Concave Shape Research Articles

Experimental investigation on the interaction between mode-2 internal solitary wave and horizontal transverse cylinder

The experimental study on the interaction between a mode-2 internal solitary wave (ISW) and a horizontal transverse cylinder has been carried out in a large gravity-stratified fluid flume. One kind of making-wave method of “rotating-blade-gate” is proposed to achieve the experimental simulation of the standard mode-2 ISW in the laboratory flume. The conductivity probe array and particle image velocimetry are used to measure the mode-2 ISW and its wave-flow structure of the interaction with the horizontal transverse cylinder, and the micro-amplitude force sensor is used to measure the forces of the mode-2 ISW on the cylinder model. It is shown that the mode-2 ISW geometric structure is characterized by a convex and concave oval wave envelope shape and the counterclockwise and clockwise circulations are formed in its convex and concave domains, respectively. The resulting pair of upper and lower antisymmetric circulations moves forward together, which causes a horizontal strong flow at the symmetric center of the wave envelope consistent with the wave propagation direction. The horizontal transverse cylinder is subjected to the combined action of horizontal flow, vertical flow, and density change induced by the mode-2 ISW, in which the horizontal strong flow, induced flow separation, and vortex structure located at the symmetric center of the wave envelope are the signature features that are different from other positions. The theoretical analysis model of the forces exerted by the mode-2 ISW on a horizontal transverse cylinder is established. The spatial distribution characteristic of the force exerted by the mode-2 ISW on a horizontal cylinder is obtained, and the essential reason for the maximum horizontal and vertical loads on the cylinder is revealed. The horizontal maximum load corresponds to the inhomogeneous change of the horizontal velocity along the depth, and the vertical maximum load depends on the maximum density change along the depth, of which variation trend corresponds to the linear change of wave amplitudes.

The Nature of γ-Ray Emission from HESS J1912+101

Since the discovery of HESS J1912+101 at teraelectronvolt energies, its nature has been extensively studied. Due to the absence of X-ray and radio counterparts, whether its γ-ray emission is produced by relativistic electrons or ions is still a matter of debate. We reanalyze its megaelectronvolt to gigaelectronvolt γ-ray emission using 14 yr of Pass 8 data of the Fermi-LAT, and find that the gigaelectronvolt γ-ray emission is more extended than the teraelectronvolt shell detected by H. E. S. S. and flux above 10 GeV from the northern half is much higher than that from the southern half, where there is evident interaction between shocks and molecular clouds. As a consequence, the gigaelectronvolt spectrum of the northern half (with an index of 2.19 ± 0.12) is much harder than that in the south (with an index of 2.72 ± 0.08), and the overall gigaelectronvolt spectrum shows a concave shape, which is distinct from most γ-ray supernova remnants (SNRs). In combination with the teraelectronvolt spectrum, the overall γ-ray spectrum can be fitted with a broken power-law model for trapped ions and a low energy component due to escaping ions. The diffusion coefficient for escaping ions however needs to be proportional to the energy, implying that the low energy component may also be attributed to ions accelerated via recent shock–cloud interactions. A hadronic origin for the γ-ray emission is therefore favored and the overall emission properties are consistent with ion acceleration by SNR shocks. On the other hand, it is still undeniable that stellar cluster or PWN may have some contribution in some parts of this extended source.

Post critical characteristics of a side-box steel concrete composite girder: Experimental investigation and mechanism analysis

