Shape Of Inclusions Research Articles

Discretization Approach for the Homogenization of Three-Dimensional Solid-Solid Phononic Crystals in the Quasi-Static Limit: Density and Elastic Moduli

With the application of a homogenization theory, based on the Fourier formalism (which provides efficient and exact formulas by which to determine all the components of the effective stiffness and mass density tensors, valid in the regime of large wavelengths), a new approach to calculate the effective quasi-static response in three-dimensional solid-solid phononic crystals is reported. The formulas derived in this work for calculating the effective elastic parameters show a dependence, in terms of summations over the vectors, of the reciprocal lattice by the discretization of the volume of the inclusion in small parts (e.g., small cubes), to obtain a system of equations from which we define the effective response. In particular, we present the numerical results calculated for several cubic lattices with solid constituents and different shapes of inclusions in the unit cell versus the filling fraction, as well as for fixed values of it. By this means, we analyzed the effect of the type of Bravais lattice of the materials, and the geometry of the inclusions that constitute the three-dimensional phononic array, on the resulting effective anisotropy. Finally, our theory confirms other well-known results with previous homogenization theories as a particular case study. In this regard, the examples and results shown here can be useful for the design of metamaterials with predetermined elastic properties.

Variable Stiffness Object Recognition with a CNN-Bayes Classifier on a Soft Gripper.

Soft grippers significantly widen the palpation capabilities of robots, ranging from soft to hard materials without the assistance of cameras. From a medical perspective, the detection of size and shape of hard inclusions concealed within soft three-dimensional (3D) objects is meaningful for the early detection of cancer through palpation. This article proposes a framework for variable-stiffness object recognition using tactile information collected by force sensitive resistors on a three-finger soft gripper. A 15 × 50 spatiotemporal tactile image is generated for each 3D palpation process and then fed into a convolutional neural network (CNN) for object identification. The training set consists of tactile images generated from different grasping orientations. We developed our own CNN architecture, named SoftTactNet, and compared its performance with several state-of-the-art CNNs on the image dataset produced by our experiments. The results show that our proposed method excels in distinguishing 3D shapes and sizes of objects enclosed by a thick soft foam. The average recognition rate is significantly improved using a Naive Bayes classifier, reaching a 97% recognition accuracy. The detection of shapes and sizes of hard objects underneath soft tissues is extremely important for breast and testicular cancer early detection, a field where Soft Robots can shine with inexpensive and ubiquitous devices.

Localized Sensitivity Analysis at High-Curvature Boundary Points of Reconstructing Inclusions in Transmission Problems

In this paper, we are concerned with the recovery of the geometric shapes of inhomogeneous inclusions from the associated far field data in electrostatics and acoustic scattering. We present a local resolution analysis and show that the local shape around a boundary point with a mean curvature of high magnitude can be reconstructed more easily and stably. In proving this, we develop a novel mathematical scheme by analyzing the generalized polarization tensors (GPTs) and the scattering coefficients (SCs) coming from the associated scattered fields, which in turn boils down to the analysis of the layer potential operators that sit inside the GPTs and SCs via microlocal analysis. In a delicate and subtle manner, we decompose the reconstruction process into several steps, where all but one step depends on the global geometry, and one particular step depends on the mean curvature at the given boundary point. Then by a sensitivity analysis with respect to local perturbations of the curvature of the boundary surface, we establish the local resolution effects. Our study opens up a new field of mathematical analysis on wave superresolution imaging.

Stress-dependent nonlinear magnetoelectric effect in press-fit composites: A numerical and experimental study

Magnetoelectric (ME) composites have posed an immense research interest over the past few decades. Their multifunctional capabilities enable a wide array of applications like field and pressure sensors, energy harvesters, gyrators, etc. The voltage developed under applied magnetic fields in these composites is governed strongly by the stress and magnetization state of the magnetostrictive phase, which needs to be characterized effectively. Towards this end, magnetostriction measurements are carried out under applied stresses in Nickel to understand its magnetomechanical response. A three-dimensional magnetostrictive constitutive model is used to predict the magnetostrictive behavior, which is later implemented in COMSOL Multiphysics® using the external material module. The FE solutions obtained are validated against analytical solutions. The model is subsequently used to obtain FE solutions for the magnetoelectric response of press-fit composites subjected to general magneto-thermo-mechanical loading. Experiments are performed on the press-fit composite to validate the voltage response predicted by the developed model, which shows a good agreement. The developed FE model is used to conduct a parametric study to quantify the effect of external loading conditions, the shape of inclusion, and the field orientation with an effort to optimize the ME response in press-fit ME composites.

