Void Shape Research Articles

Euclid: Forecasts from redshift-space distortions and the Alcock–Paczynski test with cosmic voids

Euclid is poised to survey galaxies across a cosmological volume of unprecedented size, providing observations of more than a billion objects distributed over a third of the full sky. Approximately 20 million of these galaxies will have their spectroscopy available, allowing us to map the three-dimensional large-scale structure of the Universe in great detail. This paper investigates prospects for the detection of cosmic voids therein and the unique benefit they provide for cosmological studies. In particular, we study the imprints of dynamic (redshift-space) and geometric (Alcock–Paczynski) distortions of average void shapes and their constraining power on the growth of structure and cosmological distance ratios. To this end, we made use of the Flagship mock catalog, a state-of-the-art simulation of the data expected to be observed with Euclid. We arranged the data into four adjacent redshift bins, each of which contains about 11 000 voids and we estimated the stacked void-galaxy cross-correlation function in every bin. Fitting a linear-theory model to the data, we obtained constraints on f/b and DMH, where f is the linear growth rate of density fluctuations, b the galaxy bias, DM the comoving angular diameter distance, and H the Hubble rate. In addition, we marginalized over two nuisance parameters included in our model to account for unknown systematic effects in the analysis. With this approach, Euclid will be able to reach a relative precision of about 4% on measurements of f/b and 0.5% on DMH in each redshift bin. Better modeling or calibration of the nuisance parameters may further increase this precision to 1% and 0.4%, respectively. Our results show that the exploitation of cosmic voids in Euclid will provide competitive constraints on cosmology even as a stand-alone probe. For example, the equation-of-state parameter, w, for dark energy will be measured with a precision of about 10%, consistent with previous more approximate forecasts.

Effect of Defects Part I: Degradation of Constitutive Coefficients as an Input to the Composite Failure Model with Microvoids and Porosity

It is always challenging to provide appropriate material properties for a composite progressive failure model. The nonstandard percentage reduction method that is commonly used to degrade the material constants with micro-scale defects generates tremendous uncertainty in failure prediction. The constitutive matrix is composed of multiple material constants. It is not necessary that all constants degrade either equally or linearly due to a certain state of material defects. With this very concern in mind, this article presents a guideline for using a quantified perturbation for each coefficient appropriately. It also presents distribution of effective material properties (EMPs) in unidirectional composite materials with different states of defects such as voids. Irrespective of resin transfer molding (RTM) or chemical vapor infiltration (CVI) processes, manufacturers’ defects such as voids of different shapes and sizes are the most common that occur in composite materials. Hence, it is important to quantify the ‘effects of defects’ void content herein on each material coefficient and EMP. In this article, stochastically distributed void parameters such as the void content by percent, size, shape, and location are considered. Void diameters and shapes were extracted from scanning acoustic microscope (SAM) images of 300,000 cycles of a fatigued composite. The EMPs were calculated by considering unit cells, homogenization techniques, and micromechanical concepts. The periodic boundary conditions were applied to unit cells to calculate the EMPs. The result showed that EMPs were degraded even when there was a small percentage of the void content. More importantly, the constitutive coefficients did not degrade equally but had a definitive pattern.

Annealing-induced void formation in SiO2 layers on Si substrates: Influence of surface orientation and hydrocarbon exposure

• Void formation by thermal decomposition of SiO 2 layers on Si substrates. • Void shape depends on surface orientation of a Si substrate. • Ring structures inside voids are induced by Si layer adhering to the void sidewall. • Surface carbonization strongly affects formation of ring structures. This study investigated void formation induced by annealing and subsequent cooling in SiO 2 layers grown on Si substrates using scanning electron microscopy and atomic force microscopy. The results show that distinct Si layers form along the entire sidewall of each void and that the shape of the void depends on the surface orientation of the Si substrate, despite the amorphous nature of the SiO 2 layer. These findings suggest that reaction in areas peripheral to the void is the rate-limiting step in void growth for all oxide thicknesses. The orientation dependence of the void shape reflects the anisotropic migration of Si monomers that form the Si layer on the void sidewall. Surface carbonization was also found to suppress the migration of the Si monomers, which leads the Si layer remnants to form ring structures inside the voids. The observed ring structures indicate that voids only begin to form immediately after the onset of annealing; therefore, a likely trigger of initial void formation is the differential thermal expansion between the oxide layer and the silicon substrate.

