Arbitrary Inclusion Research Articles

An isoparametric inclusion model for determining the thermo-elastic fields produced by varying Eigen-temperature gradients

The existence of inclusions or inhomogeneities may disrupt heat flow, resulting in increased stresses and temperature fluctuations at the material interface. Analyzing the thermo-elastic fields surrounding such microstructures is crucial for unveiling the intricate failure mechanisms within materials. Based on the method of Green's function and contour integral, this work presents a complete set of explicit analytical solutions for thermal and elastic fields of an arbitrary polygonal inclusion subjected to linearly varying eigen-temperature gradients or thermal eigenstrains. In contrast to the previous studies on potentials showing analogy with anti-plane elasticity, a mathematical analogy of Green's functions between steady-state heat conduction and thermal inclusion for plane elasticity is accordingly established. By employing the linear interpolation of the nodal eigen-temperature gradients or eigenstrains, the work further extends the traditional isoparametric element idea to the thermos-elastic inclusions, and proposes a novel isoparametric inclusion model to solve arbitrarily shaped inclusions with any distributed eigen-temperature gradients. Unlike the finite element method, which requires meshing for both the matrix and inclusion, the present model exhibits efficiency, flexibility, and versatility with the mesh discretization only conducted inside the inclusion domain. The inclusion based isoparametric method may have potential applications in mechanical engineering and material science for analyzing the thermo-structural behavior of various microstructures.

A finite element-convolutional neural network model (FE-CNN) for stress field analysis around arbitrary inclusions

This study presents a data-driven finite element-machine learning surrogate model for predicting the end-to-end full-field stress distribution and stress concentration around an arbitrary-shaped inclusion. This is important because the model’s capacity to handle large datasets, consider variations in size and shape, and accurately replicate stress fields makes it a valuable tool for studying how inclusion characteristics affect material performance. An automatized dataset generation method using finite element simulation is proposed, validated, and used for attaining a dataset with one thousand inclusion shapes motivated by experimental observations and their corresponding spatially-varying stress distributions. A U-Net-based convolutional neural network (CNN) is trained using the dataset, and its performance is evaluated through quantitative and qualitative comparisons. The dataset, consisting of these stress data arrays, is directly fed into the CNN model for training and evaluation. This approach bypasses the need for converting the stress data into image format, allowing for a more direct and efficient input representation for the CNN. The model was evaluated through a series of sensitivity analyses, focusing on the impact of dataset size and model resolution on accuracy and performance. The results demonstrated that increasing the dataset size significantly improved the model’s prediction accuracy, as indicated by the correlation values. Additionally, the investigation into the effect of model resolution revealed that higher resolutions led to better stress field predictions and reduced error. Overall, the surrogate model proved effective in accurately predicting the effective stress concentration in inclusions, showcasing its potential in practical applications requiring stress analysis such as structural engineering, material design, failure analysis, and multi-scale modeling.

Role of interface tension in the thermoelastic analysis of inclusions: Unified formulation and closed-form results

We study the thermoelastic problem of an inclusion of general shape surrounded by a foreign elastic matrix under plane deformation and the influence of an in-plane far-field heat flux. The small-scale interface effects, related to not only interface conductivity, interface stretching rigidity and interface thermal expansion but also (residual) interface tension, are incorporated in the corresponding analysis. We establish general boundary value formulations in both heat conduction and thermoelasticity for an arbitrary inclusion shape, allowing for analytic or at least semi-analytic treatment of the problem. Specially, we derive closed-form solutions for the case of circular inclusion and obtain concise expressions for describing the remote heat flux-induced thermal stress near the interface (at both the inclusion side and matrix side). Surprisingly, it is shown that for the case of circular inclusion, interface tension plays the same role as interface stretching rigidity in determining the full thermal stress field, or in other words, the full thermal stress field depends on only the sum of interface tension and interface stretching rigidity but not on the specific value of either of them. Numerical examples are also given to illustrate the influence of interface tension on the von Mises stress distribution in the vicinity of the interface.

A Note on Cherry-Picking in Meta-Analyses.

