Size-dependent Model Research Articles

Size-Dependent Model to Determine the Effects of Operational Parameters on the Performance of the Falcon Concentrator

Size-Dependent Model to Determine the Effects of Operational Parameters on the Performance of the Falcon Concentrator

A size-dependent quasi-3D model for bending and buckling of porous functionally graded curved nanobeam

In this work, we provide an analysis of the bending and buckling properties of functionally graded (FG) nanobeams with trigonometric function-dependent porosity distribution. Herein, a high-order curved nanobeam model considering both shear deformations and thickness stretching effect is established. Two-phase local/nonlocal stress-driven gradient theory is utilized to capture small-scale effects. Hamilton's principle is adopted to obtain the governing equation and boundary conditions, and the analytical solutions, such as exact formulas for lateral displacement and critical buckling load are obtained by employing Navier's method for simply supported boundary conditions. Furthermore, the effects of local volume fraction, nonlocal parameter, material length scale parameter, shear deformation, material distribution, and porosity distribution pattern in stress-driven models are analyzed in detail. The parametric studies indicate that the thickness stretching effect has a different influence on bending and buckling. In addition, the thickness stretching effect and the opening angle show different coupling mechanisms during bending and buckling. On the other hand, the higher-order buckling mode leads to a more significant scale effect and thickness tensile effect, but reduces the influence of the opening angle. Finally, we find that due to the coupling effect between the pore distribution pattern and the orientation bias of the FG nanobeam, the variation of the material gradient index leads to a different order of the dimensionless critical buckling loads predicted by the three pore distributions.

Parametric CAD-integrated simulation of masonry structures based on the isogeometric analysis

This publication presents a novel numerical avenue for the assessment of masonry structures. To circumvent the labor-intensive finite element method modeling and pre-processing step, the isogeometric analysis is enhanced within this contribution to cope with the necessities for masonry structures. This incorporates the study of apparent kinematic shell formulations, including their respective properties. Additionally, the connection towards non-linear material laws is outlined, and an empirically evaluated approach for the element size regularization is proposed. This generic approach would be inherently valid for other size dependent constitutive material models, as e.g. concrete models.The current paper is explored in the context of a number of experimental problems. These validation examples are used to provide structural assessments that extend beyond the scope of the experiment. Finally, a potential example that provides an outlook towards anticipated applications is presented.

A generalizable new figure of merit for dose optimization in dual energy cone beam CT scanning protocols

Objective. This study proposes and evaluates a new figure of merit (FOMn) for dose optimization of Dual-energy cone-beam CT (DE-CBCT) scanning protocols based on size-dependent modeling of radiation dose and multi-scale image quality. Approach. FOMn was defined using Z-score normalization and was proportional to the dose efficiency providing better multi-scale image quality, including comprehensive contrast-to-noise ratio (CCNR) and electron density (CED) for CatPhan604 inserts of various materials. Acrylic annuluses were combined with CatPhan604 to create four phantom sizes (diameters of the long axis are 200 mm, 270 mm, 350 mm, and 380 mm, respectively). DE-CBCT was decomposed using image-domain iterative methods based on Varian kV-CBCT images acquired using 25 protocols (100 kVp and 140 kVp combined with 5 tube currents). Main results. The accuracy of CED was approximately 1% for all protocols, but degraded monotonically with the increased phantom sizes. Combinations of lower voltage + higher current and higher voltage + lower current were optimal protocols balancing CCNR and dose. The most dose-efficient protocols for CED and CCNR were inconsistent, underlining the necessity of including multi-scale image quality in the evaluation and optimization of DE-CBCT. Pediatric and adult anthropomorphic phantom tests confirmed dose-efficiency of FOMn-recommended protocols. Significance. FOMn is a comprehensive metric that collectively evaluates radiation dose and multi-scale image quality for DE-CBCT. The models and data can also serve as lookup tables, suggesting personalized dose-efficient protocols for specific clinical imaging purposes.

