Internal Length Research Articles

Nonlocal antiplane shear interfacial waves

In this paper, non-local shear interfacial waves between two non-local elastic half-spaces in perfect contact along a common boundary are investigated. For the sake of simplicity, an anti-plane problem formulated through the framework of Eringen’s theory is considered. The non-locality is taken only in the transverse coordinate making the analysis of the problem easier than that of non-local problems of 2D. Effective boundary conditions are obtained, with the help of a small internal characteristic length scale, along the interface utilizing an asymptotic approach enabling one to write the non-local stresses through their local counterparts. Antiplane non-local shear interfacial waves are analysed by the derived formulation. Numerical results are presented for certain characteristic values of the problem parameters.

Elastic solution of surface loaded layer with couple and surface stress effects

In this study, an elastic solution of an axisymmetrically surface-loaded thin layer resting on a rigid substrate is established by taking the surface stress and material microstructural effects into account. Derived solutions provide not only a means to investigate the size effects on the mechanical response but also a set of fundamental solutions essential for tackling contact problems in a micro/nano scale. In the formulation, the couple stress and surface elasticity theories are adopted to simulate the microstructured bulk layer and the surface material, respectively. A general solution of an elastic field within the bulk layer is obtained first by Hankel transform method and subsequently used together with the surface equations and boundary conditions to form a set of conditions essential for determining all unknown constants. After being fully tested with available benchmark solutions, results are used to study the role of surface and couple stresses on the load transferring mechanism to the substrate and its size-dependent characteristic for a wide range of external length scales relative to the internal length scales.

Relative importance of two bat species as pollinators of Neobuxbaumia tetetzo (Cactaceae): Evidences from morphometric and pollen load analyses

AbstractNeobuxbaumia tetetzo is a columnar cactus whose flowers are visited by the bat species Choeronycteris mexicana and Leptonycteris yerbabuenae. Although both bat species are considered the pollinators of N. tetetzo, the probability of pollination of each bat species has not been estimated. In this study, we determine the relative importance of C. mexicana and L. yerbabuenae as pollinators of N. tetetzo. The probability of pollination was estimated using two different approaches: (i) morphological correspondence between head (linear traits [total head length, snout length, and face height and width]) and cranial traits (shape traits) of bats and flower traits (linear [internal floral tube length including and excluding the nectary, corolla diameter, stamen length, style length, and corolla tube diameter] and shape traits), and (ii) pollen load analyses to estimate the percentage of occurrence (PO) and the pollination probability index (PPI). Our results showed a lack of a significant correspondence between both head and cranial traits of C. mexicana and the flowers of N. tetetzo, and linear morphological correspondence between total head length of L. yerbabuenae and flower length. Pollen loads of C. mexicana were composed by seven different pollen types, its PO and PPI were 41.87 ± 9.53% and 0.29, respectively. Leptonycteris yerbabuenae pollen loads were composed by three pollen types, with a PO of 78.29 ± 13.67% and a PPI of 0.67. Our results suggest that whereas C. mexicana has a low constancy to the flowers of N. tetetzo, L. yerbabuenae has a higher probability of pollination.

Strength-based regularization length in phase field fracture

We propose a length-free (LF) implementation of phase field (PF) approach to fracture. The input parameters of the LF-PF model are the same as those of the coupled criterion (CC), namely the critical energy release rate Gc and the material tensile strength σc. This formulation relies on the previously determined correlation between the internal length in classical PF fracture models and the material tensile strength. Similar failure loads are obtained using either AT1 and AT2 versions of the LF-PF, a larger diffused damaged zone being observed using AT1. The LF-PF formulation allows retrieving the size effect for a crack under remote tensile stress in infinite medium and shows square hole specimen failure stresses close to the predictions obtained using the CC, which allows using both models in a complementary manner. Finally, the proposed formulation overcomes the problem of identifying different internal lengths for different specimen configurations.

