Unit Cell Model Research Articles

A novel framework to predict transversal and shear parameters of unidirectional composites by combining experimental, numerical and machine learning methods

AbstractThis work presents a new method to predict the transversal and shear properties of unidirectional composites (UD) through combining the experimental, numerical and machine learning methods. The experimental results proved the complexity and difficulty of explaining primary factors affecting the mechanical properties of UD. The representative unit cell model was then created to generate 500 virtual samples for machine learning. The results show that the back propagation neural network model (BP) is the most suitable for predicting the mechanical properties of UD, with an accuracy of 98% within a 2% error. The minimum mean square and absolute errors are 1.09E‐3 and 1.15E‐5, respectively. It is proved that the interface has significant influences on all mechanical properties of UD and shear modulus of composite in 12 directions (Gc12) of UD is affected by all input parameters through the optimized BP model. Due to the wide coverage of input data, the proposed BP model is universal and can be adopted to predict transversal and shear properties of UD made from different kinds of fibers.Highlights Interface has influences on all parameters of unidirectional composites. Shear properties of unidirectional composites along 12 directions are intricated. Machine learning can predict mechanical properties of unidirectional composites. Specific samples are beneficial to improve the predicted accuracy.

Starting Electroosmosis in a Fibrous Porous Medium with Arbitrary Electric Double-Layer Thickness

The transient electroosmotic response in a charged porous medium consisting of a uniform array of parallel circular cylindrical fibers with arbitrary electric double layers filled with an electrolyte solution, for the stepwise application of a transverse electric field, is analyzed. The fluid momentum conservation equation is solved for each cell by using a unit cell model, where a single cylinder is surrounded by a coaxial shell of the electrolyte solution. A closed-form expression for the transient electroosmotic velocity of the bulk fluid in the Laplace transform is obtained as a function of the ratio of the cylinder radius to the Debye screening length and the porosity of the fiber matrix. The effect of the fiber matrix porosity on the continuous growth of the electroosmotic velocity over time is substantial and complicated. For a fiber matrix with larger porosity, the bulk fluid velocity takes longer to reach a certain percentage of its final value. Although the final value of the bulk fluid velocity generally increases with increasing porosity, early velocities may decrease with increasing porosity. For a given fiber matrix porosity, the transient electroosmotic velocity is a monotonically increasing function of the ratio of the cylinder radius to the Debye length.

Multiscale Modeling of Thermoplastics Using Atomistic-Informed Micromechanics

A multiscale repeating unit cell model of a single spherulite containing four disparate length scales was developed to predict the thermoelastic behavior of semicrystalline thermoplastic materials for composite aerospace applications. The continuum level scales were fully coupled and modeled using the generalized method of cells and the high-fidelity generalized method of cells micromechanics theories. Data from molecular dynamics simulations were used as inputs for the amorphous and crystalline constituents in the multiscale continuum models. Effective Young’s modulus, shear modulus, Poisson’s ratio, coefficient of thermal expansion, and thermal conductivity were predicted for polyether ether ketone and polyether ketone ketone, showing good agreement with the available experimental data from the open literature. Moreover, it is shown that predicted properties are fairly insensitive to the fidelity of the micromechanics model used at the highest continuum scale or the assumed shape of the spherulite.

Analysis of deformation behavior of elliptical perforated auxetic metamaterials using a modified rotating square model

Abstract Although numerous studies have investigated the mechanical behavior of perforated auxetic metamaterials, elements, and structures, an efficient theoretical framework for quantifying the elastic properties of these extraordinary materials remains lacking. This study introduces a modified rotating square model that incorporates the deformation characteristics of auxetic materials with elliptical perforations, providing a more accurate representation of their behavior with idealized rigid square-spring-rod model. Finite element modeling of a representative unit cell of the metamaterial was employed to establish a database for parameter calibration and validation of the proposed analytical model. The results indicate that the deformation mechanism of the metamaterial is dominated by rotational deformation localized at the minimum ligaments between neighboring holes. The model predicts the elastic properties of the auxetic metamaterials with errors lower than 25%, demonstrating its effectiveness in capturing the complex deformation mechanisms of elliptical perforated auxetic structures. Additionally, the model contributes to developing design equations for lateral stiffness and shear strength in steel plate shear walls with elliptical perforated auxetic web plates. Future studies could extend the proposed model to other perforated auxetic metamaterials with various hole shapes.