A Size-Dependent Viscoelastic Model for Microbars with Variable Cross-Section

This paper presents a model for microbars with variable cross-sections using the Kelvin–Voigt model for viscoelastic material, accounting for size-dependent effects based on strain gradient theory. The size-dependent dynamic equations for the rod, which consider the variable cross-sectional area, are obtained through the extended Hamilton’s principle. These equations are then reduced in order using the Galerkin method and solved in the steady state using the harmonic response form and the algebra of complex numbers. To solve the equations from the transient state to the steady state, a combined method is implemented using the Grünwald–Letnikov derivative technique and the Newmark method. Furthermore, a model and analysis based on the finite element method are presented to validate the results. In the results section, various factors such as size-dependent effects, the order of the fractional derivative, the amount of the viscoelastic coefficient, and the shape of the section area are examined through the time history graph, frequency response, and maximum displacement in terms of force. The results demonstrate that the transient response converges to the stable response after a certain period of time. Moreover, it is observed that decreasing the order of the fractional derivative in the pre-resonance range leads to a decrease in response sensitivity, while in the resonance frequency range, the sensitivity increases with the increase in order.

Selective Oxidation of Glucose using Hydrogen Peroxide as an Oxidant: On the Structure Sensitivity of the Apparent Activation Energy

AbstractThe selective oxidation of glucose to gluconic acid with hydrogen peroxide was studied using different heterogeneous catalysts with alumina (Al2O3) and titanium silicate (TS‐1, TiMWW) as supports and different noble (Au, Pd) and non‐noble metals (Fe, W) as the catalytically active phases. Supported tungsten oxide catalysts showed a moderate selectivity and activity compared to palladium and iron catalysts. The best performance in the selective oxidation of glucose among the studied catalysts was displayed by gold on alumina. For this kind of catalyst, the structure sensitivity in glucose oxidation was explored, revealing a maximum rate shifted to larger gold particle sizes at higher temperatures in comparison with other studies involving activation of molecular oxygen on gold particles. A significant change in the apparent activation energy was established while changing the particle size of gold. These changes of the activation energy were adequately explained by a theoretical model for the cluster size dependence of the apparent activation energy.

Crystal plasticity based homogenized model for lamellar colonies of near-α and titanium alloys

The microstructure of near α and Ti-alloys consists of globular α grains, and transformed β colonies, which have a lamellar structure with alternating α hexagonal close packed and β body centered cubic laths. Due to the disparate length scales between the laths of the colonies and the globular α grains, a homogenized representation of the lath microstructure is necessary for computationally feasible and efficient crystal plasticity (CP) based full-field simulations of polycrystalline aggregates of these alloys. Thus, equivalent models of the lath microstructure based on iso-strain and virtual crystal (consisting of both α and β slip systems) assumptions were developed. However, these models fail to capture the response of the lath aggregate (colony), the individual phases (α and β laths), and slip systems, accurately. The deficiencies in the earlier models have been overcome in the equivalent model developed in this work in which the individual laths are allowed independent iso-stress and iso-strain conditions, while strain compatibility and stress equilibrium of the lath aggregate is ensured by enforcing periodic motion of the laths and traction balance at the interface. Additionally, an anisotropic size dependent CP constitutive model, due to the semi-coherent nature of the lath interfaces, is also developed for the α and β laths in the colony. The improvements of the present model are elucidated by comparing its response with the existing equivalent models and periodic CP finite element method simulations of a lath representative volume element for two different sets of Euler angles and four different deformation histories. The comparisons clearly show that the present model is significantly more accurate than the existing models in predicting the stress–strain response of the lath aggregate and the individual phases, as well as the slip activities on the various systems. The formulation of the developed model is generic and can also be applied to other materials with lamellar microstructure.

Development of size and shape dependent model for bandgap of semiconductor nanomaterials

A simple theoretical model is developed to study the effect of size and shape on the bandgap of semiconductor nanomaterials. It is found that bandgap increases by decreasing the size, which depends on the shape considered. The results obtained are compared with the available experimental data as well as with those based on earlier models. Different models predict similar trend of variations. However, such an excellent agreement with experimental data particularly in low size range using a simple model is never seen earlier. The model reduces the number of input parameters and includes more shapes as compared with earlier studies. This demonstrates the simplicity and wide applicability of the present model due to which it can be used to study the size and shape dependence of bandgap of different semiconductor nanomaterials of current interest in science and technology.

Semiconductor Nanocrystals: Unveiling the Chemistry behind Different Facets.