The present study is aimed to investigate the post-critical behavior of a side-box steel-concrete composite girder under varying wind angles of attack, by conducting a series of section model testing with single-degree and two-degrees of freedom. The essence of flutter, as well as the adverse impact of vortex shedding lock-in on exacerbating post-critical flutter responses, was revealed in detail. The results indicate that the coupled motion of flutter for the prototype composite girder can be characterized as a supercritical Hopf bifurcation with significant phase shifting between motions. The circular character of the limit cycle oscillation (LCO) expressed in the phase diagram is altered to a non-circular form due to the apparent aerodynamic stiffness nonlinearity within a wide range of wind speeds. Interestingly, the coupling vibration between vortex-induced vibrations (VIV) and flutter, i.e., VIV-flutter coupling vibration is observed for the prototype girder, due to the evolution of total damping ratio concave shape with wind speed. Two mitigation countermeasures, i.e., a L-shaped skirt plate and a sharpened wind fairing, were proposed to improve the aeroelastic stability, caused by a significant increase in uncoupled positive aerodynamic damping and alternation of VIV-flutter coupling. In addition, the specific effects of structural damping on the VIV-flutter coupling were discussed in detail.

Flexible array transducer for photoacoustic-guided interventions: phantom and ex vivo demonstrations.

Photoacoustic imaging has demonstrated recent promise for surgical guidance, enabling visualization of tool tips during surgical and non-surgical interventions. To receive photoacoustic signals, most conventional transducers are rigid, while a flexible array is able to deform and provide complete contact on surfaces with different geometries. In this work, we present photoacoustic images acquired with a flexible array transducer in multiple concave shapes in phantom and ex vivo bovine liver experiments targeted toward interventional photoacoustic applications. We validate our image reconstruction equations for known sensor geometries with simulated data, and we provide empirical elevation field-of-view, target position, and image quality measurements. The elevation field-of-view was 6.08 mm at a depth of 4 cm and greater than 13 mm at a depth of 5 cm. The target depth agreement with ground truth ranged 98.35-99.69%. The mean lateral and axial target sizes when imaging 600 μm-core-diameter optical fibers inserted within the phantoms ranged 0.98-2.14 mm and 1.61-2.24 mm, respectively. The mean ± one standard deviation of lateral and axial target sizes when surrounded by liver tissue were 1.80±0.48 mm and 2.17±0.24 mm, respectively. Contrast, signal-to-noise, and generalized contrast-to-noise ratios ranged 6.92-24.42 dB, 46.50-67.51 dB, and 0.76-1, respectively, within the elevational field-of-view. Results establish the feasibility of implementing photoacoustic-guided surgery with a flexible array transducer.

New failure mechanism for evaluating ultimate inclined load adjacent to slope.

A new failure mechanism is proposed for calculating the ultimate inclined load adjacent to the slope, i.e., the slope is in the limit state when the critical slope contour and the slope surface are at the critical position where two intersections will occur. The conventional view is that the critical slope contour calculated by the method of characteristics has only a concave shape. This study found that the critical slope contour changes from concave to convex when the inclined load imposed on the slope top surface increases. The feasibility of the proposed method is verified by the finite element limit analysis (FELA) and the definition of the ultimate load. The parametric analysis showed that the current method of characteristics (CMOC) overestimated the ultimate inclined load and gave an incorrect conclusion since it assumed larger failure models at a low strength ratio or large friction angle. The proposed method does not require assumption or search of the failure models, and it can solve the shortcomings of CMOC.

Systematic cortical thickness and curvature patterns in primates

Humans are known to have significant and consistent differences in thickness throughout the cortex, with thick outer gyral folds and thin inner sulcal folds. Our previous work has suggested a mechanical basis for this thickness pattern, with the forces generated during cortical folding leading to thick gyri and thin sulci, and shown that cortical thickness varies along a gyral–sulcal spectrum in humans. While other primate species are expected to exhibit similar patterns of cortical thickness, it is currently unknown how these patterns scale across different sizes, forms, and foldedness. Among primates, brains vary enormously from roughly the size of a grape to the size of a grapefruit, and from nearly smooth to dramatically folded; of these, human brains are the largest and most folded. These variations in size and form make comparative neuroanatomy a rich resource for investigating common trends that transcend differences between species. In this study, we examine 12 primate species in order to cover a wide range of sizes and forms, and investigate the scaling of their cortical thickness relative to the surface geometry. The 12 species were selected due to the public availability of either reconstructed surfaces and/or population templates. After obtaining or reconstructing 3D surfaces from publicly available neuroimaging data, we used our surface-based computational pipeline (https://github.com/mholla/curveball) to analyze patterns of cortical thickness and folding with respect to size (total surface area), geometry (i.e. curvature, shape, and sulcal depth), and foldedness (gyrification). In all 12 species, we found consistent cortical thickness variations along a gyral–sulcal spectrum, with convex shapes thicker than concave shapes and saddle shapes in between. Furthermore, we saw an increasing thickness difference between gyri and sulci as brain size increases. Our results suggest a systematic folding mechanism relating local cortical thickness to geometry. Finally, all of our reconstructed surfaces and morphometry data are available for future research in comparative neuroanatomy.