Advanced Computational Modeling with FVDAM for Homogenization of Reinforced Concrete Beams

Reinforced concrete is widely used in civil engineering due to its strength, durability, and versatility. This material is heterogeneous, as it combines concrete with steel bars, giving it a tensile strength much higher than that of simple concrete. However, the computational modeling of this type of material is challenging due to the need to consider the distinct properties of the phases, generating considerable computational costs. According to Almeida (2018), the simulation process of reinforced concrete beams requires a meticulous analysis of the interactions between concrete and steel, as well as the non-linear behavior of the material under different load conditions. This complexity significantly increases the time and resources needed to perform accurate computational analyses. An alternative to modeling reinforced concrete is to replace it with a homogeneous material with properties/behaviors equivalent to those of the original heterogeneous material.The Finite-Volume Direct Averaging Micromechanics (FVDAM) method emerges as a promising and efficient alternative for obtaining the effective elastic properties of composite materials with complex microstructures. In this study, the efficacy of FVDAM in the homogenization of reinforced concrete beams was evaluated. The stiffness using this technique was compared with that obtained using the calculations presented by Pinheiro (2007). In addition, two unit cell models were compared, differentiating the shape of the fiber: square and circular (Escarpini and Almeida, 2023).In this work, it is expected to understand the influence of the fiber shape in the unit cell and compare the results of FVDAM with those of Pinheiro, in terms of stiffness, evaluating issues in the context of safety.

Effect of steel fibers on the stress–strain behaviour of aligned steel fiber ultra-high performance concrete under uniaxial compression

The mechanical properties of ultra-high performance concrete (UHPC) can be significantly enhanced by aligning the fibers. Aligned steel fiber UHPC (ASF-UHPC) was fabricated using a uniform magnetic field, yet the corresponding stress-strain relationship has not been extensively studied, hindering accurate calculations. To address this gap, ASF-UHPC was prepared and subsequently subjected to CT scans and uniaxial compression tests to investigate its stress-strain behavior. The analysis of failure mode and stress-strain curves revealed distinct anisotropic characteristics in compressive stresses and fiber distributions. Various steel fiber parameters, including the alignment orientation, volume fraction, and length, were systematically analysed to assess their impact on the material properties. A unit-cell model was developed to elucidate the influence of the fiber alignment orientation on UHPC performance. The results demonstrate that a parallel fiber alignment significantly enhances the elastic modulus, albeit with a Poisson ratio similar to that of the matrix, owing to the limited lateral confinement. Conversely, perpendicular fiber alignment restrains lateral deformation, enhancing the material strength and toughness. Randomly distributed fibers offered a degree of horizontal confinement, whereas inclined fibers induced horizontal thrust, leading to excessive lateral deformation and consequent elevation of the Poisson ratio. Finally, predictive equations for UHPC elastic modulus and compressive strength, along with an analysis model for stress-strain characteristics, were refined taking into account the direction of fiber arrangement.

A simplified interpolation algorithm for the numerical simulation of the consolidation in composite foundation containing group of stone columns

Based on Biot consolidation theory, a simplified interpolation algorithm under the finite element method and a corresponding modeling method for group of stone columns are proposed to solve the consolidation simulation problem of composite foundation containing group of stone columns. The correctness of the modeling method and computational program is confirmed by comparing the results from the unit cell model with those from axisymmetric model and analytical solution. Subsequently, the composite foundation model is used to verify the accuracy of this method in calculating the settlement change and consolidation time under load for composite foundation containing group of stone columns. Compared to detailed modeling, this method gets satisfactory results with simpler modeling and less computation time. In comparison to homogenization method, this method offers better computational accuracy and enables the stress analysis of stone column. Additionally, discussions on mesh sensitivity, number of stone columns and the influence of the upper structure provide guidelines for the application of this method in practical engineering projects.

