Size-scale Effects Research Articles

Simulating breakage by compression of iron ore pellets using the discrete breakage model

Simulation of breakage embedded in the discrete element method (DEM) has evolved significantly in recent years, taking advantage of both greater computing power and novel approaches that have become available in both commercial and open-source packages. This work analyzes in detail the simulation of breakage using the discrete breakage model (DBM) in the commercial software Ansys Rocky. Breakage of iron ore pellets under slow compression was studied. After the selection of suitable contact parameters for the pellets, described as polyhedral particles, the model is used to describe their breakage considering fully resolved fragments from the beginning of the simulation. The effects of contact model, time step and number of elements on the ability of the model to represent average breakage response of iron ore pellets under compression is analyzed. An approach was then used to account for the variability in the breakage characteristics of the pellets, which provided a valid description when applied to another pellet sample, also showing capability to describe the size-scale effect on the breakage energy of pellets when applied to pellets of different sizes.

Size scale effect on mass burning flux and flame behavior of solid fuels

The study investigates the horizontal fuel size effect on free-burning fires for PMMA plates and wood cribs. The fuel size effect on mass burning flux and flame behavior is mainly discussed and compared with typical pool fires. For the PMMA plate and liquid pool, when the fuel size is small (< 10 cm), either the 3D sidewall burning of PMMA or the container wall heated by flame can promote the burning flux at the horizontal projection area. As the fuel size increases, these side wall burning or heating effects decrease, causing the drop in burning flux with fuel scale for both the PMMA plate and liquid pool. For small-scale wood cribs, fire cannot self-sustain due to the large airflow cooling. With the increase in wood crib size, the burning rate first remains constant and then gradually increases, driven by the enhanced internal radiation. As the fuel size increases above 20–30 cm, the flame radiation dominates the burning flux for all fuel types. Fire dynamics simulator (FDS) was adopted to simulate the horizontal size effect by setting a varied fire source (horizontal projection) area. First, the flame geometry and heat release rate (HRR) of simulations were validated against experimental results. Subsequently, the validated fire model generates cases covering a broad range of fire scales. Finally, a new correlation of flame height with the fire heat release rate and fuel size is proposed, and its prediction capability is validated in the numerical fire modeling. This study quantifies the size effect on the burning rate for common solid fuels and provides valuable information for the numerical modeling of multi-scale fires.

Cancelling the effect of sharp notches or cracks with graded elastic modulus materials

Recent technologies permit to build materials which have elastic spatially varying modulus which can also imitate solutions adopted in Nature to optimize some structures. It has been shown that for example the stress concentration due to a hole in an infinite plate can be cancelled with a radially varying modulus making it similar to load-bearing bones which seem to resist structural failures even in the presence of blood vessel holes (foramina). Here, we attempt to study the classical problem of a sharp wedge (which includes the important case of a crack) looking for stresses varying as power law of the distance from the notch tip, σ∼rα, with a modulus varying as E∼rβ. In the inhomogeneous case the order of singularity of the LEFM case decreases if β>0, as confirmed by FEM investigations. Hence, we can remove stress singularities, which suggests an interesting alternative to the “rounding” of the notch. More in general, since for many materials it has been found that both strength and modulus are power laws of the density, using the so called strength-modulus exponent ratio we can obtain optimal design by keeping the asymptotic stress constantly equal to the strength. The present investigation paves the way for a new optimization strategy in the problems which eliminates size-scale effects due to singular stress fields, with potentially very wide applications.

Impact of ageing on structure of random sequential adsorption packings of discorectangles

The ageing processes in the systems of elongated particles (discorectangles) adsorbed on a plane was studied numerically. An off-lattice model with continuous positional and orientational degrees of freedom was tested. The initial jammed state was produced using the random sequential adsorption (RSA) model. The transition from the jammed to equilibrium states were performed via translational and rotational Brownian motions. An aspect ratio of the particles (length-to-width ratio) was varied within the range ε=1−12 . At ɛ < 10 the relaxation into the isotropic state was always observed. In the intermediate range, 10⩽ε⩽11 , the relaxation transition into the states with ordered domains was observed. Particularly, for ɛ = 10 this transition was related with significant finite size scaling effects. For particles with ɛ = 12 formation of the large scale quasi-nematic domains and unlimited domain growth was observed. The impact of the relaxation on the domain structure, porosity, percolation connectivity and tracer particle diffusion in such barrier systems was also discussed.