Systematical structural analysis of monolithic domes

Monolithic dome structures were built in the 1970s in Europe and America. These dome structures share common benefits of being cost efficient, earth-friendly, extremely durable, and easily maintained. Monolithic shells are easily constructed and are extremely cost-effective. Monolithic domes respond efficiently to any climate, even to extremely cold or hot temperatures. In terms of utility savings, monolithic domes can cut electricity consumption by up to one-third, thereby saving 60–70% of total energy costs. Moreover, monolithic structures provide the highest survivability rates from destructions. The interior of monolithic domes have perfect, concave shapes to ensure that sound travels through the dome and perfectly collected at different vocal points. These dome structures are utilized for domestic use because the scale allows the focal points to be positioned across daily life activities, thereby affecting the sonic comfort of the internal space. This study examines the various acoustic treatments and parametric configurations of monolithic dome sizes. A geometric relationship of acoustic treatment and dome radius is established to provide architects guidelines on the correct selection of absorption needed to maintain the acoustic comfort of these special spaces. In this study we cannot take the particular research paper for comparison of results. The location of structure for terrain category I calculated and so the wind speed varies according to terrain and this results in different value of load calculation for different terrain category.

A new method for determining the shape of the sclera

Purpose. The aim of the present theoretical modelling study is to improve the fitting of scleral lenses by means of a novel determination of the scleral shape of the eye. Material and Methods. . The movement of scleral lenses and soft lenses is affected by scleral shape around the limbus. Based on this, it is important to take a closer look at the edge of the sclera. An area of 4 mm in diameter around the limbus is considered as a suitable area for shape fitting, which is shown by 44 profile photographs. As a first step, a straight line (y = m • x + b) was fitted on scleral data of 44 perpendic- ular cuts. Then, these measuring points were rotated around the first “scleral measuring point after the limbus” (angle of rotation = − arctan (m)) so that all measuring points were horizontal. A parabola was then fitted as best as possible (y = a • x2 + b • x + c) to the rotated measuring points. The parabola coefficient a or “pca value” plays a central role as a shape criterion of the corneo-scleral profile (CSP). A pca value a ≥ 0.1 means the CSP is a concave parabola, while a ≤ −0.1 implies that the CSP is a convex one. If the pca value is between −0.1 < a < 0.1, the CSP is a straight line. Results. Based on the 44 profile section photos, 85.8 % of the CSPs were straight, 11.1 % were convex and 3.1 % were concave parabolic shapes. The probability of determining a parabolic CSP section is about 18.5 % (normal distribution, the normal distribution test for the calculated pca values shows p < 0.01). Conclusion. A specification of the corneo-scleral-profile (CSP) with the corresponding scleral angle “alpha”, gives significantly more information about the scleral shape than if only one of the two parameters is specified. Furthermore, this simplifies the determination of the geometry of contact lenses with large diameters, especially scleral lenses. Keywords Soft contact lenses, scleral lenses, corneo-scleral profile, scleral shape, sclera