A transmission problem for wave equations in infinite waveguides

We prove a decay estimate for solutions to a transmission problem for wave equations with different propagation speeds in an infinite waveguide. The problem represents the wave propagation in unbounded and layered composite materials in which different properties are given. It is a new composition of a waveguide problem and a transmission problem, motivated by a unit cell model for CFRP. The proof is based on splitting variables, partial eigenfunction expansions in the bounded cross section, and on an explicit Weyl type estimate for the eigenvalues.

PyFaults: a Python tool for stacking fault screening

PyFaults is an open-source Python library designed to model stacking fault disorder in crystalline materials and qualitatively assess the characteristic selective broadening effects in powder X-ray diffraction (PXRD). Here, the main capabilities of PyFaults are presented, including unit cell and supercell model construction, PXRD pattern calculation, assessment against experimental PXRD, and methods for rapid screening of candidate models within a set of possible stacking vectors and fault occurrence probabilities. This program aims to serve as a computationally inexpensive tool for identifying and screening potential stacking fault models in materials with planar disorder. Three diverse case studies, involving GaN, Li2MnO3 and Li3YCl6, are presented to illustrate the program functionality across a range of structure types and stacking fault modalities.

Energy absorption characteristics and auxetic effect of novel elliptic-arc re-entrant honeycomb structures

The novel elliptical-arc re-entrant honeycomb (ERH) is designed by substituting the straight inclined struts within the re-entrant honeycomb with elliptical-arc struts. To assess its performance effectively, the study established the 3D equivalent Cauchy model (3D-ECM) and 2D equivalent Kirchhoff–Love model (2D-EKM) using the variational asymptotic method. The equivalent properties derived from the unit-cell constitutive model were integrated into the equivalent models for macroscopic analysis. Through 3D printing experiments and numerical simulations, the model’s accuracy in predicting the compression behaviors and auxetic effects of various uni- and multi-cellular ERHs under uniaxial compression, as well as the three-point bending behaviors of ERH panels were confirmed. In addition, this model substantially simplifies the modeling process, leading to a 8-fold increase in computational efficiency. Parametric analyses demonstrated that the ERH structure can uphold a beneficial auxetic effect while achieving lightweight and high strength characteristics when the axial ratio of the ellipse equals 1.25. Furthermore, ERH structures outperform arc-shaped re-entrant and regular re-entrant honeycombs in energy absorption and specific energy absorption capacity. These findings offer valuable insights for the preliminary design and optimization of ERH structures.

A two‐scale numerical analysis of intra‐yarn hybrid natural/synthetic woven composites

AbstractThis paper investigates how combining natural and synthetic fibers within yarns, altering the degree of hybridisation, and varying weave architectures affect the homogenized elastic properties and stress distributions in 2D woven composite laminae using a two‐scale homogenization scheme. The novelty lies in integrating a micro‐scale representative volume element model with a meso‐scale repeating unit cell model to capture intra‐yarn natural/synthetic fiber hybridisation. The study focuses on 2/2 twill and 5‐harness satin woven laminae with flax/E‐glass, hemp/E‐glass and basalt/E‐glass hybrid yarns, all with a total fiber volume fraction of 0.6. Fiber distributions are created through a random sequential expansion algorithm for hybrid RVEs, while periodic meso‐structures are used to define weave architectures for RUCs. Results show that yarn‐level fiber hybridisation significantly influences matrix stress distributions, with variations of up to 22%. In contrast, weave architecture has a minimal effect, with variations in homogenized properties below 2%. Varying fiber types, degrees of hybridisation and weave architectures allow for the tailoring of yarn and lamina properties and altering the stress distributions at micro‐ and meso‐scales and potentially influencing damage mechanisms. The modeling approach for analyzing the mechanical behavior of intra‐yarn hybrid natural/synthetic woven laminae could potentially be used to tailor their tolerance to damage.Highlights Two‐scale homogenization integrates RVE and RUC for 2D woven hybrid composites. Analyzed flax/E‐glass, hemp/E‐glass, basalt/E‐glass in twill and satin weaves. Intra‐yarn hybridisation significantly affects properties and stress fields. Hybridizing fibers offers tailored properties and may improve damage tolerance.