Interface stability problem towards the end of THM growth of cadmium zinc telluride crystals

Growth of CdZnTe crystals by Travelling Heater Method (THM) is widely investigated by different groups. Interface shape and stability are critical parameters for the successful growth of high-quality CZT crystals. Even though interface stability could be achieved for a significant portion of the CZT ingot, the situation towards the end of the growth is not well studied and understood. In this study, interface stability and the change of crystal quality towards the end of the growth are examined. The change of the interface shape and formation of large Te inclusions are observed. Moreover, towards the end of the growth, phase separation and formation of a new zinc-based phase are detected with a needle-like structure. The decrease of crystal quality and evolution of the CZT ingot towards the end of the growth are summarized.

Microstructure-Based Fatigue Modeling with Residual Stresses: Effect of Inclusion Shape on Very High Cycle Fatigue Life

When considering the effect of inclusions on fatigue life, the size effect of inclusions is well recognized. However, many of these studies overlooked or decoupled the size effect from the shape features. Therefore, in this study, the influence of the shape characteristics of inclusions with 3 equivalent sizes of 26.6 μm, 13.3 μm, and 4.2 μm on the very high cycle fatigue life of high-strength steels is investigated based on a microstructure-sensitive modeling approach, considering residual stresses. A shape parameter, unifying the aspect ratio and tilting angle of inclusion, is introduced. Based on this parameter, a new formulation of fatigue life with respect to inclusions is also proposed, extending the former one to consider the shape effect of inclusions. It is concluded that the general trend that the fatigue life increases with the decrease in inclusion size is still valid, while the shape features in terms of aspect ratio and tilting angle complicate the quantitative influence of inclusions size significantly. Even for a constant inclusion size, the combination of shape factor and tilting angle could change the fatigue life with one order of magnitude compared with the commonly assumed round shape. These findings would enhance the precision for the fatigue life estimation based on pre-inclusion analysis and also eventually provide new dimensions for inclusion engineering to improve fatigue resistance, as size will not be the only design parameter for fatigue life.

Modeling of the effective and macroscopic ageing behavior of viscoelastic composite materials

In this work, a mathematical modeling is developed to estimate the ageing macroscopic response and effective behavior of viscoelastic composites. The modeling is developed directly in time domain by considering the Volterra tensorial integral product describing the local behavior and governing equations. The ageing dynamic Green’s tensor is introduced in order to solve the partial differential equations for the time dependent displacement and make the transition between local and macroscopic fields. The localization tensor making the scale transition is obtained through using the heterogeneity problem and the Mori-Tanaka mean field approach. Once this step is completed, averaging techniques are used to derive the effective ageing behavior of viscoelastic composites. To compute the macroscopic response and the effective behavior a numerical scheme is used. Numerical results are presented with respect to the shape and volume fraction of inclusions and for different ageing viscoelastic composites.

Tracing Transformation in Turbulent Times

We live in a South Africa defined by deep inequalities. The post-apartheid promise of free and quality education is met by the realities of lasting disparities related to race, gender, socioeconomic class and disability, among other factors. The University of Cape Town (UCT) has initiated two interdependent processes to chart and track transformation, inclusion and diversity during these turbulent times. First, the university has set up an Inclusivity Survey, using a validated scale to understand staff experiences in relation to inclusion. Secondly, the university has identified and piloted a set of Transformation Benchmarks inspired by a higher education barometer for transformation in South Africa and global diversity and inclusion standards, which encourages transformation agents to take concrete actions to further transformation. Both these processes, first implemented in 2019, experimented with new ways of tracing the shape of transformation, inclusion and diversity at UCT. The paper will explore the opportunities and limitations these structured approaches to transformation offer to higher education institutions. For example, while structured approaches are useful, some argue that these reduce the complexity of social struggles (like those against racism) to simple box-ticking exercises. In unpacking these issues, the paper seeks to ask: how can we better monitor, evaluate and track progress in an increasingly turbulent world?