Flow Patterns Modeling over Spillway: Review Study

A spillway dam, constructed concurrently with concrete or masonry, is a vital infrastructure designed to provide the controlled release of surplus water that surpasses the dam's storage capacity. Since the Ogee spillway is among the best and most well-known worldwide, it deserves study. Weir flow, inertia, and gravity are crucial in many open-channel applications. Consequently, hydraulic performance data between model and prototype structures are commonly scaled using Froude similitude. As the upstream head decreases in a weir flow, the surface tension and viscosity forces become more important, perhaps to the point where Froude scaling fails to achieve complete model-prototype similarity. Size-scale effects are responsible for various alterations to the head-discharge connection, the nappe trajectory, and air entrainment. Hydraulic parameters were explored in this work utilizing Flow3D software to find weir geometry optimization using the CFD method. In addition, this study attempted to evaluate flow on various parts of crested weirs in three different models.

P‐140: The Miniaturization of InGaN/GaN Micro‐LEDs for Micro‐Displays – Size Effects, Frequency Dispersion and Compact Modeling

InGaN/GaN green micro‐light‐emitting diode (micro‐LED, μLED) arrays with varying device sizes down to 4 μm are fabricated and characterized. The size effects on current‐voltage and capacitance‐voltage characteristics are analyzed showing minimal sidewall effects only at low bias. The influence of pulse modulation frequency on luminance is also characterized and the effect of diode negative capacitance is discussed. Subsequently, a universal and comprehensive compact model for μLEDs are built based on these findings, which covers the capacitance frequency dispersion and size scaling effects. This work reveals the significance of frequency in the display driving strategy and provides design enablement for μLED micro‐display applications including augmented/mixed reality (AR/MR).

Fibrillar adhesives with unprecedented adhesion strength, switchability and scalability.

Bio-inspired fibrillar adhesives have received worldwide attention but their potentials have been limited by a trade-off between adhesion strength and adhesion switchability, and a size scale effect that restricts the fibrils to micro/nanoscales. Here, we report a class of adhesive fibrils that achieve unprecedented adhesion strength (∼2MPa), switchability (∼2000), and scalability (up to millimeter-scale at the single fibril level), by leveraging the rubber-to-glass (R2G) transition in shape memory polymers (SMPs). Moreover, R2G SMP fibrillar adhesive arrays exhibit a switchability of >1000 (with the aid of controlled buckling) and an adhesion efficiency of 57.8%, with apparent contact area scalable to 1000mm2, outperforming existing fibrillar adhesives. We further demonstrate that the SMP fibrillar adhesives can be used as soft grippers and reusable superglue devices that are capable of holding and releasing heavy objects >2000 times of their own weight. These findings represent significant advances in smart fibrillar adhesives for numerous applications, especially those involving high-payload scenarios.

Failure-mode scale transitions in RC and PC beams

Current design Standards for reinforced concrete beams prescribe to respect a minimum, ρmin, and a maximum, ρmax, reinforcement ratio in the design of structures. Below ρmin a brittle failure due to unstable crack propagation is expected. On the other hand, for ρ > ρmax a brittle failure due to concrete crushing is obtained. In this framework, a reinforced concrete element with ρmin < ρ < ρmax presents yielded steel at Ultimate Limite State (ULS) with a stable behaviour and no catastrophic loss of bearing capacity. Design Standards define ρmin and ρmax limits on the basis of the Bernoulli’s hypothesis of plane sections, and completely disregard size-scale effects. Within the present paper, Dimensional Analysis is used to determine the Brittleness Numbers that govern the behaviour of reinforced concrete (RC) as well as of prestressed reinforced concrete (PC) beams. Therefore, parametric analyses carried out by means of the Cohesive/Overlapping Crack Model (COCM) are used to study the ductile-to-brittle transitions in RC and PC beams, and to highlight the size-scale dependency of the two above-mentioned reinforcement limits.