A Gaussian statistics-based unit-cell modeling method for the mechanical behavior prediction of 2.5D shallow straight-link-shaped woven composites

The shallow straight-link-shaped structure of 2.5D woven composites (2.5D-SSLS-WC) is a novel material with a wide range of promising applications, but the randomness of its internal structure has brought challenges to performance prediction and engineering design. The gap of existing unit-cell models in capturing the internal randomness of the 2.5D-SSLS-WC material limits the accurate prediction of properties and the optimization of engineering design. In this work, the modeling method for random unit-cell model based on Gaussian distribution is proposed for 2.5D-SSLS-WC structure considering random distribution property of weft yarns and extrusion effects between structural surfaces and internal yarns during the molding process, which can more effectively reflect the practical mesoscopic structure of the material, reveal the micro mechanical behavior inside materials and provide theoretical basis for material design and performance optimization. The mechanical property and damage evolution of the proposed model is predicted and analyzed using finite element (FE) analysis and progressive damage method. The maximum errors of equivalent stiffness and strength between prediction and experimental values are 6.7% and 2.3%, respectively. The results show that the proposed model has high prediction accuracy and can reasonably reflect the damage extension and ultimate failure mode of the material during the loading process, which verifies the rationality of the proposed unit-cell modeling strategy. The modeling method proposed in this paper provides a new perspective for the in-depth understanding and description of the microstructure and mechanical behavior of 2.5D-SSLS-WC materials, which is of significant theoretical and engineering value and can be extended to the modeling of other woven composites.

Extended Unit Cell Model Employing Two Vectors for Crystal Structure Analysis in IrPd Nanoparticles for Catalysis

Extended Unit Cell Model Employing Two Vectors for Crystal Structure Analysis in IrPd Nanoparticles for Catalysis

Influence of concentration on thermophoresis of spherical aerosol particles within a Brinkman medium

Abstract We are examining the thermophoretic movement of a uniform mixture of spherical aerosol particles, all with the same properties, as they are situated within a porous material. These particles can have various thermal conductivity and surface characteristics. This analysis focuses on situations where the Péclet and Reynolds numbers are small. The influence of particle interactions is carefully considered by using a unit cell model, a well-established method known for its accurate predictions in the context of sedimentation for monodisperse suspensions of spherical particles. The porous medium is represented as a Brinkman fluid characterized by a Darcy permeability, which can be determined directly from experimental observations. This medium is considered to be uniform and isotropic, and the solid matrix is in thermal equilibrium with the fluid flowing through the voids of the medium. The Knudsen number is assumed to be low, enabling the description of fluid flow through the porous medium using a continuum model that includes temperature jump, thermal creep, frictional slip, and thermal stress slip at the aerosol particle’s surface. The conservation equations for energy and momentum are individually tackled within each cell. In this model, each cell represents a spherical particle enclosed by a concentric shell of surrounding fluid. The thermophoretic particle migration velocity is determined across different cases. We derive analytical expressions for this average particle velocity, expressing it in terms of the particle volume fraction. It is observed that different cell models yield somewhat varied results for particle velocity. Generally, with a fixed permeability parameter characterizing the porous medium, an increase in the thermal stress slip coefficient tends to decrease the normalized thermophoretic velocity across the different cell models. The results are in good agreement with the available data as documented in the existing literature. Additionally, a parallel examination of aerosol sphere sedimentation is provided.