Influence of modification with highly dispersed silicon carbide on the casting properties of the secondary alloy of the Al-Si system

One of the main areas of application of aluminum is the aerospace and transport industries, which are constantly increasing the requirements for the properties of cast products. The use of aluminum as the main material for the manufacture of various parts of vehicles can significantly reduce their weight, which leads to a decrease in fuel consumption. In order to meet the requirements of the modern world, the work considers studies to improve the quality and increase the properties of products from the secondary aluminum alloy AlSi12. Modern technologies for processing liquid aluminum alloy are analyzed. According to the results of an analytical review, it was found that modifiers that affect the size of the primary grain and the shape of inclusions of eutectic silicon are of the greatest interest. It was found that the modification processes do not change the chemical composition of the alloy, but rather contribute to a change in the size and shape of the structural components of the alloy. The paper considers the influence of an ultradispersed SiC modifier with a particle size of up to 200 nm on the casting properties of secondary aluminum alloys: fluidity, linear and volumetric shrinkage. The fluidity was studied in green sand and metal mould. It was found that the addition of 0.1 % SiC improves the fluidity of the secondary alloy from 560 to 630 mm for green sand mould and from 230 to 295 mm for a metal mould due to cleaning from non-metallic inclusions. A further increase in the SiC content to 0.2 % does not lead to an obvious increase in fluidity. The study of linear shrinkage found that increasing the content of the modifier to 0.2 % contributes to its decrease. At the same time, an increase in the pouring temperature of the alloy promotes an increase in the total linear shrinkage, which is associated with the long residence time of the metal in the liquid state. As a result of the rapid crystallization of the melt with additional nucleation centers in the role of which are particles of the ultradispersed modifier, the coefficient of volumetric shrinkage decreases from 28 to 20 %. The proposed technical solutions for the modification of alloys of the secondary alloy AlSi12 can be used in processes that will improve the quality of cast metal products with the economical use of energy resources and materials for its production.

FORECASTING THE ENERGY CAPACITY OF CUTTING SOILS CONTAINING STONE INCLUSIONS IN A PROBABLE ASPECT

It has been established that the geometric shapes, sizes of stony inclusions, and their location in the soil massif are stochastic in nature. In the article, on the basis of the known laws of distribution of mineral soil particles is analytically determined, the probabilistic rounded amount of pebble and boulder inclusions of soil. An analytical expression is given to determine the probabilistic energy intensity of cutting soil containing various stony inclusions. Taking into account the probabilistic amount of a stony inclusion is calculated of the i-th size, j-th shape, which progressively moves in different ways when cutting the soil, the energy intensity of cutting the soil with various stony inclusions. A computational analysis of the change in the energy consumption of soil cutting is carried out depending on the size, shape of a rocky inclusion, the type of destruction, strength and rockiness of the soil, by the working body of an earth-moving machine.

Deep learning techniques elucidate and modify the shape factor to extend the effective medium theory beyond its original formulation

The effective medium theories (EMTs) can reliably approximate the property of a composite using properties of the inclusion and matrix phase. However, their inherent assumptions and the availability of mathematical forms for describing the inclusion structure limit their accuracy and applicability. In this work, we utilize the capabilities of a deep learning method to ameliorate the latter restriction for a particular EMT formulation. Our deep learning models elucidate the inclusion structure using several physics-based descriptors and can be easily adapted for other inclusion shapes through transfer learning. Using our models, we shed light on the interpretation of the shape factor in the chosen EMT. More importantly, we extend, not replace, the EMT for cases beyond its original formulation. Our proposed transfer learning approach requires relatively low computation cost and a small sample number, making it especially useful when new data is limited.

Blast resistant enhancement of meta-panels using multiple types of resonators

A new design is proposed for the meta-panel that consists of three components including two thin face-sheets bonded to meta-truss cores to enhance its blast resistance and energy absorption capacity. The meta-truss core comprising solid inclusions with coated soft layers exhibits exceptional wave-filtering properties by activating the local vibration of the inclusions, leading to the negative effective mass and stiffness of the meta-truss core in the corresponding frequency bandgaps, hence reducing the wave propagations. When frequencies of the applied loading fall within the bandgaps, the loading effects are not able to be transferred or significantly mitigated by the meta-truss core. In this study, the result from a previous theoretical derivation of wave propagation in an idealized meta-truss bar is used to validate the numerical model. Then, analyses of the meta-truss core configurations, e.g. the inclusion arrangement and inclusion shape on its bandgap regions and the transient responses of the meta-panel are carried out with the verified numerical model. It is revealed that a complete wave attenuation design can be achieved by utilizing properly tailored arrangements of inclusions, leading to a significantly improved protective effectiveness of the panel against blast loading. The results present a base for the optimal design of the meta-panel for structural protections against blast loading.