Potential of fixed-plane-perforation fracturing technique in enhanced geothermal system

Fixed-plane-perforation fracturing (PFFP) has been employed to construct complex fracture networks to stimulate unconventional reservoirs. Few studies have been reported on its application potential in geothermal energy extraction. Here we first introduced the PFFP to the enhanced geothermal system (EGS) and numerically examined its heat extraction performance by comparing to those of differing stimulation strategies. We found that much longer fractures and significantly larger damage area are induced by the PFFP than the single-perforation fracturing (SPF), and the heat extraction of the reservoir stimulated by the FPPF is approximately 60% higher than that by the SPF, suggesting the great potential of the PFFP in deep geothermal energy harvest. We further improved our previously-proposed sensitivity indicator to assess the influence degree of critical factors on the PFFP where fracture networks were characterized by the pore pressure of hot dry rock. We found that a high in-situ stress difference reduces the spacing between hydraulic fractures and increases the stress shadowing, causing an increase in heat extraction. The injection rate affects strongest on fracture network area whereas the initial fracture angle is the least. When the injection rate increases from 0.0005 m 3 /s to 0.0020 m 3 /s, the internal fracture length grows by 61.3%, the fracture network area expands by 74.7% of the total area, and the heat extraction increases by 54 GJ. Our findings benefit hydraulic stimulation strategy selection and heat extraction optimization over EGS construction. • We assess the potential of fixed-plane-perforation fracturing (FPPF) in EGS. • Geothermal mining models are optimized by considering pore pressure distribution. • PFFP creates a favorable fracture network and benefits geothermal mining. • Injection rate affects strongest on fracture network area and heat extraction.

Quantitative sonoelastography of the uterine cervix in predicting successful outcome of induction of labour.

The aim of the study was to evaluate the stiffness of cervix and determine its significance in predicting successful outcome of induction of labour. The primary objective was to determine the differences in elastography indices of different areas of cervix between the outcome groups of successful and failed induction of labour. A secondary objective was to find out the correlation of these elastography indices with Bishop's score and cervical length. This was a prospective, observational study conducted over a period of 6 months on pregnant women admitted in the labour room for induction of labour. Establishment of adequate regular uterine contractions - at least three contractions lasting 40-45 s in a 10-min period - was taken as end point for successful outcome of induction of labour. Even after 24 h of initiation of induction of labour, regular, adequate and painful uterine contractions were not established, then induction of labour was described as having failed. Prior to induction, cervical length measurement, Bishop's scoring and elastographic evaluation of the cervix were done by stress-strain elastography. A colour map was produced from purple to red and a five-step scale - the elastography index - was used to describe the various parts of the cervix. The differences between elastography indices of different parts of cervix were estimated using Mann-Whitney U test. Correlation of the indices with cervical length and Bishop's score was determined by Spearman's correlation coefficient. A total of 64 women were included in the study. A significant difference (p < 0.001) was found in the elastography index of internal os between the two outcome groups of success (1.76 ± 0.64) and failure (0.54 ± 0.18). However, the elastography index of central cervical canal, external os, anterior lip and posterior lips did not differ significantly across the outcome groups. A significant positive correlation was found between elastography index of internal os and cervical length (Spearman's correlation coefficient, r = 0.441, p < 0.001) and between elastography index of external os and cervical length (r = 0.347, p = 0.005), whereas a negative correlation was seen between elastography index of external os and Bishop's score (r = -0.270, p = 0.031). Elastography index of internal os can be used to predict outcome of induction of labour. Cervical elastography is a promising new technique for cervical consistency assessment. Further larger studies are required to determine some cut-off point for elastography index of internal os in prediction of outcome of induction of labour and to strongly establish the usefulness of cervical elastography for pregnancy management, preventing preterm delivery and establishment of cut-off points to determine successful induction.

