Unit Cell Model Research Articles

Size-dependent yield criterion for single crystals containing spherical voids

A micromechanics-based yield criterion is derived for a porous single crystal containing a random distribution of spherical voids, using homogenization and limit analysis of a hollow spherical representative volume element obeying a strain gradient crystal plasticity model. The criterion captures the effect of plastic anisotropy due to crystallographic slip on a set of discrete slip systems, as well as the void size dependence of yielding. The yield criterion is formally similar to the well known Gurson model for isotropic porous materials, and reduces to existing results in the literature in the limiting case of large void sizes relative to the length scale in the gradient plasticity model. The yield criterion is validated by comparison with rigorous upper bound yield loci obtained using a numerical limit analysis procedure. Predictions for the size dependence of void growth are obtained by integrating the porous plasticity model, and shown to be consistent with the observations from lower scale discrete dislocation dynamics simulations. The loading path dependence of void growth in the size-independent limit are compared with finite element simulations of void growth in a single crystal using the unit cell model.

Multiscale Evaluation of Mechanical Properties for Metal-Coated Lattice Structures

With the combination of 3D printing and electroplating technique, metal-coated resin lattice is a viable way to achieve lightweight design with desirable responses. However, due to high structural complexity, mechanical analysis of the macroscopic lattice structure demands high experimental or numerical costs. To efficiently investigate the mechanical behaviors of such structure, in this paper a multiscale numerical method is proposed to study the effective properties of the metal-coated Body-Centered-Cubic (BCC) lattices. Unlike studies of a similar kind in which the effective parameters can be predicted from a single unit cell model, it is noticed that the size effect of representative volume element (RVE) is severe and an insensitive prediction can be only obtained from models containing multiple-unit-cells. To this end, the paper determines the minimum number of unit cells in single RVE. Based on the proposed method that is validated through the experimental comparison, parametric studies are conducted to estimate the impact of strut diameter and coating film thickness on structural responses. It is shown that the increase of volume fraction may improve the elastic modulus and specific modulus remarkably. In contrast, the increase of thickness of coating film only leads to monotonously increased elastic modulus. For this reason, there should be an optimal coating film thickness for the specific modulus of the lattice structure. This work provides an effective method for evaluating structural mechanical properties via the mesoscopic model.

An approach to investigate the crystallographic unit cell of human tooth enamel.

Human tooth enamel (HTE) is the hardest tissue in the human body and its structural organization shows a hierarchical composite material. At the nanometric level, HTE is composed of approximately 97% hydroxyapatite [HAP, Ca10(PO4)6(OH)2] as inorganic phase, and of 3% as organic phase and water. However, it is still controversial whether the hexagonal HAP phase crystallizes in P63/m or another space group. The observance in HTE of Ca2+, Mg2+ and Na+ ions using X-ray characteristic energy-dispersive spectroscopy in the scanning electron microscope has been explained by substitutions in the HAP unit cell. Thus, Ca2+ can be replaced by Na+ and Mg2+ ions; the PO43- group can be replaced by CO32- ions; and the OH- ions can also be replaced by CO32-. A unit-cell model of the hexagonal structure of HTE is not fully defined yet. In this work, density functional theory calculations are performed to study the hexagonal HAP unit cell when substitution by OH-, CO32-, Mg2+ and Na+ ions are carried out. An approach is presented to study the crystallographic unit cell of HTE by examining the changes resulting from the inclusion of these different ions in the unit cell of HAP. Enthalpies of formation and crystallographic characteristics of the electron diffraction patterns are analysed in each case. The results show an enhancement in structural stability of HAP with OH defects, atomic substitution of Mg2+, carbonate and interstitial Na+. Simulated electron diffraction patterns of the generated structures show similar characteristics to those of human tooth enamel. Hence, the results explain the indiscernible structural changes shown in experimental X-ray diffractograms and electron diffraction patterns.

Physics-informed machine learning of redox flow battery based on a two-dimensional unit cell model

In this paper, we present a physics-informed neural network (PINN) approach for predicting the performance of an all-vanadium redox flow battery, with its physics constraints enforced by a two-dimensional (2D) mathematical model. The 2D model, which includes 6 governing equations and 24 boundary conditions, provides a detailed representation of the electrochemical reactions, mass transport and hydrodynamics occurring inside the redox flow battery. To solve the 2D model with the PINN approach, a composite neural network is employed to approximate species concentration and potentials; the input and output are normalized according to prior knowledge of the battery system; the governing equations and boundary conditions are first scaled to an order of magnitude around 1, and then further balanced with a self-weighting method. Our numerical results show that the PINN is able to predict cell voltage correctly, but the prediction of potentials shows a constant-like shift. To fix the shift, the PINN is enhanced by further constrains derived from the current collector boundary. Finally, we show that the enhanced PINN can be even further improved if a small number of labeled data is available.