Assessing Crack‐Induced Compliance in Low Porosity Rocks Damaged by Thermo‐Hydro‐Chemo‐Mechanical Processes

AbstractFracture geometry, density, and distribution control fluid and thermal transport in low porosity rocks, as well as their seismic attributes. The creation of cracks throughout the matrix can result in large and disparate reductions in P and S wave velocities with negligible porosity development, which breaks the classic velocity‐porosity relationship. Properly interpreting these signatures in seismic surveys from stimulated geothermal, oil, and gas reservoirs or seismogenic areas requires a rock physics model that uses realistic elastic properties of fractures. Conventional models for cracked rocks employ specific inclusion shapes such as spheroids with small aspect ratios. However, all these exhibit the same normal‐to‐shear compliance ratio—regardless of aspect ratio—and therefore impact the bulk and shear moduli in the same qualitative way. As such they are inadequate for describing many of the complementary evolutions of P and S wave velocities that transpire with the generation of cracks. Using a differential model of dimensionless compliances, we analyze published velocities for granite, basalt, and limestone to quantify typical compliance ratios and find that they are often different from those assumed in conventional crack models, which then affects crack density estimates. We also investigate how the total normal and shear compliances change due to certain thermo‐hydro‐chemo‐mechanical processes that generate large crack densities, and conclude that the final ratios often still deviate from that of conventional models. Finally, we demonstrate how the model can be used to describe scatter in both P and S wave velocity‐porosity trends. Implications for energy extraction and seismic monitoring are discussed.

Mathematical Modeling of Electrical Conductivity of Anisotropic Nanocomposite with Periodic Structure

Composite materials consisting of a dielectric matrix with conductive inclusions are promising in the field of micro- and optoelectronics. The properties of a nanocomposite material are strongly influenced by the characteristics of the substances included in its composition, as well as the shape and size of inclusions and the orientation of particles in the matrix. The use of nanocomposite material has significantly expanded and covers various systems. The anisotropic form of inclusions is the main reason for the appearance of optical anisotropy. In this article, models and methods describing the electrical conductivity of a layered nanocomposite of a self-similar structure are proposed. The method of modeling the electrical conductivity of individual blocks, layers, and composite as a whole is carried out similarly to the method of determining the dielectric constant. The advantage of the method proposed in this paper is the removal of restrictions imposed on the theory of generalized conductivity associated with the need to set the dielectric constant.

Identifying inclusions in a non-uniform thermally conductive plate under external flows and internal heat sources using topological optimization

We propose applying topological optimization methods based on measuring temperature and heat fluxes to estimate the thermal conductivity of inhomogeneous thermally conductive plates and determine the shape and location of foreign inclusions. Examples of plates subjected to external heat fluxes and heat sources are considered. The solutions are obtained with the help of the finite element method combined with the method of moving asymptotes. The results show that identification accuracy depends on the defined boundary conditions, the source intensity value, heat fluxes, temperature distribution and the shape of the inclusions. For the problem of 18 circular inclusions under different heat fluxes, identification accuracy increases with increasing source intensity values.

Numerical simulation of the size, quantity and shape of non-metallic inclusions in rails

There are several ways to improve the quality of rail steels. Among them: alloying, changing the conditions of rolling, surface hardening, and reducing the number of non-metallic inclusions. The high content of non-metallic inclusions in the material is one of the most common causes of rail failure during operation. This problem is especially relevant for regions with low temperatures, for example, Siberia, the Far East, regions of the North. Since the durability of rail steel directly depends on the size, quantity, and shape of non-metallic inclusions, they must be strictly controlled. Requirements for the content of non-metallic inclusions in the material are given in Russian and foreign standards, some of which are outdated today and require clarification. This can be done through experimental research. However, they will require a significant investment of time and money. Meanwhile, the influence of inclusions on the durability of the material can be determined using digital modeling, which is widely used to optimize technological processes in various fields of mechanical engineering. Thanks to digitalization, it is now possible to predict the behavior of a material under certain conditions without costly experiments. This not only saves resources but also makes the analysis process more accessible and intuitive.