ConspectusDeveloping next-generation colloidal semiconductor nanocrystals with high-quality optoelectronic properties and precise processability relies on achieving complete mastery over the surface characteristics of nanocrystals (NCs). This requires precise engineering of the ligand-NC surface interactions, which poses a challenge due to the complex reactivity of the multiple binding sites across the entire surface. Accordingly, recent progress has been made by strategically combining well-defined surface models with quantitative surface reactions to advance our understanding and manipulation of NC surface chemistry. Our lab has contributed to this progress by developing a size-dependent shape model of IV-VI NCs, gaining insights into their unique facet-specific chemistry, and developing a systematic ligand modification strategy for target applications. Furthermore, we have created well-defined facets in III-V NCs via a co-passivation strategy, addressing the previously lacking specific shapes.This Account is divided into three parts. First, we discuss the complexities involved in comprehensively understanding the nanocrystal surface structure at the atomistic level. We explain why we focused on well-defined NCs with a large exciton Bohr radius to explore facets, an essential aspect of surface heterogeneity across the entire NC. Second, we present our work on one of the most studied nanocrystals, IV-VI materials, and how facet-specific surface chemistry has led to a meaningful understanding and control of the NC's surface. We discovered a size-dependent facet distribution in IV-VI NCs and suggested facet-specific surface chemistry to improve the photophysical properties of NCs. We further modulate the electronic properties of NC assemblies for efficient optoelectronic applications. Third, we describe our recent success in achieving well-defined facets and their facet-specific chemistry in III-V NCs, which have yet to be explored as much as classical II-VI or IV-VI materials. We explain how controlling the surfaces in III-V NCs has been challenging. We present a precise growth platform for the geometric modulation of NCs, which can be further explored for shape-dependent exciton behavior and surface reactivities.Taken together, we present a compelling case for utilizing facet-specific chemistry as a platform for mechanistic investigation and morphology exploration, which can pave the way for developing high-quality and precisely designed NCs for optoelectronic technologies, unlocking new multidisciplinary applications.

Size effect on the compressive behavior of BFRP RC circular columns: Experiments and a size-dependent stress-strain model

To investigate the size effect on compressive performance of circular concrete columns reinforced with basalt fiber-reinforced polymer (BFRP) bars and spirals, nine geometrically similar columns were fabricated and tested under concentric compression. The variables tested were cross-sectional diameters (200, 400, and 600 mm) and transverse reinforcement ratios (1.2%, 2.2%, and 3.3%). The results evidently indicated the size effect on the confined strength, corresponding strain and deterioration rate (in the post-peak branch) of concrete core confined by BFRP spirals. Specifically, with the cross-sectional diameter changing from 200 mm to 600 mm, the maximum decreases in the confined strength and corresponding strain were 14.1% and 31.9%, respectively, while the maximum increase in the deterioration rate was 318%. In addition, the size effect on confined strength could be weakened with the increase of transverse reinforcement ratio. Increasing the transverse reinforcement ratio could enhance the load-carrying capacity as well as effectively increase the confinement strength and ductility. Finally, a size-dependent stress–strain model, which considers the size effect of confined strength, corresponding strain and deterioration rate, was developed for evaluating the confined behavior of FRP RC columns.

A numerical study on the effect of porosity distribution on ductile failure using size-dependent finite element-based representative volume elements

In this work, we use the size-dependent Monchiet-Bonnet porous plasticity model to study the influence of void size distribution on ductile fracture. The size effect implies that the void growth depends on the material intrinsic length scale in addition to the plastic deformation and stress state of the material, and smaller voids grow more slowly than larger voids. Finite element-based representative volume elements (RVEs) are built where each element is given an initial porosity and initial void size according to the specified void size distribution. The RVEs are loaded plastically to fracture under different stress states to study the influence of the void size distribution on ductility. The results show that heterogeneity can trigger a macroscopic failure mode caused by localized plastic flow. The onset of localized plastic flow is sensitive to the material heterogeneity while the stress-strain response up to the point of localization is not.

Modelling mechanical behaviour of a gradient-microstructured material obtained by surface mechanical attrition treatment accounting for residual stresses

In this work, an austenitic 316 L steel was processed by surface mechanical attrition treatment (SMAT), and the induced gradient microstructure was highlighted by experimental measurements. A combined dislocation density-based and grain size-dependent constitutive model is developed to describe the mechanical behaviour of the gradient-microstructured material. In addition, this model also incorporates the grain size-dependent initial twin distribution and evolution of deformation twinning. Residual stress, initial dislocation density and twins are considered to reconstruct the depth-dependent residual fields induced by SMAT. Furthermore, the evolution of dislocation density and twin volume fraction is described during uniaxial tensile loading. Particular attention is devoted to investigate the effect of residual stress and deformation twinning on mechanical behaviour. Results of finite element simulation showed that the gradient microstructure enhances the yield strength, which is in agreement with previous experimental observations. It was revealed that residual stress significantly weakens the yield strength at the initial deformation stage, whereas it has little influence on the plastic behaviour at large deformation. The assumed grain size-dependent deformation twinning model allows describing the evolution of deformation twinning on gradient microstructure. The deformation twinning increases in relation to increased strain hardening during tensile loading. However, the evolution of twin volume fraction shows almost no twin and no variation of twinning within the nanocrystalline grain region.