3D printed Inconel mechanical response related to volumetric energy density

This work aims to provide a methodology for producing Inconel 718 specimens ISO 527–2-5B with a tailored mechanical response, by Selective Laser Melting (SLM). Since the macroscopic mechanical behavior of 3D printed metals is dictated by their microstructure, the effect of the printing parameters such as the laser power, the scan speed, the hatching distance and the layer thickness was considered. To evaluate the maximum dimensional accuracy and optimum Volumetric Energy Density (VED) value, the specimens were printed with a constant layer height, hatching distance and spot size and with a varying combination of laser power with scan speed. The 3D printed specimens were subjected to uniaxial tension. The experiments have shown an increased reproducibility of the specimens’ microstructure that led to a more consistent mechanical behavior, when lower scan speed and power were used. Specimens printed with higher speed and power seem to have a more heterogeneous microstructure leading to a more varying mechanical response. While the differences in the mechanical response between specimens of different batches are attributed to different laser power and scan speed, different response between specimens of the same batch is attributed to the inherent inhomogeneity of their microstructure. A simple elasticity model was used to describe their elastic behavior, while a 1D gradient plasticity model was utilized to describe their post-yield tensile response, in which the effect of microstructural heterogeneity on macroscopic behavior was taken into account through a respective internal length. The combined elasto-plastic model was used to capture mechanical response until failure, in good agreement with the experiments. The predicted mechanical characteristics were related to the specimens’ VED to come up with simple relations providing optimum 3D printing parameters for producing specimens with a certain mechanical response. For a complete characterization, the specimens’ roughness was studied and its VED dependence was performed.

A comprehensive characterization of fracture in unit cell open foams generated from Triply Periodic Minimal Surfaces

The main scope of the proposed study is to assess the occurrence of fracture in Triply Periodic Minimal Surfaces (TPMS) foams subjected to compressive loading. TPMS, developed by the mathematics community, may be exploited as a backbone for developing a new class of foams with open porosity for a wide range of engineering and biomedical applications. Therefore, a comprehensive analysis of their fracture response is fundamental and is herein attempted. To this aim, a 3D phase field model is herein proposed and applied to TPMS foam structures under compression, with the goal to predict critical points for crack nucleation, potential crack paths, and the stiffness and maximum force of the unit cell, which can be related to the apparent Young’s modulus and apparent strength of a macro-scale composite made of such TPMS unit cells. A careful mesh sensitivity analysis was conducted on the specimens, to provide guidelines on how to identify the optimal finite element discretization consistent with the internal length scale parameter of the phase field approach to fracture. The major predicted mechanical properties for five different TPMS open foams, and for different levels of porosity, are summarized in Ashby plots. The predicted trends are in agreement with previous results on TPMS taken from the literature and show that TPMS can outperform standard Aluminium open foams.

A note on the applicability of Eringen’s nonlocal model to functionally graded materials

In this note, the use of Eringen’s nonlocal theory for the analysis of functionally graded beams, plates, and shells is discussed. The properties of the nonlocal modulus and its dependence on the internal length scale are brought out. The use of Eringen’s nonlocal model with different nonlocal approaches is discussed with an evidence from the literature.

Thermoelastic damping in circular microplate resonators based on fractional dual-phase-lag model and couple stress theory

In the present work, thermoelastic damping in a micro-resonator operating in vacuum as a vibrating size-dependent circular thin plate is studied. To better describe the heat conduction process, a generalized thermoelasticity theory of fractional dual-phase-lag (DPL) incorporating the couple stress theory is put forward to capture the experimentally observed small-scale effect of thermoelastic dissipation. The complex frequency of the micro-plate is obtained through Laplace transform technique. Finally, Lifshitz and Roukes’s complex frequency method is employed to derive an analytical expression for thermoelastic damping. The influences of the parameters including fractional order, phase-lag time, and internal characteristic length on the inverse quality factor Q−1 are analyzed. The obtained results show that the influences of these parameters on thermoelastic damping are pronounced. These results are helpful to the design of micro-/nano-resonators with high-performance.