On a possibility of replacing grey cast iron for manufacturing cast elements of electrolyzer gas collecting bell

The main process leading to the destruction of the cast elements of gas-collection bell of electrolyzer, made of grey cast iron, is the oxidation of iron by oxygen, SO2 gas and sulfur vapors to form magnetite, hematite and pyrrhotin. The simultaneous formation of iron oxides and sulfides does not prevent further corrosion, since scale is formed with a loose structure that does not have protective properties. Reducing the length of the interfacial boundaries inside the material of the cast enables to reduce the rate of corrosion destruction, which can be achieved by modifying the cast iron to change the shape of graphite inclusions, i.e. obtaining high-strength cast iron with a spherical shape of graphite inclusions. However, the obtaining spherical graphite in cast iron using magnesium modification does not exclude the access of aggressive gases to the surface of the products and the possibility of their diffusion along the grain boundaries. It was shown that alloying can be an alternative, which leads not only to the exclusion of lamellar secretions of graphite in the structure of cast iron, but also to the formation of surface oxide layers based on the alloying element preventing the corrosion. Alloying with chromium gives cast iron high abrasive resistance due to the presence of a carbide component in the structure, as well as corrosion resistance due to the alloying of the metal base, heat resistance due to increasing the electrochemical potential of the metal base and creating a strong neutral oxide film on the surface of the castings, heat resistance, etc. An experimental comparative analysis of the corrosion resistance of cast iron used for manufacturing of gas collecting bell of electrolyzers showed that chromic cast iron ЧХ3 has a higher corrosion resistance than high-strength cast iron with spherical graphite ВЧ50 and much higher than grey cast iron with lamellar graphite. However, chromic cast iron ЧХ3 has low casting properties, is very sensitive to the cooling rate and has a large heterogeneity in structure, which makes it difficult to use it for the manufacture of gas collecting bell of electrolyzers.

Effect of test velocity on the tensile strength of high strength steels using the small punch test in a hydrogen environment

This study aims at evaluating the effect of test velocity associated with the Small Punch Test on the ultimate tensile strength. The velocity factor was investigated on two levels (1.0 μm/s and 0.1 μm/s) based on a single factor design. This design was applied to three high strength steels (AISI 4130 M, 4137 M and 4140) widely used in the oil and gas offshore industry. The tests were performed in a cathodic protection environment, which consisted of a 3.5 wt% NaCl aqueous solution to simulate hydrogen embrittlement. For each material, one specimen in air at the conventional rate (0.02 mm/s) was also tested. An increasing trend was noted toward the susceptibility to hydrogen embrittlement when the test velocity was reduced from 1.0 μm/s to 0.1 μm/s. However, the Analysis of Variance showed that the test velocity factor caused statistically significant effects on the ultimate tensile strength only for 4137 M steel. The distinct behavior shown by the 4137 M, 4130 M and 4140 steels, under the experimental conditions investigated, was attributed to the combination of several factors: test velocity in the investigated H-charged environment; shape and volume fraction of non-metallic inclusion; calcium addition; tensile strength and hardness in air at the as-received condition.

Shape of a single inclusion enclosing uniform stress for a non-uniform far-field loading in anti-plane shear

The problem as to whether an inclusion when embedded in an elastic infinite matrix with a perfectly bonded interface could achieve uniform internal stress has been studied extensively in the literature. It has been shown that in almost all cases ellipsoidal shape (including elliptical shape for two-dimensional deformation) is the only inclusion shape ensuring the uniformity of the stress inside the inclusion if the external loading exerted remotely on the edge of the matrix is uniform. From a practical point of view, this result remains valid for a non-uniform remote loading imposed on the matrix provided the product of the inclusion's size and the gradient of the non-uniform loading is small enough (as compared with the overall level of the stress field induced by the non-uniform loading at the inclusion's position). In this paper, we explore the possibility of designing an inclusion enclosing uniform internal stress in an elastic infinite plane under anti-plane shear deformation for a non-uniform remote loading with arbitrary gradients. We derive the equations with respect to the parameters describing the configuration of the inclusion leading to a uniform internal stress inside the inclusion for a general polynomial remote loading, and establish the analytic and numerical solutions for the shape of the inclusion which are illustrated via several examples.

Relating matrix stress to local stress on a hard microstructural inclusion for understanding cleavage fracture in high strength steel

Macroscale cleavage fracture toughness of high strength steels is strongly related to the fracture of hard microstructural inclusions. Therefore, an accurate determination of the local stress on these inclusions based on the matrix stress is necessary for the statistical modelling of macroscale cleavage fracture. This paper presents analytical equations to quantitatively estimate the stress of the microstructural inclusions from the far-field stress of the matrix. The analytical equations account for the inclusion shape, the inclusion orientation, the far-field stress state and matrix material properties. Finite element modelling of a representative volume element containing a hard inclusion shows that the equations provide an accurate representation of the local stress state. The equations are implemented into a multi-barrier model and compared with CTOD experiments with two different levels of constraint.