Bandgap Control of Local Resonance Sandwich Meta-Plate with Cantilevered Archimedean Spiral Beam-Mass Resonators

In order to attenuate the various low-frequency vibrations that may cause structural fatigue and damage, impact human health and affect work efficiency, this paper presents a novel local resonance metamaterial sandwich meta-plate structure containing a cantilever spiral beam-mass resonator, and investigates vibration reduction effects of it within the obtained low-frequency bandgap range. For this purpose, a theoretical model of the low-frequency resonator being composed by a cantilever Archimedean spiral beam and cylindrical mass is established. The natural frequency of it is calculated by solving the Euler-Lagrange equation of the resonator. The accuracy and reliability of the theoretical model are verified through COMSOL simulation. The stress distribution of five types of cantilever spiral beam mass resonators (i.e. Archimedes spiral, triangle spiral, square spiral, pentagon spiral and hexagon spiral) and different cross-sectional shapes (rectangular, square, circular, diamond and triangular) are analyzed. Then, a unit cell model of a sandwich meta-plate with a cantilever Archimedean spiral beam resonator is selected. Hamilton’s principle is used to deduce the bandgap range under infinite periods, and the theoretical solutions are also verified. The parameter optimization of the substrate plate and resonator are also studied. Moreover, the effects of the various structural variables on the bandgap range are systematically explored. Finally, the dynamic responses of the sandwich meta-plate composed of [Formula: see text]-unit cells under different excitation frequencies, boundary conditions and structural damping are analyzed.

Rate-dependent constitutive behavior and mechanism of CMDB under tension loading

The composite modified double-base propellants (CMDB) were experimentally investigated for mechanical behavior under wide tension strain rate loading from 0.0001 s−1 to 2500 s−1, based on Instron mechanical machine and modified Hopkinson tension bar technique. Stress-strain curves were obtained for its strain rate effect and integrality evaluation. The results indicated that CMDB presents high rate-dependence with flow stress distinctly increase as loading strain rate increasing. A succinct constitutive formulation is established with only five parameters, to characterize well the rate-dependence and strain hardening behavior. The fracture morphologies were investigated by scanning electron microscopy, and it is indicated that they are also rate-dependent: the cavitation and matrix damage induced from matrix deformation work less but more RDX particles fractures with strain rate increasing. Equivalent unit cell model with brittle cracking was established to simulate the mechanical behavior and failure characteristics of CMDB. The results reveal that with increasing loading strain rates, CMDB presents a tough-brittle transition, with less cavitation and matrix damage induced by matrix deformation, while more RDX particles fracture. Series of simulated results confirm qualitatively the experimental observations, and the obtained stress contours facilitate to validate the observed characteristics and propose reasonable mechanisms.

Analytical prediction of the formation factor for anisotropic mono-sized unconsolidated porous media

The rectangular Representative Unit Cell (RUC) models for mono-sized isotropic unconsolidated porous media have been extended to anisotropic media. Volume averaging was applied to Ohm's law in order to propose analytical expressions for the formation factor for electrical conduction in terms of the pore-scale linear dimensions. The formation factor, crucial for understanding electrical conduction in porous media, has significant applications in subsurface geophysics, petroleum reservoir characterization, and the durability assessment of construction materials. These analytical models provide valuable insights for optimizing the electrical properties of porous structures in various engineering fields, for example in mapping groundwater resources, differentiating oil-bearing zones in reservoirs, and predicting ion migration in concrete. Aspect ratios of the cell and solid dimensions have been introduced, and the formation factor expressed in terms thereof for five different arrays, i.e. a regular, a non-overlapping streamwisely fully staggered, an overlapping streamwisely fully staggered, a non-overlapping transversally fully staggered, and an overlapping transversally fully staggered array. The Laplace equation has furthermore been solved numerically for two-dimensional versions of the different arrays and the formation factor computed for several values of the aspect ratios. The proposed analytical models have been validated against the generated numerical data and compared to experimental and numerical data obtained from the literature. The proposed models have also been adapted to include a percolation threshold porosity in order to improve the model predictions for very low porosity media.