Role of void shape on shock responses of nanoporous metallic glasses via molecular dynamics simulation

The void shape significantly affects the mechanical properties of nanoporous metallic glasses (NPMGs) under conventional loading. However, how the shock responses of NPMGs depend on the void shape has been rarely studied. In this work, shock simulations of Cu50Zr50 NPMGs containing voids with different shapes are performed by molecular dynamics, aiming to investigate the roles of the void shape on plastic deformation, void collapse, and spallation. The results reveal that the void shape has a significant effect on the peak value of the atomic strain curve and the fraction of atoms participating in the plastic deformation. There is a very weak dependence of the void collapse mode on the void shape under the weak shocks, where the voids collapse perpendicularly to the shock direction. As the shock strength increases, the void collapse mechanism gradually transforms into an internal jet, and the void shape plays an important role in the jet formation. During spallation, the initial damages tend to concentrate in the void collapse regions and then coalesce into large damages. The void shape influences the coalescence degree of spall damage. The spall strength is positively correlated with strain rate and local five-fold symmetry, but negatively correlated with temperature on the spall plane. Additionally, the void influences the spall strength due to the different distribution of the above factors after voids collapse in nanoporous samples.

Effect of voids shape on deformation of 3D-printed closed-cell porous structures

The aim of this work is to investigate the influence of the shape of voids in porous 3D printed closed-cell porous structures on their elastic properties and mechanical behavior using the results of morphological analysis of microstructure based on multipoint statistical characterization, finite element modelling and experimental data. The geometrical models of representative volume elements (RVEs) for structures with non-overlapping inclusions of different shapes and parameters were created and produced using FDM/FFF 3D printing technology. Evaluation of various morphological parameters has been performed based on the analysis of multipoint statistical characteristics. The elastic behavior and properties of the studied RVEs were modelled using finite element analysis. The relationship between mechanical properties and statistical characteristics has been analyzed.

Void-growth computational analysis in elastic-plastic porous materials

This study aims to model the effective mechanical response of highly porous materials using computational homogenisation. A two-phase material is considered here in the form of a von Mises elastic-plastic matrix that includes spherical identical voids. A wide range of void volume fractions from 0.1% to 24% is investigated. The representative volume element principle is adopted to determine the effective yield surface of each case. Its representativeness is checked from a statistical point of view and the mechanical response is set for each porosity rate considering a wide range of stress triaxiality ratios. The relation between void volume fraction and stress triaxiality is discussed and an analysis based on the unit cell computation is proposed to examine the void shape evolution according to these parameters. Therefore, an improvement of the Gurson–Tvergaard–Needleman (GTN) model considering a wide range of void volume fractions is presented. The computational data are subsequently used to enhance the original GTN model. The parameter q1 is translated as a linear function of the porosity while q2 is kept equal to 1. This makes the model simpler and more suitable for a wide range of porous materials.

Effect of shape on void growth: A coupled Extended Finite Element Method (XFEM) and Discrete Dislocation Plasticity (DDP) study

Voids are one of the many material defects present at the microscopic length scale. They are primarily responsible for the formation of cracks and hence contribute to ductile fracture. Circular voids tend to deform into elliptical voids just before their coalescence to form cracks. The principle aim of this study is to investigate the effect of void shape on the micro-mechanism of void growth by using Discrete Dislocation Plasticity simulations. For voided crystals, conventional DDP produces a continuous slip step throughout the material even if a dislocation escapes from a non-convex domain. To overcome this issue, the Extended Finite Element Method (XFEM) is used here to incorporate the displacement discontinuity. Different aspect ratios of elliptical voids are considered under uniaxial and biaxial deformation boundary conditions. The results suggest that voids having the largest surface area tend to have maximum growth rate as compared to void with lower surface area, i.e. “larger is faster”. Under biaxial loading, a higher magnitude of strain hardening, and void growth rate are observed as compared to uniaxial loading. The results also suggest that the orientation of slip planes as well as voids, affect the overall plastic behavior of the voided-ductile material. Furthermore, circular void tends to induce minimum growth rate but have the maximum strain hardening effect as compared to other void shapes under both loading conditions. The results of this study provide a deeper understanding of ductile fracture with applications in manufacturing industry, aerospace industry and in the design of nano/micro-electromechanical devices i.e. NEMS/MEMS.