We study selection bias in meta-analyses by assuming the presence of researchers (meta-analysts) who intentionally or unintentionally cherry-pick a subset of studies by defining arbitrary inclusion and/or exclusion criteria that will lead to their desired results. When the number of studies is sufficiently large, we theoretically show that a meta-analysts might falsely obtain (non)significant overall treatment effects, regardless of the actual effectiveness of a treatment. We analyze all theoretical findings based on extensive simulation experiments and practical clinical examples. Numerical evaluations demonstrate that the standard method for meta-analyses has the potential to be cherry-picked.

A Novel Embedded Domain Decomposition Method for Electromagnetic Simulation of Structures in Inhomogeneous Medium

A novel embedded domain decomposition method (EDDM) is proposed to simulate electromagnetic scattering from structures in an inhomogeneous medium. In this method, the inhomogeneous medium (e.g., layered substrate) is set as the background subdomain, and the integrated structures (e.g., metallic/dielectric components) with properly defined buffer regions (BRs) are set as the embedded subdomains, where the meshes of two can be completely independent and arbitrarily overlapping. The major contribution of this work lies in the following three aspects. First, to allow for arbitrary inclusion of the embedded subdomains in an inhomogeneous background subdomain, an adaptive BR method is developed. The self-coupling equation is rederived to ensure the consistency of the BR and the inhomogeneous background, and a new mutual-coupling equation is introduced to account for the material and/or conductor differences. Second, the boundary element method (BEM) accelerated by the multilevel fast multipole algorithm (MLFMA) is utilized to truncate the finite-element region so that the computation capability can be enhanced and the extra air box setting of the background subdomain in the original EDDM can be avoided. Third, for structure adjustments such as translations and rotations, we further propose an inherited calculation to avoid mesh regeneration and repeated computation of the self-coupling and preconditioning matrices and also reduce the iteration counts and solution time. Numerical examples have shown the accuracy, robustness, and efficiency of the proposed method.

Automated computation of topological derivatives with application to nonlinear elasticity and reaction–diffusion problems

While topological derivatives have proven useful in applications of topology optimization and inverse problems, their mathematically rigorous derivation remains an ongoing research topic, in particular in the context of nonlinear partial differential equation (PDE) constraints. We present a systematic yet formal approach for the numerical computation of topological derivatives of a large class of PDE-constrained topology optimization problems with respect to arbitrary inclusion shapes. Scalar and vector-valued as well as linear and nonlinear elliptic PDE constraints are considered in two and three space dimensions including a nonlinear elasticity model and nonlinear reaction–diffusion problems. The systematic procedure follows a Lagrangian approach for computing topological derivatives. For problems where the exact formula is known, the numerically computed values show good coincidence. Moreover, by inserting the computed values into the topological asymptotic expansion, we verify that the obtained values satisfy the expected behavior also for other, previously unknown problems, indicating the correctness of the procedure.

A computationally efficient approach for generating RVEs of various inclusion/fibre shapes

A computationally efficient method for generating virtual periodic representative volume element (RVE), capable of handling arbitrary inclusion shapes, is developed. A universal collision/overlap detection and repair method is proposed, where each inclusion shape is represented as a union of n-Spheres (UnS). A constrained optimization problem is formulated and solved to remove inclusion overlaps; a closed-form solution is derived for calculating the degree of inclusions overlap and its gradient vector with respect to inclusion position. RVE generation is illustrated with circular, spherical, four non-circular and four non-spherical inclusion shapes. Computational efficiency is demonstrated using an elaborate RVE generation time study. The generated RVEs are evaluated using various statistical metrics; results confirm the random distribution of inclusions. Effective properties of RVEs, representing unidirectional composites, are determined using homogenization with various fibre cross-section shapes; obtained mechanical properties have shown transverse isotropy.

Low-strain effective Young’s modulus model and validation for multi-layer vocal fold-based silicone specimens with inclusions

A model of the effective low-strain elastic Young’s modulus of multi-layer stacked composites is proposed, which is capable to account for an arbitrary stacked inclusion. Geometrical and discretization-based model results are validated against measured effective Young’s moduli (from 10 up to 40 kPa) on 14 molded silicone specimens embedding a stiff (298 kPa) inclusion with variable size, position, and stacking. Specimens without inclusion represent the muscle, superficial, and epithelium layers in a human vocal fold with Young’s moduli between 4 and 65 kPa. The proposed model allows to predict the influence of a stiff inclusion, mimicking a structural abnormality or pathology somewhere within the vocal fold, on the low-strain effective Young’s modulus. Quantifying the influence of an inclusion or local stiffening on the vocal fold bio-mechanics is a necessary step toward the understanding and mitigation of structural vocal fold pathologies and associated voice disorders.