Predicting beach profiles for thickened tailings surface deposition

Thickened tailings deposition technology can form a stack with a certain slope by depositing high-concentration tailings slurries to reduce the footprint of tailings storage facilities and water consumption. Thickened tailings slurries exhibit complex non-Newtonian behaviors. Predicting the beach profile evolution of thickened tailings is important for the tailings storage facility design and management. A novel governing differential equation (GDE) derived from the lubrication theory is proposed in this work to capture laws of beach profile formation. Experimental data from three-dimensional laboratory-scale flume tests are analyzed using the proposed GDE. The GDE avoids the discrepancy from an inappropriate coordinate system, which exists in some state-of-the-art models and exhibits higher accuracy when predicting the beach shape near the toe of a preexisted layer. Compared with the Herschel–Bulkley (H–B) model, the Zhang’s equilibrium rheological model is preferred to determine the static yield stress, which leads to the accurate estimation of the stack profile in single- and multilayer thickened tailings depositions. The in-situ beach profile of thickened tailings is predicted using a numerical technique. A case study is included to demonstrate that the prediction based on the proposed GDE is consistent with the field measurement. The beach profile prediction of thickened tailings considering thixotropy is also discussed in this study. Results indicated that the decrease of yield stress along the flow path due to thixotropy leads to the concave beach shape of thickened tailings.

Enhancement of KMnO4 treatment on cyanobacteria laden-water via 1000 kHz ultrasound at a moderate intensity

1000 kHz high-frequency ultrasound at 0.12 and 0.39 W/mL intensity was used to enhance the inactivation of suspensions of Microcystis aeruginosa cells using KMnO4. With 10 mg/L of KMnO4, ultrasound at 0.12 W/mL intensity was found to be effective in inactivating the cyanobacteria within 10 min. A Weibull model was found to describes the inactivation well. Its concave shape shows that some cells have a certain resistance to this treatment. Cytometry and microscopic analysis confirm that the treatment damages cell integrity. Despite that the extracellular organic matter in the water was not significantly increased. The concentration of extracellular cyanobacterial toxins even decreased. The filtered suspension of inactivated cyanobacteria was used to cultivate mung beans, and the suspension did not hinder their germination. This provides a new idea for using cyanobacteria-laden wastewater. These findings suggest a technique for speeding up the oxidation of Microcystis cells using KMnO4 with ultrasound at moderate intensity, which provide new insights into the biological effects of ultrasound.

Optimal utilization of hydrokinetic energy resources through performance improvement of the darrieus turbine using concave and flat blocking plates

Energy extraction from renewable sources like hydrokinetic energy from the flowing water of rivers and canals is one of the affordable and clean energy generation technique. The current work is carried out towards performance enhancement of the Darrieus hydrokinetic turbine for open water channel utilization application. The investigation has been done using the flat and concave shape of blocking plate. Both blocking plates have been analyzed for different sizes as well as location at the upstream side of the turbine. The obtained results are reported after considering appropriate velocity correction. The blocking plates with projected width of 76 mm, 89 mm, 101 mm, 127 mm, 152 mm, and 203 mm are selected for the investigation. It is observed that 101 mm (Width Ratio, WR=0.36) with concave blocking plate provides maximum Cp of 0.245 at 0.99 TSR. Also, the optimum region is found between 0.143 and 0.286 Distance Ratio (DR) from the top corner of the acrylic plate. The concave blocking plate enhance the performance more compared to flat blocking plate. The conclusion is made that, the performance with flat blocking plate with optimized width and location improve the power coefficient by 10.92% and that of concave blocking plate by 18.45%.

Effect of Lankford Coefficients on Springback Behavior during Deep Drawing of Stainless Steel Cylinders.

Accurate prediction of springback is increasingly required during deep-drawing formation of anisotropic stainless steel sheets. The anisotropy of sheet thickness direction is very important for predicting the springback and final shape of a workpiece. The effect of Lankford coefficients (r00, r45, r90) with different angles on springback was investigated using numerical simulation and experiments. The results show that the Lankford coefficients with different angles each have a different influence on springback. The diameter of the straight wall of the cylinder along the 45-degree direction decreased after springback, and showed a concave valley shape. The Lankford coefficient r90 had the greatest effect on the bottom ground springback, followed by r45 and then r00. A correlation was established between the springback of workpiece and Lankford coefficients. The experimental springback values were obtained by using a coordinate-measuring machine and showed good agreement with the numerical simulation results.