Analytical investigation of the influence of various void shape and spacing on the load-bearing behavior of concrete hollow core slabs

Analytical investigation of the influence of various void shape and spacing on the load-bearing behavior of concrete hollow core slabs

Study of shrinkage effect of aluminium based binary alloys as phase change materials for latent heat thermal energy storage applications

In this paper, the effect of shrinkage voids during the solidification of binary alloy as phase change material (PCM) on the thermal performance of a latent heat thermal energy storage is studied. Al-Cu 4.1% wt., Al-Si 7% wt., and Al-Mg 30% wt. are the three binary alloys considered as the PCMs. A generalized numerical model considering differences in density, thermal conductivity, and specific heat between liquid and solid phases is developed. A novel method of fluid fraction update scheme is employed to account for the change in volume fraction due to concentration variation induced due to shrinkage and buoyancy flows. The proposed numerical model is validated using reported numerical and experimental results. The density ratio is found to have a pronounced effect on the solidification of binary alloys. With an increasing density ratio, a faster solidification rate along with a thicker mushy region is observed. This effect of density ratio is found to be much more prominent for higher cold wall temperatures. The performance of three binary alloys, namely, Al-Cu 4.1% wt., Al-Si 7% wt., and Al-Mg 30% wt. is examined. Al-Cu 4.1% wt. alloy is found to solidify much earlier with the release of higher energy, followed by Al-Si and Al-Mg, respectively. The model is further used to predict the size and shape of shrinkage void produced for the binary alloys.

Simulation and experiment analysis of relationship between voids and permeability of composites

Due to the significant weight reduction advantage, aerospace composite tanks have become the focus of international competition of spacecraft. However, the permeation of small molecules at low temperature caused by the internal voids of composites is one of the key technical problems which restrict the engineering application of composite tanks. In this study, a combination of theoretical research and experimental research was adopted. By changing the curing pressures of the composites’ autoclave process, laminates with different porosities were prepared and tested for low-temperature permeability. Based on the grayscale processing and median filtering methods, a permeability prediction model with the true voids morphology of composite materials was established. Based on the random medium theory, the random voids model of composites was built to study the effect of void size and shape on the permeability of laminates. The results showed that the finite element analysis of composites, permeability based on the real voids morphology model was in good agreement with the experimental results, which proved the feasibility of this method. The permeation rate of laminates increased with the raised of porosity, and the internal porosity of the laminates could be diminished by improving the curing pressure so as to reduce the permeation of the composite components. Under the condition of a certain porosity, the laminates with small, stripe voids had a higher permeation rate than the laminates with large, circular voids.

Three-dimensional mesoscale modeling of foamed cement paste using peridynamics

Foamed concrete’s unique mesoscale porous structures influence its mechanical performance. This study adopted peridynamics method to build the three-dimensional (3-D) porous structure of a foamed cement paste specimen. The numerical model was verified through a comparison with the experimental results. Based on the model validation, a series of models were established to investigate the influence factors of porosity and void shape on the mechanical performance of foamed cement paste under uniaxial compression. The porosity was ranged from 10% to 70%, and the sphericity of a single void was ranged from 0.6 to 1.0. The results showed that the mechanical properties, including modulus, peak strength and fracture energy, decreased with the increase of porosity, while increased with the increase of void sphericity. Significant heterogeneity was noted among the models with the same porosity, as the void sphericity could cause a different wall thickness between voids. The internal stress could easily cause a damage to a local area with thin wall thickness, leading to weakening the mechanical performance of foamed cement paste.

Quantitative evaluation of the characteristics of air voids and their relationship with the permeability and salt freeze–thaw resistance of hybrid steel-polypropylene fiber–reinforced concrete composites

Hybrid fiber affects the structure of air voids of hardened concrete and further affects the performance of concrete. A laboratory test quantitatively analyzes the characteristics of air voids and their relationship with the permeability and salt freeze-thaw (F-T) resistance of hybrid steel fiber (ST)–polypropylene fiber (PP) reinforced concrete. Quantitative parameters such as the fractal dimension, number, tortuosity, and shape factor of the air voids are used to characterize their structure. In addition, the relationship between the structural characteristics of air voids and the permeability and salt F-T resistance of concrete is analyzed using the rough set theory. The hybrid ST–PP fiber can reduce the total air-void content, spacing factor, average chord length, and total chord length of the air voids. However, the number and specific surface area of the air voids increased by 113.9–380.2% and 185.3–422.7%, respectively. In addition, the tortuosity of air voids with a diameter of 180–500 μm is more complex than that of other apertures. Moreover, hybrid ST–PP fibers can change the shape of air voids in concrete and make the shape of air voids in concrete simple and round. The compressive strength and splitting tensile strength of concrete after salt F-T cycles are enhanced by the hybrid ST–PP fiber. Nevertheless, this hybrid fiber has a negative effect on the permeability of the concrete. The total air–void content, number of air voids and tortuosity are the main factors affecting the permeability and F-T resistance of concrete.