Dynamic Analysis of Nanosized Arbitrary Shape Inclusion under SH Waves

The scattering of shear waves (SH waves) by nano-scale arbitrary shape inclusion in infinite plane is studied by complex variable function theory. Firstly, the governing equation and the relationships between stress and displacement are given by classical elastic theory. Secondly, the arbitrary shape inclusion in the two-dimensional plane is transformed into a unit circle domain by conformal mapping, the incident wave field and the scattered wave field are presented. Next, the stress and displacement boundary conditions are established by considering surface elasticity theory, The infinite algebraic equations for solving the unknown coefficients of the scattered and standing waves are obtained. Finally, the influence of surface effect, non-dimensional wave number, Shear modulus and hole curvature on the dynamic stress concentration factor are analyzed by some examples, the numerical results show that the surface effect weakens the dynamic stress concentration. With the increase of wave number, the dynamic stress concentration factor (DSCF) decreases. Shear modulus and hole curvature have significant effects on DSCF.

On a boundary value problem of arbitrary orders differential inclusion with nonlocal, integral and infinite points boundary conditions

<abstract><p>In this work, we are concerned with a boundary value problem of fractional orders differential inclusion with nonlocal, integral and infinite points boundary conditions. We prove some existence results for that nonlocal boundary value problem. Next, the existence of maximal and minimal solutions is proved. Finally, the sufficient condition for the uniqueness and continuous dependence of solution are studied.</p></abstract>

Kapitza thermal resistance in linear and nonlinear chain models: Isotopic defect.

Kapitza resistance in the chain models with internal defects is considered. For the case of the linear chain, the exact analytic solution for the boundary resistance is derived for arbitrary linear time-independent conservative inclusion or defect. A simple case of isolated isotopic defects is explored in more detail. Contrary to the bulk conductivity in the linear chain, the Kapitza resistance is finite. However, the universal thermodynamic limit does not exist in this case. In other terms, the exact value of the resistance is not uniquely defined, and depends on the way of approaching the infinite lengths of the chain fragments. By this reason, and also due to the explicit dependence on the parameters of the thermostats, the resistance cannot be considered as a local property of the defect. Asymptotic scaling behavior of the heat flux in the case of very heavy defect is explored and compared to the nonlinear counterparts; similarities in the scaling behavior are revealed. For the lightweight isotopic defect in the linear chain, one encounters a typical dip of the temperature profile, related to weak excitation of the localized mode in the attenuation zone. If the nonlinear interactions are included, this dip can still appear at a relatively short timescale, with subsequent elimination due to the nonlinear interactions. This observation implies that even in the nonlinear chains, the linear dynamics can predict the main features of the short-time evolution of the thermal profile if the temperature is low enough.

Analytical solution for residual stress and strain preserved in anisotropic inclusion entrapped in an isotropic host

Abstract. Raman elastic thermobarometry has recently been applied in many petrological studies to recover the pressure and temperature (P–T) conditions of mineral inclusion entrapment. Existing modelling methods in petrology either adopt an assumption of a spherical, isotropic inclusion embedded in an isotropic, infinite host or use numerical techniques such as the finite-element method to simulate the residual stress and strain state preserved in the non-spherical anisotropic inclusions. Here, we use the Eshelby solution to develop an analytical framework for calculating the residual stress and strain state of an elastically anisotropic, ellipsoidal inclusion in an infinite, isotropic host. The analytical solution is applicable to any class of inclusion symmetry and an arbitrary inclusion aspect ratio. Explicit expressions are derived for some symmetry classes, including tetragonal, hexagonal, and trigonal. The effect of changing the aspect ratio on residual stress is investigated, including quartz, zircon, rutile, apatite, and diamond inclusions in garnet host. Quartz is demonstrated to be the least affected, while rutile is the most affected. For prolate quartz inclusion (c axis longer than a axis), the effect of varying the aspect ratio on Raman shift is demonstrated to be insignificant. When c/a=5, only ca. 0.3 cm−1 wavenumber variation is induced as compared to the spherical inclusion shape. For oblate quartz inclusions, the effect is more significant, when c/a=0.5, ca. 0.8 cm−1 wavenumber variation for the 464 cm−1 band is induced compared to the reference spherical inclusion case. We also show that it is possible to fit an effective ellipsoid to obtain a proxy for the averaged residual stress or strain within a faceted inclusion. The difference between the volumetrically averaged stress of a faceted inclusion and the analytically calculated stress from the best-fitted effective ellipsoid is calculated to obtain the root-mean-square deviation (RMSD) for quartz, zircon, rutile, apatite, and diamond inclusions in garnet host. Based on the results of 500 randomly generated (a wide range of aspect ratio and random crystallographic orientation) faceted inclusions, we show that the volumetrically averaged stress serves as an excellent stress measure and the associated RMSD is less than 2 %, except for diamond, which has a systematically higher RMSD (ca. 8 %). This expands the applicability of the analytical solution for any arbitrary inclusion shape in practical Raman measurements.