Grain size and shape dependent crystal plasticity finite element model and its application to electron beam welded SS316L

Electron beam welding is an autogenous welding process that leads to microstructural heterogeneities; crystallographic texture, elongated and larger grain size relative to the surrounding parent material. The goal of this study is to predict the changes in mechanical response of the weld fusion zone as a function of grain morphology and texture by using the parent material properties to avoid extensive and costly experimental campaigns. For this reason, a crystal plasticity solver, “University of BRIstol cryStal plasTicity sOLver” (BRISTOL), is implemented in a finite element framework with new constitutive laws to account for the length-scale dependence considering the size and shape of the grains. It is found that the crystallographic texture governs the orientation specific elastic stiffness and yield stress having the most dominant effect on the macroscopic response of the weldment at the grain size scales considered. Crucially the length-scale dependent model allows accurate prediction of the yield strength of the weldment over a range of microstructures, also highlighting the presence of other factors such as prior strain hardening during the welding process and residual stresses.

High-fidelity moulding growth and cross-section shaping of ultrathin monocrystalline silicon nanowires

Catalytic growth of ultrathin silicon nanowires (SiNWs) provides ideal 1D channel materials for the construction of high-performance field effect transistors, where the diameter, uniformity and crystalline qualities are of utmost importance. In this work, a high-fidelity moulding growth of orderly ultrathin monocrystalline SiNWs, with diameter of 17±2nm, has been accomplished within tightly confined nanogrooves. A continuous and deterministic groove-width-transition or squeezing strategy has also been developed to accomplish an effective cross-section tailoring of the as-grown SiNW channels, while enabling a close-to-unity growth filling rate within the guiding grooves. Finally, a size-dependent adatom-searching model is proposed to explain how a monocrystalline SiNWs can be obtained even at such a low growth temperature of < 350 ℃. These results indicate a feasible catalytic growth fabrication route to implement monolithic 3D integration of advanced in-memory-computing and neuromorphic electronics.

An integrated experimental and numerical study of size effect on the mode I fracture toughness of rock

Rock is a typical quasi-brittle and heterogeneous material that shows the apparent size effect of mode I fracture toughness (KIc). To further explore the mechanism of the size effect on the KIc of rocks, a novel experimental procedure, i.e., combining a semi-circular bend test with a small-scale direct tension test, is conducted to determine the KIc and fracture process zone (FPZ) length of rock specimens of various sizes. Meanwhile, the four-dimensional lattice spring model (4D-LSM), incorporating a cohesive zone model (CZM) and the modified Mohr–Coulomb strength criterion for bond fracturing, is adopted to interpret these experimental results. After a detailed comparison between experimental and numerical results, we conclude that the size effect is dominated by the softening zone size of the mesoscale grain bond’s constitutive behaviour, rather than other mechanical parameters of rock, e.g., tensile strength, cohesion, and internal friction angle. Without introducing the size-dependent constitutive model into the discrete numerical model but only using a softening model for the mesoscale grain bond, we have successfully reproduced the change in KIc values and FPZ length of the rock specimens of various sizes with high goodness-of-it for the Bazant size effect curve, which indicates that the discrete numerical model can sufficiently reproduce or interpret the size effect in the KIc of rocks.

Soil particle size-dependent constitutive modeling of frozen soil under impact loading

In this study, the soil particle size dependence of the impact dynamic mechanical properties of frozen soil was investigated using a split Hopkinson pressure bar, and the meso-deformation mechanism of frozen soil was analyzed via electron microscopy. Under impact loading, the dynamic stress-strain curves of frozen soil showed strain hardening, strain softening, strain rate-temperature sensitivity, and soil particle size dependence, and the soil particle size dependence of frozen soil was considered to be significantly influenced by non-uniform meso-deformation, which primarily appeared in the form of microcracks surrounding the coarse particles. A constitutive model comprising a multiplicative hardening law was proposed, and soil particle size dependence was introduced through the equivalent strain gradient of the soil cell element. The impact compression process of frozen soil was simulated in ABAQUS/Explicit using the proposed model, and the mechanism of frozen soil deformation was summarized by the finite element analysis: the stress concentration around coarse particles induces the initiation of microcracks, the propagation of microcracks forms a crack network, eventually leading to the softening behavior of frozen soil.