Effective medium theory for second-gradient elasticity with chirality

We derive effective models for a heterogeneous second-gradient elastic material taking into account chiral scale-size effects. Our classification of the effective equations depends on the hierarchy of four characteristic lengths: The size of the heterogeneities ℓ, the intrinsic lengths of the constituents ℓ SG and ℓ chiral , and the overall characteristic length of the domain L. Depending on the different scale interactions between ℓ SG , ℓ chiral , ℓ, and L we obtain either an effective Cauchy continuum or an effective second-gradient continuum. The working technique combines scaling arguments with the periodic homogenization asymptotic procedure. Both the passage to the homogenization limit and the unveiling of the correctors’ structure rely on a suitable use of the periodic unfolding operator.

The Effect of Dairy Farm Size on the Economic Structure and Feed Consumption: A Case Study of the Aegean Region

Dairy farming has an important place in the agricultural activities in Türkiye. Cow's milk production constitutes 92.11% of the total milk production in Türkiye. The purpose of this study is to demonstrate the effect of scale size on the economic structure and feed consumption in dairy farms. The research data were obtained from face-to-face surveys conducted with 143 farmers in the Aegean Region. In the study, the farms were divided into four groups based on the number of cows: 5-15 cows, 16-25 cows, 26-40 cows, and 41 cows and above. The total variable cost per livestock unit in the 4th group farms was 26.07% less than the farms in the 1st group. The total production cost per livestock unit in the largest farm group is 25.81% less than that of the smallest farm group. The research findings indicate that large-scale farms take advantage of economies of scale, resulting in lower cost per livestock unit. Additionally, it was observed that as farm size increases, the feed conversion ratio also increases. As farms grow larger, they often have access to economies of scale, better management practices, and improved infrastructure.

Collective catalysis under spatial constraints: Phase separation and size-scaling effects on mass action kinetics.

Chemical reactions are usually studied under the assumption that both substrates and catalysts are well-mixed (WM) throughout the system. Although this is often applicable to test-tube experimental conditions, it is not realistic in cellular environments, where biomolecules can undergo liquid-liquid phase separation (LLPS) and form condensates, leading to important functional outcomes, including the modulation of catalytic action. Similar processes may also play a role in protocellular systems, like primitive coacervates, or in membrane-assisted prebiotic pathways. Here we explore whether the demixing of catalysts could lead to the formation of microenvironments that influence the kinetics of a linear (multistep) reaction pathway, as compared to a WM system. We implemented a general lattice model to simulate LLPS of a collection of different catalysts and extended it to include diffusion and a sequence of reactions of small substrates. We carried out a quantitative analysis of how the phase separation of the catalysts affects reaction times depending on the affinity between substrates and catalysts, the length of the reaction pathway, the system size, and the degree of homogeneity of the condensate. A key aspect underlying the differences reported between the two scenarios is that the scale invariance observed in the WM system is broken by condensation processes. The main theoretical implications of our results for mean-field chemistry are drawn, extending the mass action kinetics scheme to include substrate initial "hitting times" to reach the catalysts condensate. We finally test this approach by considering open nonlinear conditions, where we successfully predict, through microscopic simulations, that phase separation inhibits chemical oscillatory behavior, providing a possible explanation for the marginal role that this complex dynamic behavior plays in real metabolisms.

Scale effect on unnotched and open-hole cross-ply glass fiber/epoxy non-crimp fabric (NCF) composites under quasi-static tensile loading

This study explores the effect of size scaling and stacking sequence on the quasi-static tensile behavior of sublaminate-level and ply-level scaled glass/epoxy laminates. Test results showed that the unnotched tensile strengths of both scaled specimens were comparable for a given scaling factor, even though ply-level scaled specimens suffered extensive delamination between and ply blocks. In contrast, the open hole tensile (OHT) strength was reduced with increased scale in sublaminate-level and was marginally increased in ply-level scaled specimens. Similar to unnotched specimens, ply-level scaled OHT specimens exhibited extensive delamination.