Effective electrical resistivity in a square array of oriented square inclusions

The continuing miniaturization of optoelectronic devices, alongside the rise of electromagnetic metamaterials, poses an ongoing challenge to nanofabrication. With the increasing impracticality of quality control at a single-feature (-device) resolution, there is an increasing demand for array-based metrologies, where compliance to specifications can be monitored via signals arising from a multitude of features (devices). To this end, a square grid with quadratic sub-features is amongst the more common designs in nanotechnology (e.g. nanofishnets, nanoholes, nanopyramids, μLED arrays etc). The electrical resistivity of such a quadratic grid may be essential to its functionality; it can also be used to characterize the critical dimensions of the periodic features. While the problem of the effective electrical resistivity ρ eff of a thin sheet with resistivity ρ 1, hosting a doubly-periodic array of oriented square inclusions with resistivity ρ 2, has been treated before (Obnosov 1999 SIAM J. Appl. Math. 59 1267–87), a closed-form solution has been found for only one case, where the inclusion occupies c = 1/4 of the unit cell. Here we combine first-principle approximations, numerical modeling, and mathematical analysis to generalize ρ eff for an arbitrary inclusion size (0 < c < 1). We find that in the range 0.01 ≤ c ≤ 0.99, ρ eff may be approximated (to within <0.3% error with respect to finite element simulations) by: whereby at the limiting cases of c → 0 and c → 1, α approaches asymptotic values of α = 2.039 and α = 1/c − 1, respectively. The applicability of the approximation to considerably more complex structures, such as recursively-nested inclusions and/or nonplanar topologies, is demonstrated and discussed. While certainly not limited to, the theory is examined from within the scope of micro four-point probe (M4PP) metrology, which currently lacks data reduction schemes for periodic materials whose cell is smaller than the typical μm-scale M4PP footprint.

Las especies del género Liolaemus (Liolaemidae). Lista de taxones y comentarios sobre los cambios taxonómicos más recientes

Taxonomic lists are important tools for understanding biodiversity and they provide informationat different scales about the species distributed within a region; as such, they allow us tounderstand the identities of the species that compose a given supra-specific taxon. While listsof the species of the genus Liolaemus have been published over the past few decades, providingtaxonomic and systematic information, these lists are now outdated and the number of validspecies within the genus has fluctuated rapidly over time and many taxonomic changes havegone unregistered. Although there are alternative means to consult this information, thesesources have suffered from a number of involuntary errors as well as some arbitrary omissionsor inclusions that have affected the dynamics of species inventories. In this work, we presentthe most complete taxonomic enumeration of the species of Liolaemus to date, including theavailable names for all of the valid and invalid species associated with these taxonomic changes.We recognize a total of 283 valid species in Liolaemus, along with another 65 invalid names.Fifteen taxa are recognized as species inquirenda, eight as nomina dubia, and two as nomina nuda.We hope that the careful review of each case and the exhaustive literature review will make thiswork a primary reference on South America's most speciose lizard genus.

Off-label use of intravenous thrombolysis for acute ischemic stroke: a critical appraisal of randomized and real-world evidence.