A micro-mechanics based extension of the GTN continuum model accounting for random void distributions

Randomness in the void distribution within a ductile metal complicates quantitative modeling of damage following the void growth to coalescence failure process. Though the sequence of micro-mechanisms leading to ductile failure is known from unit cell models, often based on assumptions of a regular distribution of voids, the effect of randomness remains a challenge. In the present work, mesoscale unit cell models, each containing an ensemble of four voids of equal size that are randomly distributed, are used to find statistical effects on the yield surface of the homogenized material. A yield locus is found based on a mean yield surface and a standard deviation of yield points obtained from 15 realizations of the four-void unit cells. It is found that the classical GTN model very closely agrees with the mean of the yield points extracted from the unit cell calculations with random void distributions, while the standard deviation S varies with the imposed stress state. It is shown that the standard deviation is nearly zero for stress triaxialities T≤1/3, while it rapidly increases for triaxialities above T≈1, reaching maximum values of about S/σ0≈0.1 at T≈4. At even higher triaxialities it decreases slightly. The results indicate that the dependence of the standard deviation on the stress state follows from variations in the deformation mechanism since a well-correlated variation is found for the volume fraction of the unit cell that deforms plastically at yield. Thus, the random void distribution activates different complex localization mechanisms at high stress triaxialities that differ from the ligament thinning mechanism forming the basis for the classical GTN model. A method for introducing the effect of randomness into the GTN continuum model is presented, and an excellent comparison to the unit cell yield locus is achieved.

Effect of geometrical defects on the acoustical transport properties of periodic porous absorbers manufactured using stereolithography

Additive manufacturing allows the fabrication of acoustical materials with previously unrealizable micro- and macrostructural complexities. However, the still nascent understanding of various geometrical defects occurring during the additive process remains a barrier to accurately predicting the acoustical behavior of such complex absorbers. In this study, we present the results from our efforts on numerically modeling the absorption behavior of periodic porous absorbers fabricated using the stereolithography (SLA) technique using the hybrid micro-macro multiphysics approach. Specifically, we focus on understanding the role played by the expansion or shrinkage of the solid ligaments during the SLA process on the acoustical properties of the final printed samples. First, the periodic absorbers are modeled using COMSOL multiphysics, where the transport properties are derived using the micro-modeling method and sound absorption behavior using the Johnson-Champoux-Allard-Lafarge-Pride semi-empirical model. Then, results from the expansion study guide the changes in the ligament sizes in the unit cell modeling. Finally, the fabricated samples are tested using an impedance tube, and the measured absorption properties are compared to the a priori numerical predictions. Results indicate that accounting for fabrication defects within the numerical modeling schema can provide reliable sound absorption predictions for additively manufactured porous absorbers.

Numerical study of thermomechanical delamination mechanisms in segmented high-temperature coatings

This work addresses the thermomechanical delamination mechanisms in segmented multilayered high-temperature coatings system using computational fracture mechanics approach. A representative unit cell model is presented, where the thermomechanical load is generated by combining uniform temperature changes and boundary-loaded displacements. The model is used to analyze coatings over a broad range of material properties, geometries, and loads. The findings suggest that, for a given coatings system, the mechanical load carried by the top-coat layer is the only force that drives delamination developing along the top-coat/bond-coat interface. The introduced multiple vertical cracks lead to stiffness release over a limited region, resulting in reductions in stress and delamination driving forces within that region. An empirical equation is established using multiple regression analyses to evaluate the delamination driving forces. Accordingly, the importance of the influential factors on the delamination is ranked, and design maps are constructed to facilitate the development of durable coatings.

Structure of the Hexadecane Rotator Phase: Combination of X-ray Spectra and Molecular Dynamics Simulation.

Rotator phases are rotationally disordered plastic crystals, some of which can form upon freezing of alkane at alkane-water interfaces. Existing X-ray diffraction studies show only partial unit cell information for rotator phases of some alkanes. This includes the rotator phase of n-hexadecane, which is a transient metastable phase in pure alkane systems, but shows remarkable stability at interfaces when mediated by a surfactant. Here, we combine synchrotron X-ray diffraction data and molecular dynamics (MD) simulations, reporting clear evidence of the face-centered orthorhombic RI rotator phase from spectra for two hexadecane emulsions, one stabilized by Brij C10 and another by Tween 40 surfactants. MD simulations of pure hexadecane use the recently developed Williams 7B force field, which is capable of reproducing crystal-to-rotator phase transitions, and it also predicts the crystal structure of the RI phase. Full unit cell information is obtained by combining unit cell dimensions from synchrotron data and molecular orientations from MD simulations. A unit cell model of the RI phase is produced in the crystallographic information file (CIF) format, with each molecule represented by a superposition of four rotational positions, each with 25% occupancy. Powder diffraction spectra computed using this model are in good agreement with the experimental spectra.

