researchers. Specifically, when the nanomaterials become part of the friction layer they will increase the nominal area of contact, the mechanical properties and typically increase or stabilize the coefficient of friction and reduce wear.
Nanomaterials were added (nanoadditives) to commercial C/C composites using ultrasonics attempting to fill in some of the open porosity. The nanoadditives used were Si, SiC, and SWCNT's. Two different concentrations of each nanoadditive in isopropyl alcohol were attempted. A total of 6 pairs of nanoadditive disks and 1 baseline pair were made. The finished 2.75
in. (69.85
mm) diameter disks were tested on a LINK ring-on-ring subscale aircraft brake dynamometer. A series of braking engagements simulating an aircraft taxiing to the runway, landing, and taxiing back to the terminal were performed totalling 50 landings. Wear was measured as mass and thickness changes of the original disks. It was found that Si and SiC had significant effects on the friction performance in the “hot” taxi after a landing with very small weight percentages. The presence of Si led to chemical changes of the friction layer and the formation of carbides. These changes would occur when the interface reaches a temperature high enough to activate the chemical process. As a consequence, the dominating oxidative wear mechanism changed to mild abrasion. Friction and wear performance is shown and discussed. Analysis of the friction layer was performed using SEM and polarized light microscopy and is presented.
Abstract
Comprehensive information on the characteristics of surgical heart valves (SHVs) is essential for optimal valve selection. Such information is also important in assessing SHV function after ...valve replacement. Despite the existing regulatory framework for SHV sizing and labelling, this information is challenging to obtain in a uniform manner for various SHVs. To ensure that clinicians are adequately informed, the European Association for Cardio-Thoracic Surgery (EACTS), The Society of Thoracic Surgeons (STS) and American Association for Thoracic Surgery (AATS) set up a Task Force comprised of cardiac surgeons, cardiologists, engineers, regulatory bodies, representatives of the International Organization for Standardization and major valve manufacturers. Previously, the EACTS–STS–AATS Valve Labelling Task Force identified the most important problems around SHV sizing and labelling. This Expert Consensus Document formulates recommendations for providing SHV physical dimensions, intended implant position and haemodynamic performance in a transparent, uniform manner. Furthermore, the Task Force advocates for the introduction and use of a standardized chart to assess the probability of prosthesis–patient mismatch and calls valve manufacturers to provide essential information required for SHV choice on standardized Valve Charts, uniformly for all SHV models.
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