Intravenous thrombolysis (IVT) represents the only systemic reperfusion therapy able to reverse neurological deficit in patients with acute ischemic stroke (AIS). Despite its effectiveness in patients with or without large vessel occlusion, it can be offered only to a minority of them, because of the short therapeutic window and additional contraindications derived from stringent but arbitrary inclusion and exclusion criteria used in landmark randomized controlled clinical trials. Many absolute or relative contraindications lead to disparities between the official drug label and guidelines or expert recommendations. Based on recent advances in neuroimaging and evidence from cohort studies, off-label use of IVT is increasingly incorporated into the daily practice of many stroke centers. They relate to extension of therapeutic time windows, and expansion of indications in co-existing conditions originally listed in exclusion criteria, such as use of alternative thrombolytic agents, pre-treatment with antiplatelets, anticoagulants or low molecular weight heparins. In this narrative review, we summarize recent randomized and real-world data on the safety and efficacy of off-label use of IVT for AIS. We also make some practical recommendations to stroke physicians regarding the off-label use of thrombolytic agents in complex and uncommon presentations of AIS or other conditions mimicking acute cerebral ischemia. Finally, we provide guidance on the risks and benefits of IVT in numerous AIS subgroups, where equipoise exists and guidelines and treatment practices vary.

Stiffness of composites with coated inclusions

Stiffness of composites with coated inclusions can be determined by a variety of micromechanical methods. The present method approaches the problem by modeling the stiffness of a multi-phase composite with coated inclusions as a combination of stiffness tensors obtained for two-phase models. The potential advantage of the present method is its applicability to arbitrary inclusion geometries and multiple coatings. The numerical analysis conducted on the examples of coated fibers demonstrated a good agreement with available solutions for a low to moderate fiber volume fraction and a thin relatively compliant coating and for a low fiber volume fraction and a relatively thick coating.

A stochastic multiscale formulation for isogeometric composite Kirchhoff–Love shells

This work extends isogeometric thin shell formulations to incorporate constitutive laws generated by stochastic multiscale analyses. The integration of the constitutive law is performed through the thickness of the shell, in order to account for material heterogeneity. At each thickness integration point, a corresponding representative volume element is assigned, defining the microstructural topology of a composite material comprised of a matrix with arbitrary volumetric inclusions. With the aid of stochastic processes, the impact of material and inclusion variability on the structural response is demonstrated in benchmark and real-scale numerical examples. Spatial material variability is considered in both surface and through thickness coordinates of the shell. As a result, the elimination of geometric error, together with the realistic material descriptions, renders this formulation an ideal candidate for the simulation of shell structures made of composite materials.

An efficient method for the elastic field in a transversely isotropic full space due to arbitrary inclusions

The present study is on the analytical solution for the elastic field due to a cuboidal inclusion of uniform eigenstrain within a transversely isotropic full-space material, and a numerical method to model inclusions of any arbitrary shapes and with any eigenstrain distributions as the integration of a set of such cuboidal inclusions. The fast Fourier transform (FFT) is applied for efficient computation. The developed method and results are implemented to analyze the elastic field in a transversely isotropic full-space material containing inclusions of different shapes, different eigenstrain distributions, and multiple cuboids of different densities. Furthermore, the effect of material anisotropy on the stress field subjected to a spherical inclusion with pure dilatant eigenstrains is explored by comparing the behavior of a transversely isotropic material with that of a corresponding isotropic one. The numerical results show that the induced stresses are drastically influenced by the Young’s moduli of transversely isotropic materials, and that material constant C33 has a large influence on normal stress σ33.

Numerical solution to the interface problem in a general domain using Moser’s deformation method

When seeking a solution to the interface problem, the potential theory to represent solution has been widely used. As the solution representation of the interface problem is only well-known for domains with simple inclusion, such as a disk, conformal mapping is often used to transform the arbitrary inclusion to a manageable inclusion to utilize the known solution representation. This paper proposes the construction of a conformal mapping based on Moser’s grid deformation method that generates a transformation with positive Jacobian determinant. By establishing an optimal control problem that minimizes the dissimilarity between transformed and reference images with desired constraints, we constructed an appropriate conformal mapping. Several numerical results prove the validity of our approach.

Existence Results for Fractional Order Single-Valued and Multi-Valued Problems with Integro-Multistrip-Multipoint Boundary Conditions

We study the existence of solutions for a new class of boundary value problems of arbitrary order fractional differential equations and inclusions, supplemented with integro-multistrip-multipoint boundary conditions. Suitable fixed point theorems are applied to prove some new existence results. The inclusion problem is discussed for convex valued as well as non-convex valued multi-valued map. Examples are also constructed to illustrate the main results. The results presented in this paper are not only new in the given configuration but also provide some interesting special cases.