Heat treatment of 3D printed polyethylene terephthalate glycol in a supporting powder bed

Material extrusion 3D printing is a fabrication process that produces layered polymer parts with complex geometry but with inferior mechanical properties compared to parts made with other methods such as injection molding. Post fabrication heat treatment is a valid post-processing method that reduces the internal thermal stresses and improves layer adhesion in 3D printed polymers, resulting in superior mechanical properties. This study investigates the mechanical changes produced in 3D printed PETG (polyethylene terephthalate glycol-modified) parts after heat treatment. A novel technique is used, where the parts are embedded into a bed of sodium chloride powder in order to prevent deformation during postprocessing. Fully filled 3D printed PETG parts with various geometries are tightly packed in a bed of powder. The parts are subjected to heat treatment at a temperature above the material’s glass transition temperature but below its melting temperature. Destructive and non-destructive testing performed on the treated 3D printed samples shows a substantial improvement of mechanical properties. Tensile strength testing reveals an increase of tensile strength by 40% for parts printed horizontally and by over 100% for parts printed vertically. Increased stiffness is also observed in treated parts. Compressive strength testing shows a strength increase of 43% after treatment. Dimensional measurements made prior to and after treatment show significantly reduced deformation when using the supporting powder method versus unsupported treatment. Scanning electron microscopy (SEM) analysis is used to assess internal structural changes in the polymer after post-processing. This analysis reveals changes in internal void shape and distribution, increased interlayer adhesion and increased interface area of deposited filaments, providing insight into the mechanisms that lead to the improved properties observed in destructive testing. The supporting powder heat treatment allows the fabrication of parts with complex geometry through material extrusion 3D printing while mitigating the inherent disadvantage of the fabrication process of producing parts with inferior mechanical properties.

Ductile Fracture in Plane Stress

Abstract A micromechanics-based ductile fracture initiation theory is developed and applied for high-throughput assessment of ductile failure in plane stress. A key concept is that of inhomogeneous yielding such that microscopic failure occurs in bands with the driving force being a combination of band-resolved normal and shear tractions. The new criterion is similar to the phenomenological Mohr–Coulomb model, but the sensitivity of fracture initiation to the third stress invariant constitutes an emergent outcome of the formulation. Salient features of a fracture locus in plane stress are parametrically analyzed. In particular, it is shown that a finite shear ductility cannot be rationalized based on an isotropic theory that proceeds from first principles. Thus, the isotropic formulation is supplemented with an anisotropic model accounting for void rotation and shape change to complete the prediction of a fracture locus and compare with experiments. A wide body of experimental data from the literature is explored, and a simple procedure for calibrating the theory is outlined. Comparisons with experiments are discussed in some detail.

Fatigue Performance of Concrete–Polyurethane Composite Materials under Compression

Polyurethane grouting technology has been applied in the maintenance and reinforcement of transportation infrastructure such as airports, expressways, and high-speed railways. For rigid pavements with voids underneath concrete slabs, it can make a quick and efficient fix. However, polyurethane grouting materials applied underneath slabs for base enhancement are subjected to cyclic compressive loading from traffic, so their fatigue performance is critical in the concrete–polyurethane composite structure. There have not been many studies of this aspect. This paper investigated the influence of several key design factors, including grout thickness, grout density, and void shape, on the stress–strain and fatigue performance of the concrete–polyurethane composite structure. Laboratory compressive tests were conducted at various stress levels following a four-factor, three-level orthogonal experiment design. The results showed that the strain response of composite specimens under stress-controlled cyclic loading may be divided into three stages: an initial stage in which the cumulative strain changes little with the number of load repetitions, a second stage in which the cumulative strain increases steadily with the number of load repetitions, and a third stage in which the cumulative strain increases rapidly with the number of load repetitions. The third stage represents the occurrence of fatigue failure. The rank of the influences of the four factors on fatigue performance is, from high to low, grout thickness, stress ratio, void shape, and grout density.