Interferometry Observations of the Gravity Wave Effect on the Sporadic E Layer

On the basis of interferometry measurement made with the Chung-Li VHF radar, we investigated the effects of upward propagating gravity waves on the spatial structures and dynamic behavior of the 3 m field-aligned irregularities (FAIs) of the sporadic E (Es) layer. The results demonstrate that the quasi-periodic gravity waves oscillating at a dominant wave period of about 46.3 min propagating from east-southeast to west-northwest not only modulated the Es layer but also significantly disturbed the Es layer. Interferometry analysis indicates that the plasma structures associated with gravity wave propagation were in clumpy or plume-like structures, while those not disturbed by the gravity waves were in a thin layer structure that descended over time at a rate of about 2.17 km/h. Observation reveals that the height of a thin Es layer with a thickness of about 2–4 km can be severely modulated by the gravity wave with a height as large as 10 km or more. Moreover, sharply inclined plume-like plasma irregularities with a tilted angle of about 55° or more with respect to the zonal direction were observed. In addition, concave and convex shapes of the Es layer caused by the gravity wave modulations were also found. Some of the wave-generated electric fields were so intense that the corresponding E × B drift velocities of the 3 m Es FAIs approximated 90 m s−1. Most interestingly, sharp Doppler velocity shear as large as 68 m/s/km of the Es FAIs at a height of around 108 km, which bore a strong association with the result of the gravity wave propagation, was provided. The plausible mechanisms responsible for this tremendously large Doppler velocity shear are discussed.

Predicting soil erosion and deposition on sloping farmland with different shapes in northeast China by using 137Cs

Slope shape has an important influence on soil erosion. However, the distribution of erosion and deposition on sloping farmland with different shapes is still unclear. This severely restricts the soil loss evaluation and protection of Mollisol resources in northeast China, where sloping farmland (<10°) accounts for 60 % of the cultivated land. In this study, the 137Cs technique combined with wavelet analysis theory was employed to study the spatial distribution characteristics of erosion–deposition rates along three slopes with straight, convex, and concave shapes in northeast China. The results indicated that the average erosion rates of the three slopes were in the following order: convex > straight > concave. The soil erosion and deposition rates fluctuated along the slope length. The primary fluctuation periods in the straight slope, convex slope and concave slope were 45.1 m, 55.0 m, and 40.4 m, respectively. Three relationships of coupled effects of slope gradient and slope length on straight, convex and concave slope were established and verified. It can be concluded that the relationship between the soil erosion rate and slope length was not simple monotonous but showed a certain periodic fluctuation, which was related to the change in transport capacity of runoff on the slope. The change in the erosion–deposition rate with slope length in a straight slope shape can be described by the cosine function. The cumulative soil erosion–deposition rates along the slope had very significant binary power function relationships with both slope length and gradient on convex and concave slopes. The coupled effects of slope gradient and length on soil erosion–deposition for different slope shapes should be fully considered for soil erosion prediction. This study could provide theoretical support for improving erosion prediction models and a scientific basis for the rational arrangement of soil and water conservation measures on slopes at appropriate locations.