Design parameter study to extend the capacity range of dry twin screw compressors

The possibility for extending the capacity range for oil-free dry twin screw compressors has been studied. Basic geometry parameters influence on compressor performance has been derived. The two parameters shaft speed and rotor diameter are critical. The lower capacity limit for dry screw compressors depends on maximum acceptable shaft speed, considering bearings, gearbox or power electronics. The higher capacity limit depends on rotor size, considering machining costs and tolerances for large rotor diameters. Thermodynamic efficiency and optimal rotor tip speed are dependent on internal throttling and leakage losses. Simplified analytical modelling has been applied, neglecting detailed geometry with minor influence on compressor performance. Basic kinematic relations give shaft speed as dependent on screw geometry non-dimensional specific displacement, on rotor tip speed (moderately dependent of machine size), and on capacity. Basic kinematic relations also define the rotor diameter dependence on these three parameters, specific displacement; tip speed, and capacity. The rotor profile geometry, i.e. number of lobes, rotor lobe depth/diameter, male tip width/diameter; as well as rotor length/diameter ratio and wrap angle determine the specific displacement. The specific displacement is non-dimensional and hence independent of the machine size or capacity. Also the specific internal leakage path lengths in the rotor mesh and between rotors and casing, as well as the specific outlet port size will be determined by the rotor profile major geometry parameters. Here specific means in relation to the male rotor diameter. A fixed internal pressure ratio (volume ratio) has been assumed.A simplified computerized model was developed to calculate the necessary geometry data and in particular the specific displacement and the optimal tip speed, from basic geometry parameters. For the case of constant specific clearances (non-dimensional), the optimal tip speed is constant, independent of compressor size and capacity. For the case of constant absolute clearances, the optimal tip speed is slightly dependent on the compressor size and capacity. A simplified, non-female addendum, point generated, asymmetric profile was assumed. Rotor profile details with minor influence on performance have then been omitted. A cylindrical part of the male tip would allow a bigger outlet port while maintaining the built-in volume ratio.The theoretical results from this study indicate that optimal compressor data should primarily be dependent on the number of male lobes and the lobe depth, i.e. the specific displacement. A screw profile with a lower number of lobes will result in a lower optimal shaft speed and should hence enable the design of dry screw compressors for lower capacity than the commonly used 4:6 lobe configuration, without exceeding the drive train high speed constraint. A screw profile with a higher number of lobes would result in a higher optimal shaft speed and in particular reduced rotor size (rotor diameter). It should hence enable the design of dry screw compressors for higher capacity than for the commonly used 4:6 lobe configuration, without having the machining problems of too large a rotor diameter.Considering both the potential capacity range extension and the efficiency, low capacity dry screw compressors with fewer rotor lobes, e.g. 2:4, might be the most promising option.

A new approach to analyze the equilibrium and transient behaviors of particulate systems and the subsequent application to multiphase fluid systems

Fast and robust computation for population balance models is a crucial requirement for simulating particulate systems. Despite all the recent advances in developing relevant computational algorithms, either efficiency or robustness can only be achieved at the expense of the other. However, optimal compromise is possible by having prior estimates of the system's internal length and time scales. Thus, an approximation technique is introduced in this study to extract equilibrium and transient behaviors for a particulate system considering coalescence and breakage phenomena. The approximation method is developed by simplifying assumptions on the available analytical solution for a spatially homogeneous population balance equation with simple kernels. The derived equilibrium and transient equations suggest that the system is governed by a dimensionless group that can describe the equilibrium distribution of the system as well as the rate and the direction that the system is likely to evolve. The method is applied to two different sets of complex breakage and coalescence kernels used for liquid-liquid dispersed systems. The approximated time and length scales were validated with numerical results; thus, the approximation can be used to generate targeted element-based orthogonal collocation grids for fast and robust computation of transient and steady-state particulate systems. This approach can significantly decrease the computation time, typically by 40–70 % for steady-state conditions.

Comment on Association of FLT3-internal duplication length with overall survival in acute myeloid leukemia: a systematic review and meta-analysis.