Prediction of the stress distributions and strength properties of 3-D braided composites with an eccentric circular hole

Due to their low delaminating tendency and high damage tolerance, 3-D braided composites are capable of being utilized in notched components. However, a few studies have investigated the mechanical properties of braided composites with open holes in multi-scale. In this paper, a multi-scale study on the mechanical properties of 3-D 4-directional braided composites with an eccentric circular hole is carried out. The equivalent elastic properties of 3-D 4-directional braided composites are calculated by the homogenization method based on the geometry of the meso unit cells. According to Lekhnitskii's theory, the local stress correction (LSC) method for computing the transverse stress around the eccentric hole is proposed. The models of meso unit cells with different braided angles are established, and the strength of the defect-free composites is predicted by the Tsai-Wu criterion. In the macroscopic view, using the point stress criterion (PSC), the average stress criterion (ASC), and numerical analysis, the strength properties of braided composites with different hole radii, braided angles, and eccentric distances are predicted. This study can be utilized to estimate the stress distributions and strength properties of 3-D braided composites with an eccentric hole and provides theoretical and simulation foundations for the problems of orthotropic materials with holes.

Probing low-frequency terahertz calculation: A comparison between periodic boundary conditions and cluster models

Terahertz spectroscopy performs as a powerful tool for revealing valuable information on molecular interactions. In recent years, low-frequency terahertz simulation through periodic boundary conditions has proved to be a great success with regard to long-range force and complete noncovalent interaction rather than cluster models or unit cell models. However, quantum chemistry simulation with a limited number of molecules also enables many in-depth and comprehensive analytical methods, therefore, encouraging proving the outcome validity of the cluster models based on quantum chemistry calculation. In this article, we compared the computational results of both periodic boundary conditions and cluster models through solid-state density functional theory, revealing the necessity of a periodic structure in calculating low-frequency terahertz bands, which is instrumental for the selection of computational models for terahertz spectra.

Geometrical imperfection sensitivity on in-plane compressive modulus and strength of honeycomb core and deviations from isotropy

Honeycomb core sandwich may suffer from face/core debonding. Candidate debond fracture test specimens such as End-Notch Flexure (ENF) and Mixed Mode Bending (MMB) contain unbonded regions of the sandwich where the core is required to carry in-plane com-pressive load. In-plane modulus and compressive strength of honeycomb core are not pro-vided by core producers and must be estimated from unit cell models assuming perfect hexagonal cells. In this study it is shown that geometrical imperfections, such as deviations in the angle between cell walls and curved cell walls have a strong influence on modulus and strength because of deviations from transverse isotropy. A range of Nomex honeycomb cores were tested under in-plane compression. Modulus and strength ratios ( L/W) were found to vary from 0.3 to 3.24 and 0.96 to 1.8, respectively. Analysis based on unit cell models verified that deviations of the inclined cell wall angle, θ, from 30 ◦ is a major cause for orthotropy. Rounded corners and curved walls were analyzed using finite element analysis. Both principal elastic moduli of the core ( E L and E W) were reduced by the curvature while the Poisson’s ratios remained largely unaffected. Implications of the results for design of MMB and ENF fracture test specimens are discussed.

Electromagnetic–Thermal Analyses of Distributed Antennas Embedded Into a Load-Bearing Wall

The importance of indoor mobile connectivity has increased during the last years, especially during the Covid-19 pandemic. In contrast, new energy-efficient buildings contain structures like low-emissive windows and multi-layered thermal insulations which all block radio signals effectively. To solve this problem with indoor connectivity, we study passive antenna systems embedded in walls of low-energy buildings. We provide analytical models of a load bearing wall along with numerical and empirical evaluations of wideband back-to-back spiral antenna system in terms of electromagnetic- and thermal insulation. The antenna systems are optimized to operate well when embedded into load bearing walls. Unit cell models of the antenna embedded load bearing wall, which are called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">signal-transmissive walls</i> in this paper, are developed to analyze their electromagnetic and thermal insulation properties. We show that our signal-transmissive wall improves the electromagnetic transmission compared to a raw load bearing wall over a wide bandwidth of 2.6-8 GHz, covering most of the cellular new radio frequency range 1, without compromising the thermal insulation capability of the wall demanded by the building regulation. Optimized antenna deployment is shown with 22 dB improvement in electromagnetic transmission through the load bearing wall.