Storage infiltration of rock-soil interface soil on rock surface flow in the rocky desertification area

Rock surface flow, formed from the rock surface of outcrops after receiving rainwater, has become a main form of runoff in rocky desertification ecosystems with frequent regional and seasonal droughts. However, as a main flow path of rock surface flow into the surrounding soil of outcrops, how much the rock-soil interface soil can store and infiltrate the rock surface flow from outcrops is not well known. The goals of this study were to explore the storage-infiltration effect of soil at the rock-soil interface on rock surface flow in rocky desertification areas. Hence, a typical rocky land with large bulk rock outcrops, of which the surrounding soil has experienced five years of rock surface flow, and three special rock surfaces with shapes of convex, straight, and concave with different hydrological paths were selected in a typical rocky desertification county of China. Field investigation, ring knife soaking and infiltration methods were applied to indicate the difference in storage-infiltration between rock-soil interface soil and non-rock-soil interface soil on the rock surface flow in these different rock surface shapes. The results showed that the rock-soil interface soils around outcrops with different rock surface shapes exhibited different storage-infiltration capabilities for rock surface flow. The space of soil carrying water at the rock-soil interface showed the order of the convex shape, the straight shape and the concave shape, in which the non-rock-soil interface soil around the convex shape had greater space, followed by the rock-soil interface soil. The rock-soil interface soil of all three shapes had higher water storage performance than the non-rock-soil interface soil in terms of the field capacity and usable storage, where the rock-soil interface soil at the soil depth of 0–10 cm of the concave shape had lower water storage and lower conservation capacity than the 10–20 cm depth, and this was of positive significance for retaining the rock surface flow. The soil infiltration rate at the rock-soil interface with only the concave shape was greater than that at the non-rock-soil interface, where the concave shape had the greatest soil infiltration rate at the rock-soil interface. The results from this study can be used to understand the influence of outcrops on the soil properties of karst ecosystems.

Predictors of treatment discontinuation during an 18-month multi-site randomized trial of Cognitive Enhancement Therapy for early course schizophrenia

Treatment discontinuation during clinical trials in schizophrenia is a critical challenge, especially for longer-term interventions in the early course. This research explored predictors of treatment discontinuation in an outpatient early course schizophrenia sample (N = 102) during an 18-month multi-site trial of Cognitive Enhancement Therapy (n = 58) and Enriched Supportive Therapy (n = 44). Fifty-three (52%) participants discontinued, with no significant difference between the treatment groups in discontinuation rate. Univariate and multivariate binary logistic regression models explored differences in key demographic and cognitive and behavioral outcomes between participants who completed and discontinued treatment. Significant multivariate predictors of discontinuation included IQ (linear) and problem solving (curvilinear). The concave shape of the problem solving prediction demonstrated that initially as scores were increasing the probability of non-completion was increasing. However, after a score of 41 (below average problem solving), the probability of being a non-completer decreased as performance increased. Non-completers had significantly lower IQ scores compared to completers. Post-hoc analyses indicated that participants who discontinued prior to mid-treatment exhibited the greatest intellectual challenges, with comparisons moderate-to-large in strength. IQ and problem solving are likely important factors to assess at pre-treatment in early course schizophrenia trials to identify those most vulnerable to discontinuation.

Temperature-Dependent Anisotropy and Two-Band Superconductivity Revealed by Lower Critical Field in Organic Superconductor κ-(BEDT-TTF)2Cu[N(CN)2]Br

Resistivity and magnetization have been measured at different temperatures and magnetic fields in organic superconductors κ-(BEDT-TTF)2Cu[N(CN)2]Br. The lower critical field and upper critical field are determined, which allow to depict a complete phase diagram. Through the comparison between the upper critical fields with magnetic field perpendicular and parallel to the conducting ac-planes, and the scaling of the in-plane resistivity with field along different directions, we find that the anisotropy Γ is strongly dependent on temperature. It is realized that Γ is quite large (above 20) near T c, which satisfies the 2D model, but approaches a small value in the low-temperature region. The 2D-Tinkham model can also be used to fit the data at high temperatures. This is explained as a crossover from the orbital depairing mechanism in high-temperature and low-field region to the paramagnetic depairing mechanism in the high-field and low-temperature region. The temperature dependence of lower critical field, H c1(T), shows a concave shape in wide temperature region. It is found that neither a single d-wave nor a single s-wave gap can fit the H c1(T), however a two-gap model containing an s-wave and a d-wave can fit the data rather well, suggesting two-band superconductivity and an unconventional pairing mechanism in this organic superconductor.