Compression and spallation properties of polyethylene terephthalate under plate impact loading

We conduct plate impact experiments to investigate shock compression and spallation properties of polyethylene terephthalate. The Hugoniot equation of state, the apparent velocity–particle velocity relation, and the indices of refraction are obtained from Hugoniot experiments. Spall strength, as well as tensile strain rate is deduced at shock pressures up to ∼2.4 GPa in spallation shots. At low shock pressures (<0.6 GPa), the spall strength increases slightly with increasing shock pressure, as a result of increasing tensile strain rate. Release melting is observed at high impact velocities (>816 m s−1). Via X-ray computed tomography, three-dimensional void and crack structures are revealed for shock-recovered specimens. Small voids appear thin and curved for low-speed impacts but become ellipsoidal for high-speed impacts. Such different void shapes may be attributed to the diverse damage mechanisms at different impact velocities.

Effect of shear localisation on yield surface for porous metals containing ellipsoidal voids

Diffused and localised plasticity in a narrow band between the pre-existing micro-voids are the dominant modes of deformation in a ductile material. In this paper, a yield function is presented for porous metallic materials accounting for these two modes of deformation. The model has been proposed by modifying Madou and Leblond’s model taking into account the effect of shear localisation between the inter voids ligaments on evolution of yield surface. The proposed model gives a smooth yield locus and captures the competition between defused plasticity and shear localisation as a function of void shape. The results of proposed model have been extensively validated with numerically evaluated yield locus using the finite element based limit analysis for a wide range of ellipsoidal void geometries. It has been shown that the model accurately predicts the effect of shear localisation on the yield surface.

Field Observations of the Evolution of Plunging‐Wave Shapes

AbstractThere are few high‐resolution field observations of the water surface during breaking owing to the difficulty of collecting spatially dense measurements in the surf zone, and thus the factors influencing breaking‐wave shape in field conditions remain poorly understood. Here, the shape and evolution of plunging breakers is analyzed quantitatively using three‐dimensional scans of the water surface collected at high spatial and temporal resolution with a multi‐beam terrestrial lidar scanner. The observed internal void shapes in plunging breakers agree well with previously developed theoretical shapes at the onset of breaking, and become more elongated and less steep as breaking progresses. The normalized void area increases as the local bottom slope steepens and as the breaking depth decreases. The void shape becomes more circular as the local bottom slope and the ratio of breaking water depth to wavelength increase, as well as in conditions with opposing winds.

Effect of void shape and highly conducting boundary on 2D conductivity of porous materials

In this paper, the heat conductivity of two-dimensional (2D) media made of an arbitrarily thermal anisotropic material and containing pores with arbitrary shape and superconductive boundary is considered. In addition to the bulk behavior, the line conduction model is used for the boundary behavior. Such idealized mathematical model can be seen as the limit case of very thin material layer with very high conductivity. The fundamental heterogeneity problem in the micromechanics of a single void embedded in an infinite matrix with both boundary and bulk behavior is then investigated and solved with the complex variable and the Conformal Mapping (CM) techniques. The heterogeneity problem results are then used to obtain the effective heat conductivity of the porous material with different homogenization schemes.

A Finite Element Analysis and an Improved Induced Charge Concept for Partial Discharge Modeling

Although much work has been done and significant progress has been made on partial discharges (PD) measurement and detection techniques, this is not the case for PD modeling. Four types of internal PD modeling, in sequential order from first to last developed, are three-capacitance (abc), induced charge concept (ICC), finite element analysis (FEA), and Multiphysics models. The abc model is too simple to provide an understanding of the physical phenomena affecting PD. In contrast, Multiphysics models are immature. Multiphysics models require a high number of physical parameters that need to be experimentally determined, which is not a trivial task. Moreover, adjusting the physical parameters to achieve a good agreement between simulation results and measurement results for a specific geometry and dimension may not work for other geometries and dimensions. The FEA model, a relatively recent model, and the ICC model, which fall between the abc and Multiphysics models in terms of modeling complexity, can partly explain mechanisms and physical phenomena associated with internal PD. However, to the best of our knowledge, there is only one paper comparing ICC and FEA models for a case study; thus, further research is needed to elucidate various aspects of these two models. In this paper, 1) an improved ICC and a FEA capable of describing phenomena occurring during PD are developed, 2) both developed models are coded and implemented either in MATLAB or in COMSOL Multiphysics linked with MATLAB, and their simulation results are compared and analyzed, and 3) the influence of different parameters including void shape, void size, and void air pressure on PD parameters are studied.