An investigation of the transient electrophoresis of conducting colloidal particles in porous media using a cell model

A comprehensive analytical study of the electrophoresis of a suspension of charged spherical particles in an arbitrary electrolyte solution through a porous medium is analyzed using a unit cell model. The unsteady Brinkman equation with the term of the electric force governing the fluid velocity fields is solved by means of the Laplace transform. The porous medium is uniformly charged by fixed charge density Q, and the embedded spherical particle is conductive and charged with constant zeta potential. Two different accurate concepts of the boundary conditions at the outer virtual surface, are presented to solve the governing equations for the flow field. Steady-state electrophoretic velocity is obtained analytically and displayed graphically for different physical parameters. Also, a closed form of the transient electrophoretic velocity versus the dimensionless elapsed time is plotted and discussed for different values of the Debye length parameter, particle volume fraction, density ratio, permeability of the porous medium, and for highly- and non-conducting particles. The steady/ transient electrophoretic velocity is a monotonic decreasing function of the permeability parameter, the particle-to-fluid density ratio, and the particle volume fraction, but it increases with an increase in the Debye length parameter with constant zeta potential. In general, the Kuwabara cell model predicts a smaller value for the electrophoresis velocity than the Happel model, but the difference is not significant. On the other hand, when the transient velocity is normalized by its steady state, the Happel model has smaller values than the Kuwabara model. The effects of the relevant parameters on the transient starting electrokinetic flow in the porous medium are interesting and significant. The results are found to be in excellent agreement with the exact numerical results obtained by Lai and Keh.

A numerical unit cell model for predicting the failure stress state of vertically perforated clay block masonry under arbitrary in-plane loads

As vertically perforated clay block masonry advances into more demanding building categories, knowledge of the effective masonry strength under different loading states becomes crucial. However, experimentally identifying macroscopic failure surfaces for such masonry requires a massive effort. In this study, we propose a FEM-based simulation concept to predict failure stress states of masonry under arbitrary in-plane loading. The proposed concept is validated using seven experiments from the literature. Subsequently, subjecting the validated model to various load cases allows for deriving a failure surface comparable to the Rankine–Hill surface. Thus, by applying the presented concept, we can effectively generate macroscopic failure surfaces for any perforated clay block design.

Bending study of submarine power cables based on a repeated unit cell model

Predicting the bending behaviours of a submarine power cable (SPC) is always a tough task due to its complex geometry and inner layer contact, not to mention the stick–slip mechanism. A full-scale finite element model is cumbersome during the early design stage and a more efficient model for practical use is required. Therefore, in this paper, a repeated unit cell (RUC) technique-based FE model is developed, which simplifies the bending analysis of SPCs using a short-length representative cell with periodic conditions. The verification of this RUC model is conducted from cable and component levels, respectively. The cable overall response is validated by the curvature-moment relationships from our cable bending tests regarding four cable samples whose material properties are obtained through a set of material tests. As for the component level, the behaviours of particular components are studied and compared with the results from a full-scale numerical model. Discrepancy is observed between the RUC model and the test, which can be explained by the distinctions of boundary conditions between these two methods. The proposed Cable-RUC model has been found robust and computationally efficient for studying SPCs under bending.

Reflection Phase Compensation for Finite Metasurface Using Notches and Slots on the Backing Conductor

This study described a technique to compensate for the difference in reflection phase characteristics yielded by a finite-size meta-surface (MS) to render them identical to the reflection characteristics analyzed using the unit cell model corresponding to the infinite MS structure. Thus, an MS with a backing conductor having notches and slots to compensate for the reflection phase affected by the complex diffraction at the edge, was proposed. The notches and slots’ mechanism inducing the inductive reactions was discussed based on the current distributions. The proposed and conventional MSs were fabricated to verify the deterioration and compensation effect; the former was consistent with the designed performance based on the unit cell analysis corresponding to the infinite structure.