Heat transfer mechanism and thermal conductivity prediction in short carbon fiber reinforced polymer composites

Carbon fiber is commonly used as a heat dissipation filler for composite materials in aerospace and electrical systems. Based on representative volume element (RVE) finite element simulation and mathematical analysis, the anisotropic thermal conductivity of short carbon fiber/polymer (SCF/polymer) composites under non-uniform factors was predicted and analyzed. A joint analysis method was proposed for uniform unit cell (UUC) model considering uniform factors and correction unit cell (CUC) model considering non-uniform factors. This article establishes a UUC model for SCF/polymer composites and investigates the effects of factors such as the thermal conductivity of the polymer matrix, the anisotropic thermal conductivity, aspect ratio, and deflection angle of SCF, and interfacial thermal resistance on the anisotropic thermal conductivity of the composite material. In order to study the influence of non-uniform factors, a CUC model of SCF/polymer composite materials was established, and the effects of position offset, angle deviation, and distribution ratio of SCF in different directions on the anisotropic thermal conductivity of composite materials were discussed. The results of the above non-uniform factors were analyzed, and the range of correction factors for three non-uniform factors was obtained. The accuracy of the joint analysis method of UUC and CUC in predicting the anisotropic thermal conductivity of SCF/polymer composites was verified by comparing experimental results.

Interaction of defects, martensitic transformation and slip in metastable body centred cubic crystals of Ti-10V-2Fe-3Al: A study via crystal plasticity finite element methods (CPFEM)

Metastable β titanium alloys are widely applied in many industries. These alloys can have plastic deformation via dislocation slip, twinning, stress-induced martensite (SIM), or a combination of these. These alloys fail in a ductile manner via a process of void nucleation, growth, and coalescence. Inherent defects, such as voids, are commonly attributed to poor mechanical properties. In this study, aspects of plastic anisotropy in damage accumulation are investigated for metastable crystals that deform by combined slip and SIM. The focus of this study is to understand the evolution of damage due to inherent voids in metastable Ti-10V-2Fe-3Al single crystals. This investigation is conducted using crystal plasticity-based 3D finite element (FE) calculations. A unit-cell FE model involving a spherical void is deformed under constant stress triaxiality and lode parameter. We investigated four triaxiality values at differing lode parameters in three crystal orientations. The void growth was found to be heavily dependent on crystal orientation at low triaxialities. At higher triaxialities, SIM is found to inhibit the void growth via accommodation of the required deformation in the surrounding material. Orientations aligned favourable with SIM undergo significantly less void growth. The accommodation of deformation in the surrounding matrix was found to help preserve the integrity of the void, preventing the localisation of deformation around the void. At lower lode parameter and at higher stress triaxiality this impedes the exponential growth of the void. While, at higher lode parameter with low triaxiality SIM was found to delay the collapse of the void into a crack like morphology. This study not only deepens our understanding of the mechanical behaviour of metastable β titanium alloys, but also unveils the complex interplay between inherent defects, stress-induced martensite, and slip-based plasticity within their crystalline structure, offering fresh perspectives on enhancing material performance.

Comparative analysis of varied thermal conductivity and viscosity models in a hybrid nanofluid flow - a non-similar solution

ABSTRACT We aim to investigate the flow of an ethylene glycol-based hybrid nanofluid over a horizontal surface with a free stream velocity. To assess the viscosity and thermal conductivity of nanoparticles with various shapes, we employed the Brinkman, Timofeeva, and Yamada Ota unit cell models. The study explores heat transfer in the flow system considering the effects of viscous and ohmic dissipations, linear radiative heat flux, and heat generation under convective boundary conditions. A non-similar system is developed using appropriate non-similarity transformations up to the third-level truncation and numerically solved using the bvp4c algorithm. The novelty of the proposed model lies in obtaining the non-similar solution and incorporating the Brinkman, Timofeeva, and Yamada Ota unit cell models. The results indicated that the Brinkman viscosity model resulted in an increase in the wall heat transfer rate with a rise in particle volume fraction. It is also inferred that platelet-shaped nanoparticles exhibit a significantly higher heat transfer rate compared to spherical-shaped nanoparticles.