A multi-length-scale investigation of the applicability of ductility laws for annealed and work-hardened copper

Small-scale mechanical testing provides unique advantages over conventional testing in investigating the mechanical response of nuclear materials. While small-scale testing enables accelerated materials research, it raises the question of comparability to large-scale properties for engineering design considerations. Among different mechanical properties for structural design considerations such as yield and ultimate tensile stress, ductility is of critical importance with respect to structural component health. The effectiveness of using small-scale mechanical testing for probing these mechanical properties is dictated by understanding how the mechanical responses translate from the microscale to the engineering scale. Therefore, a better understanding of size scaling effects via gathering and analysis of experimental data is required to bridge length-scales. This work builds upon previous reports to provide statistical data on how mechanical response changes as the size of the specimens are reduced from conventional sizes. One hundred twenty mesoscale tensile coupons of oxygen-free high thermal conductivity (OFHC) copper in work-hardened and annealed state have been manufactured using micro-wire electrical discharge machining (EDM) and tested under uniaxial tension. The mesoscale specimens have dimensions dictated by pre-selected geometric ratios (i.e., gauge section length over the square root of the cross-section area) with gauge length dimensions of 3 mm (or less) and sub-millimeter gauge widths and thicknesses. The mesoscale responses were compared to bulkscale properties to reveal the effect of specimen size on the mechanical response as a function of grain size and material state for a single phase face-centered cubic metal.

The Projectile Perforation Resistance of Materials: Scaling the Impact Resistance of Thin Films to Macroscale Materials.

From drug delivery to ballistic impact, the ability to control or mitigate the puncture of a fast-moving projectile through a material is critical. While puncture is a common occurrence, which can span many orders of magnitude in the size, speed, and energy of the projectile, there remains a need to connect our understanding of the perforation resistance of materials at the nano- and microscale to the actual behavior at the macroscale that is relevant for engineering applications. In this article, we address this challenge by combining a new dimensional analysis scheme with experimental data from micro- and macroscale impact tests to develop a relationship that connects the size-scale effects and materials properties during high-speed puncture events. By relating the minimum perforation velocity to fundamental material properties and geometric test conditions, we provide new insights and establish an alternative methodology for evaluating the performance of materials that is independent of the impact energy or the specific projectile puncture experiment type. Finally, we demonstrate the utility of this approach by assessing the relevance of novel materials, such as nanocomposites and graphene for real-world impact applications.

Size-scale effects and modelling issues of fibre-reinforced concrete beams

This paper compares numerical and analytical predictions for the shear capacity of fibre-reinforced concrete beams based on experimental literature tests. The authors compared the outcomes of a FE model using the DamageTC3d constitutive model, a literature formulation, and the current proposal of the Eurocode 2 draft for fibre-reinforced structures. The paper evaluates the sensitivity of the beam response to the fracture energy Gf, modified after the Model Code 2010 formulation. The investigation reveals a dependence of the estimated fracture energy on the beam size. Furthermore, the comparison between the numerical estimates and the analytical predictions using the MC2010 and the current EC2 draft proves that the error is substantially independent of the model selection but is strongly affected by the specific case study. This fact confirms the absence of weaknesses in the numerical modelling and highlights the aleatoric uncertainties of the experimental data.

On a hierarchy of effective models for the biomechanics of human compact bone tissue

Abstract We derive a hierarchy of effective models that can be used to model the biomechanics of human compact bone taking into account scale-size effects observed experimentally. The classification of the effective models depends on the hierarchy of four characteristic lengths: the size of the heterogeneities, two intrinsic lengths of the constituents and the overall characteristic length of the domain. Depending on the different scale interactions between the size of the heterogeneities, the two intrinsic lengths of the constituents, and the characteristic length of the domain we obtain either an effective Cauchy continuum or an effective Cosserat continuum. The passage to the limit relies on suitable use of the periodic unfolding operator. Moreover, we perform numerical simulations to validate our results.