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Microstructure size-dependent contact behavior of a thermoelectric film bonded to an elastic substrate with couple stress theory

Thermoelectric films linked to elastic substrates are typical engineering structures and have applications in heat recovery systems. This article uses the nonlocal heat conduction and couple stress theory to investigate the electric-thermal-elastic behavior of the thermoelectric film placed on the elastic half-plane. The internal characteristic lengths of both the thermoelectric film and the elastic substrate are introduced to reveal the scale effects. The coupling governing integro-differential equations in terms of the interface shear stress and tensile stress are derived for the thermoelectric film and the elastic substrate. The numerical results show how the distribution of the tensile and shear stress intensity factors is affected by the stiffness ratio of the substrate to the thermoelectric film, the internal characteristic lengths of the thermoelectric film and the elastic substrate, and the thickness to length ratio of the thermoelectric film. Compared with the classical model for a thicker thermoelectric film and stiffer elastic substrate, the present study demonstrates the necessity of taking into account the microstructure lengths of the thermoelectric film and the elastic substrate.

A meshless thermal modelling for functionally graded porous materials under the influence of temperature dependent heat sources

In this study, a meshless thermal modeling with meshless local moving kriging interpolation method is presented for analysis of functionally graded porous (FGP) materials under the influence of temperature dependent heat sources. The method is developed based on local collocation with moving kriging shape function. It is truly meshless and having the Kronecker delta property for accurate imposition of boundary conditions. In the proposed model, the weight function is used with correlation parameter treated as the model internal length factor. This produces a local moving kriging method with improved accuracy together with an ease to choose the weight function factor. The method can hence be used in an efficient manner without cumbersome effort for choosing its parameter. The contribution is highlighted in the present study, which is still unexplored in detail in literature. Different forms of porosity are considered to investigate the effect of porosity to heat transfer performance of FGP materials subjected to temperature dependent heat sources. In addition, the method is applied for thermal analysis of FGP materials considering arbitrary geometries, mixed boundary conditions and varied power-law index. Numerical results show the effectiveness and accuracy of the meshless method for thermal modeling and analysis of FGP materials.

Geometric characterization of polymeric capillaries

There are few methods in the literature to measure the inner diameter of very small capillaries. Although silica capillaries are more commonly used, synthetic polymer capillaries are preferred in some applications. The technology for producing them is not as mature. Aside from the absolute value of the inner diameter, the circularity, concentricity (a quantitative index is defined here for the first time) and the bore uniformity of such capillaries are of interest. Beyond microscopy, we describe multiple methods that determine the capillary inner diameter, averaged over a given length. The measurements variously depended on the capillary internal volume, length and cross section, and the resistance to fluid flow. The different approaches produced mutually consistent results. We show that when the internal diameter is not uniform, the different dependence on diameter that two such methods may exhibit, can be exploited to determine the true mean diameter as well as its variance. Finally, for open tubular liquid chromatography, where performance acutely depends on the inner diameter, we surprisingly find that while the mean i.d. may be the dominant determinant of efficiency, bore variance has little to no effect on the performance.

The accuracy of methods for determining the internal length of a nasogastric tube in adult patients: a systematic review

Blind insertion of nasogastric (NG) tubes is performed for several reasons: nutrition and medication administration, gastric aspiration/decompression, and other, diagnostic reasons. Accidental intraesophageal and intestinal placement is common, and increases the risk of serious complications. Therefore, accurate determination of the internal length of the NG tube before placement is considered a prerequisite for achieving correct gastric positioning. We aimed to identify, assess, and summarize the evidence on the accuracy of methods for determining the internal length of an NG tube in adults. Cochrane Library, Excerpta Medica database (EMBASE), PubMed, Cumulative Index to Nursing and Allied Health Literature (CINAHL), and Web of Science were searched up to 31 January, 2022. Studies were eligible when reporting data on the accuracy of methods for determining internal NG tube length in adults. Study selection, risk-of-bias assessment, and data extraction were performed independently by 2 investigators. Risk-of-bias was assessed using the Cochrane Risk-of-Bias Tool and the Joanna Briggs Institute Critical Appraisal Checklist for Cross Sectional Studies. A narrative synthesis of the results was then conducted. Twelve articles were included in this review. All studies were observational, cross-sectional in nature, except for 1 randomized controlled trial. Ten methods for determining the internal length of an NG tube were described. Correctly positioned NG tubes ranged from 13% to 99%. Results showed that the tip of the nose-earlobe-xiphoid distance (NEX) + 10cm (mean: 59.9-60.7cm) and (NEX × 0.38696) + 30.37 + 6cm (mean: 56.6-56.7cm) could potentially result in accuracy as high as 97.4% and 99.0%, respectively. Current data do not provide conclusive evidence of 100% accuracy in finding a correctly placed NG tube when using a method for determining the internal length. Blind placement, using any of the documented methods, cannot be considered safe without additional verification of tube tip positioning. Furthermore, using any of these 10 methods does not reduce the risk of pulmonary intubation.This systematic review was registered at https://www.crd.york.ac.uk/PROSPERO/ as CRD42021243180.