Shape Optimization of Concave Crossbars to Increase Threshing Performance of Moist Corn Ears

Harvesting of high-moisture corn ears poses a challenge due to the high level of grain damage. In the present study, a series of concaves adapted to moist corn ears threshing was developed and evaluated. The key improvements include a concave arc shape and oblique crossbars to reduce corn grain damage and threshing losses. Results show that the geometrical shape of the concave arc and its crossbars have a significant influence on the grain detachment from the ears, grain separation through the concave, and grain damage during the threshing process of moist ears of corn. Studies show that replacing the concave rounded crossbars with oblique ones can increase threshing performance of moist corn ears. A concave with an Archimedes’ spiral arc and oblique concave crossbars is an effective approach to improve corn grain quality and reduce harvest losses due to grain damage. We identify the optimal design for threshing corn ears as an experimental concave with an Archimedes’ spiral arc of 8 mm height, with 19 mm wide crossbars of the concave with an oblique working plane (tilt angle 25°). This design achieves minimal threshing grain losses (0.03%) when threshing moist ears (grain moisture content ~35%), and damaged grain in the threshing apparatus does not exceed the permissible limit of 3% at an ear feed rate of 16.8 kg s−1.

Enhanced solder fatigue life of chip resistor by optimizing solder shape

As surface-mounted components get smaller, especially passive components such as chip resistor or chip capacitor, small apertures on a stencil are required, which generates higher variations in the printed solder paste volume and solder joint shape. In this study, the board-level fatigue life of chip resistor assemblies with SAC305 was investigated. Different volumes of solder paste are printed, which varies the shape of solder joints. Four solder joint shapes are compared: concave, straight, tiny convex, and convex, which are achieved using a stencil with differently sized openings. Thermal shock cycling shows that the convex shape exhibits the best thermal shock reliability while the concave shape has the shortest fatigue life. Additionally, different sizes of chip resistor package are compared. A comparison of the size of components concludes that the R0402 chip resistor has relatively better thermal shock resistance than the larger chip resistor, R1005 due to larger change in length of R1005 during thermal cycling. Based on the experimental results of fatigue life, the parameters of a constitutive equation are calculated to evaluate the fatigue life of the solder joint. This study provides criteria manufacturers can use to improve the reliability of chip assemblies though inspecting solder paste volumes and shapes.

Soft interphase volume fraction of composites containing arbitrarily shaped mono−/poly-disperse fillers: Theoretical and numerical investigations

Interphase, a crucial structural component in composite materials connecting the fillers and matrix, typically possesses unique physical properties and plays a crucial role in determining the overall transport and mechanical behaviors of the material system. In this work, we propose a generic theoretical framework to precisely determine the volume fraction fsi of soft interphase around arbitrarily shaped hard fillers, including both convex and concave shapes with arbitrary size dispersity, in three−/two-dimensional (3D/2D) heterogeneous material systems. Specifically, a composite material is regarded as a three-phase structure composed of a homogeneous matrix, hard anisotropic fillers, and their surrounding interpenetrable interphase layers with a constant “thickness” for each filler volume fraction. The seminal hard -core soft-shell (i.e., cherry-pit) model and statistical geometry theories are employed to derive explicit analytical formalism of fsi which is subsequently verified via a series of numerical experiments using Monte Carlo sampling. We systematically investigate the dependence of fsi on the filler characteristics, including filler volume fraction, geometric size factor, fineness, and filler shape and size distributions. Interestingly, we find that filler sphericity can be used as the sole shape descriptor to control the interphase volume fraction for all filler shapes, including those with irregular non-convex morphologies. Our framework provides an efficient and accurate tool for composite design that complements expansive numerical simulations, which is also readily applicable to understanding the effect of fsi on physical properties of composites.