Particle-matrix debonding with Strength-Differential effects

In this work the onset of failure caused by particle-matrix debonding in aluminum alloy 2090-T3 and magnesium alloy AZ31 under either overall uniaxial plane strain tension or compression load is studied numerically using a unit cell model. Especially for magnesium AZ31, experiments show a significant difference in the tensile-compressive yield stresses, the so-called Strength-Differential-effect (SD-effect). This SD-effect cannot be captured by any isotropic yield function and only by recent anisotropic yield functions. To accurately model AA 2090-T3 and magnesium AZ31 the general yield function by Yoon et al. (2014) is adopted in addition to the isotropic von Mises plasticity yield function and the anisotropic yield function of Hill (1948). The numerically predicted strain at which void nucleation initiates is generally found to be larger for magnesium AZ31 than for AA 2090-T3. However, depending on the orientation of the principal axes of plastic anisotropy this void nucleation strain varies significantly. This holds true for both materials, but the void nucleation strain of AA 2090-T3 in compression is numerically predicted to be practically identical whether or not isotropic or anisotropic plasticity is considered. In tension the void nucleation strain of AA 2090-T3 based on anisotropic plasticity is found to be more than double the strain obtained by von Mises plasticity. The numerically predicted void nucleation strain of magnesium AZ31 is significantly affected by the yield function adopted. For the von Mises yield function the value of the void nucleation strain is in between the predictions based on the anisotropic yield functions. For both tension and compression, the yield function of Yoon et al. (2014) results in the largest void nucleation strain, whereas the yield function of Hill results in the smallest strain value. This holds true for all five orientations of the principal axes of plastic anisotropy investigated.

An improved analytic model for extracting plastic mechanical property of matrix in hot-extruded in-situ TiB2/2024 composite based on Berkovich indentation experimental results

Due to the strengthening mechanisms mainly contributed to dispersed nano TiB2 particles, plastic mechanical property of Al matrix in hot-extruded in-situ TiB2/2024 composite, referring to yield strength (YS) and strain hardening exponent (SHE), are considerably improved compared with 2024 Al alloy. In addition, the plastic mechanical property of Al matrix cannot be obtained directly through traditional uniaxial tensile tests. After carrying out dimensional analysis and FE simulations, an improved analytical model with no need of characteristic stress/strain is proposed found on existing model, to extract plastic mechanical property parameters of Al matrix based on sufficient Berkovich indentation experimental results. The indentation experiments carried out using the custom method “G-Series Basic Hardness, Modulus, Tip Cal, Load Control” were implemented in case of four different maximum indentation loads to get indentation load-depth curves (ILDCs) of Al matrix, where the corresponding morphologies of residual indents were obtained by SEM observation. With these experimental results as input, the YS and SHE of Al matrix can be calculated by utilizing the proposed analytic model. To verify the effectiveness of proposed improved model, a unit-cell FE model with same particle volume fraction as the macroscopic composite is established and analyzed, and the calculated results are in good agreement with the uniaxial tensile test results.

A novel analysis method for mechanical properties of 3D needled twill composites based on virtual fibers

Compared with the traditional 3D needled composites with non-woven structure, the composites with twill layers have an extremely complex mesostructure. Three representative regions are divided based on the mesostructure observation of 3D needled twill composites. At the same time, the needling process of the 3D preform is simulated based on the digital element method, and the fiber deflection formulas in the needled region are built. Considering the distribution of different needling points, the periodic unit cell models of 3D needled twill composites that include three representative regions are established to predict the mechanical properties. It is verified that the results predicted by the proposed model agree well with the experimental data. Moreover, the effects of different needling angles and needling points on the mesostructure and mechanical properties of the composites are further studied, which helps guide the design and manufacture of 3D needled twill composites.

Analysis of evaporation and autoignition of droplet clouds with a unit cell model considering transient evaporating boundary layer

Liquid clouds (sprays) are commonly encountered in nature and industrial applications, where droplets are subject to complex interactions. In this paper, an extended unit cell model is proposed to analyze the evaporation and autoignition of monodisperse, single-component, and quiescent droplet clouds. The extended model incorporates the transient development of the evaporating boundary layer attached to the droplet surface. Due to the inclusion of this gas-phase transient effect, the current theory can be applied to both dilute and dense clouds across a wide range of ambient pressures. In the absence of chemical reactions, the effects of multiple parameters, such as droplet spacing and ambient pressure, on the evaporation rate and lifetime of droplets are examined. The critical condition for fuel vapor saturation in the gas phase is re-obtained. Based on this, we further investigate the autoignition of droplet clouds exposed to hot oxidizing environments and derive the corresponding ignition criterion. Effects of various factors, including droplet size, droplet spacing, ambient pressure, initial oxygen concentration, and reaction order, on critical ignition temperatures are also considered. In comparison with transient numerical results, it is found that the current theoretical solutions predict well for a broad variety of parameters.