Topology optimization of scale-dependent non-local plates

The main objective of this work is to extend finite element-based topology optimization problem to the two-dimensional, size-dependent structures described using weakly non-local Cosserat (micropolar) and strongly non-local Eringen’s theories, the latter of which finds an application for the first time, to the best of Authors’ knowledge. The optimum material layouts that minimize the structural compliance are attained by means of Solid Isotropic Material with Penalization approach, while the desired smooth, mesh-independent, binary solutions are obtained using density filter accompanied by volume preserving Heaviside projection method. The algorithms are enhanced by including an element removal and reintroduction strategy to reduce the computational cost, and to prevent spurious excessive distortion of elements with very low density. Example problems of practical importance are investigated under the assumption of linear elasticity to validate the code and to clearly demonstrate the influence of internal length scales and different non-locality mechanisms on final configurations. Obtained macro-scale optimum topologies admit the characteristics of corresponding continuum theories, and appear to be in agreement with the mechanical response governed by particle interactions in micro/nanoscale.

Progressive failure analysis of cylindrical shell under hydrostatic pressure based on an extended bond-based peridynamic method

A three-dimensional extended bond-based peridynamic (BPD) model, which considers the influence of internal length effect of long-range force on calculation accuracy, is proposed for progressive failure analysis of cylindrical shell subjected to hydrostatic pressure. The maximum strain criterion is introduced into the model to be a benchmark to judge whether bond breakage occurs as the hydrostatic pressure increase. Numerical results reveal that the initiation strength failure zones originated from the inner wall of the middle part of the cylinder, and are uniformly distributed at 90° in the circumferential direction. As the damage evolution continue, two new failure zones occur in the outer wall of the cylinder. Furthermore, the failure zones initiation in the inner and outer walls propagates toward to the middle surface of the cylindrical shell, and eventually they connect together. Throughout the failure evolution history, the failure degree of cylindrical shell behaves exponential growth with the loading linear increase. Once strength failure occurs, a small pressure increment would prompt the structure failure rapidly.

Numerical simulation of strain localization through an integrated Cosserat continuum theory and strong discontinuity approach

In this paper, we propose a new numerical approach abbreviated as Cos-SDA for analyzing strain localization problems of geomaterials. The Cos-SDA is achieved by implanting the strong discontinuity approach (SDA) into the computational framework of the Cosserat continuum finite element approach (Cos-FEA). Through two numerical examples of plane strain compression test and slope stability, it is demonstrated that the Cos-SDA model can effectively simulate the entire progressive failure process of geomaterials from weak discontinuity to strong discontinuity. Cos-SDA can effectively alleviate the influence of mesh distortion in shear zone, and the numerical solution can still maintain convergence even under large deformation. Cos-FEA and Cos-SDA have much stiffer mechanical response than SDA-FEA since an internal length scale is introduced into the governing equations. In contrast, the SDA-FEA shows more conservative as the unmature bifurcation occurs and weak discontinuous stage is ignored in the numerical simulation, while Cos-FEA numerical results show an over-stiff mechanical response in the stage of post failure. Cos-SDA inherits the advantages of both SDA-FEA and Cos-FEA and neutralizes their mechanical responses, so it is more reasonable in simulating the progressive failure process from weak discontinuity deformation (strain localization) to strong discontinuity deformation (slip) occurring in geomaerials.