A size-dependent analytical model to predict sound transmission loss of double-walled fiber metal laminated nanoplates

In the present study, the sound transmission loss (STL) through the air-filled rectangular double-walled cross-ply fiber metal laminated (FML) nanoplates under simply supported and clamped boundary conditions is studied using the nonlocal strain gradient theory (NSGT) and third-order shear deformation theory (TSDT). NSGT is complemented with hardening and softening material effects, which can significantly enhance the accuracy of small-scale results. The sound velocity potential and Hamilton’s principle are employed to derive the coupled size-dependent vibroacoustic equations. The Galerkin method is exploited to solve vibroacoustic equations and obtain the STL. The developed solution is examined in terms of its accuracy and precision via a comparison with other available data in existing research. The effects of different parameters such as boundary conditions, nonlocal and strain gradient parameters, lay-ups, incident angles, and acoustic cavity depth on the STL through the double-walled FML nanoplates are investigated.

Size-dependence of AM Ti–6Al–4V: Experimental characterization and applications in thin-walled structures simulations

Previous studies show that the properties of parts manufactured via additive manufacturing, such as selective laser melting, depend on local feature sizes like lattice wall thickness and strut diameter. Although size dependence has been studied extensively, it was not included in constitutive models for numerical simulations. In this work, flat dog-bone tensile specimens of different thicknesses were manufactured and tested under quasi-static conditions to characterize the size-dependent properties experimentally. It was observed that key mechanical properties decrease with specimen thickness. Through curve-fitting to experimental data, this work provides approximate analytical expressions for the material properties values as a function of specimen thickness, furnishing a phenomenological size-dependent constitutive model. The interpolating capability of the model is cross-validated with existing experimental data. Two numerical examples demonstrate the application of the size-dependent material model. The axial crushing of thin-walled lattices at varying wall thicknesses was simulated by the size-dependent material model and one that ignores size effects. Results show that ignoring size effects leads to overestimated peak crushing force and specific energy absorption. The two material models were also compared in the topology optimization of thin-walled structures. Results show that the size-dependent model leads to a more robust optimized design: having higher energy absorption and sustaining less material fracture.

Analysis of the magneto-thermoelastic vibrations of rotating Euler–Bernoulli nanobeams using the nonlocal elasticity model

This paper introduces size-dependent modeling and investigation of the transverse vibrational behavior of rotating thermoelastic nanobeams by means of nonlocal elasticity theory. In the formulation, a model of thermal conductivity with two-phase delays (DPL) was utilized. By incorporating the interactions between phonons and electrons, this model took into account microstructural influences. Also, we have employed the state-space approach and Laplace transform approach to solve the governing equations, which were developed in the context of the nonlocal Eringen model. The nanobeam material is subjected to a changeable temperature field produced by the graphene tape attached to the nanobeam and connected to an electrical source. In addition, the nanobeam material is fully encompassed by an axially applied magnetic field. It has been revealed how coefficients such as the rotational angular velocity of the nanobeam, nonlocal coefficient, voltage, electrical resistance, and applied magnetic field influence its behavior.

Dispersed strain bands promote the ductility of gradient nano-grained material: A strain gradient constitutive modeling considering damage effect

Gradient nano-grained (GNG) metals have achieved superior strength-ductility synergy than their homogeneous counterparts. The high strength is usually attributed to the grain size effect and hetero-deformation-induced strengthening. However, incommensurate work on ductility leads to an incomplete understanding of the strength-ductility combination. In this work, a dislocation density-based strain gradient plasticity model coupling with a damage model is developed to describe the strain hardening and softening behavior of GNG material. A grain size-dependent back stress model derived from the generation of dislocation pileups is invoked to describe the widely-concerned back stress hardening. Finite element implementation of the model quantitatively predicts the tensile response of GNG nickel with various degrees of grain size gradient. The results reveal that dispersed strain bands propagate stably in the nano-grained surface layer of GNG material, which is totally different from those occurring in a freestanding nano-grained material. The stabilization of dispersed strain bands enables the nano-grained layer to deform uniformly, thus premature failure of the whole GNG material is suppressed and improved ductility is achieved. Furthermore, increasing the grain size gradient renders the strain bands more stable, leading to enhanced ductility. The method developed in this work is helpful for understanding the strength-ductility synergy of GNG materials and for optimizing the microstructure gradient in GNG materials.