Thermodynamic behavior of rectangular nanoplate under moving laser pulse based on nonlocal dual-phase-lag model

Recently, the moving laser pulse is commonly employed in laser-assisted manufacturing for nanostructures synthesis and modification, however, the involved thermodynamic coupling process is still unclear. In the present work, a nonlocal thermo-elastic model is formulated to reveal the thermodynamic response of rectangular nanoplate subjected to a moving laser pulse, in which the heat conduction at the nanoscale is captured via the nonlocal dual-phase-lag (DPL) model. The temperature distribution in the nanoplate is obtained by Green's function method, which is inserted into the governing equation of the nonlocal nanoplate to obtain its dynamic response. The proposed theoretical model is validated by comparing with the previous experimental study and a good agreement is achieved. This study demonstrates that the size-scale effect plays a significant role in the dynamic response of nanoplate under a moving laser pulse, i.e., the nonlocal heat parameter can reduce the deflection, while the nonlocal structural parameter can enlarge the deflection amplitude of the nanoplate. Furthermore, the influences of size-scale parameters, the moving speed and pulse duration of the laser spot on the temperature profile and dynamic response of the rectangular nanoplate are also investigated in detail. The estimation method presented in this work can be used to guide the laser-assisted manufacturing process for nanostructures.

Spatial modulation of scalable nanostructures by combining maskless plasmonic lithography and grayscale-patterned strategy.

Nanolithography techniques providing good scalability and feature size controllability are of great importance for the fabrication of integrated circuits (IC), MEMS/NEMS, optical devices, nanophotonics, etc. Herein, a cost-effective, easy access, and high-fidelity patterning strategy that combines the high-resolution capability of maskless plasmonic lithography with the spatial morphology controllability of grayscale lithography is proposed to generate the customized pattern profile from microscale to nanoscale. Notably, the scaling effect of gap size in plasmonic lithography with a contact bowtie-shaped nanoaperture (BNA) is found to be essential to the rapid decay characteristics of an evanescent field, which leads to a wide energy bandwidth of the required optimal dose to record pattern in per unit volume, and hence, achieves the volumetrically scalable control of the photon energy deposition in the space more precisely. Based on the proper calibration and cooperation of pattern width and depth, a grayscale-patterned map is designed to compensate for the dose difference caused by the loss of the high spatial frequency component of the evanescent field. A Lena nanostructure with varying feature sizes by spatially modulating the exposure dose distribution was successfully demonstrated, and besides, we also successfully generated a microlens array (MLA) with high uniformity. The practical patterning method makes plasmonic lithography significant in the fabrication of functional nanostructures with high performance, including metasurfaces, plasmonics, and optical imaging systems.

NANOINDENTATION OF SOFT MATERIALS. ANALYSIS OF THE EXPERIMENTAL FACTORS IN CONSTRUCTING A MATHEMATICAL MODEL

The authors call for attention to the specifics of conducting experiments on nanoindentation of soft materials (elastomers, polymers), the features of the experimental setup, the material itself, the interaction of the material under study with the scanning elements of the setup, and environmental conditions. The paper shows which of them require to be taken into account in mathematical models, and which can be neglected, or can be almost completely compensated for by others. The following topics are considered: influence of cantilever bending and its inclination, humidity, plasticity, and viscosity, probe jump to the surface, determining the radius of the probe tip curvature, plastics, destruction of the sample during double indentation, size (scale) effect, sample drift, preservation of the probe shape before and after the experiment, time-varying surface properties, and surface energy during contact formation. This work is intended both to simplify further research and to focus efforts on solving acute problems.

Relevance of displacement softening model in discrete element method to investigate structural and grain size scaling effect

A local crack opening displacement softening model is used in the framework of discrete element method to investigate the fracture propagation and post-peak behaviour of concrete that remains a problem in the linear parallel bond model. Modelling approach is validated for mechanical behaviour by three-point bending tests on mortar and concrete. The numerical fracture propagation is compared with the damage pattern obtained using acoustic emission and digital image correlation techniques. In the three phase concrete microstructure, a comprehensive approach is used to determine the model parameters from laboratory tests and literature. The model is then applied to study the variation of aggregate size on fracture behaviour using three different concretes where only aggregate sizes were scaled. The results are compared with experiments. The model is further tested to investigate effect of specimen size and compared with experimental results. It is shown that softening model in DEM can effectively reproduce concrete behaviour and complex fracture process.