Effective Modulus Research Articles

Novel experimental and multiscale study of additively manufactured ABS-carbon nanotubes nanocomposites

The additively manufactured (3D printed) nanocomposite parts demonstrate challenges in terms of poor dispersion and agglomeration. To investigate such structures advanced computational models are required to capture smaller-scale phenomena. This study proposes a novel three-scale computational model for calculating the mechanical properties of 3D-printed nanocomposites. The study also proposes a novel water-quenching experimental technique to prepare in situ nanocomposite sheets during nanocomposite filament manufacturing. The computational model integrates Halpin Tsai and Eshelby Mori Tanaka model at the microscale integrated with the asymptotic homogenization model at meso and macro scales to calculate the effective elastic modulus of 3D printed nanocomposite parts. The experimental characterization was performed by using the water quenching method to prepare 0.5 wt%, 1 wt%, 1.5 wt%, and 2 wt% multiwalled carbon nanotube (MWCNT)-ABS nanocomposite filaments, 3D printed parts, and finally tensile testing them. Furthermore, morphological analysis was conducted to study the dispersion and agglomeration effect and effectiveness of the proposed new method. Finally, the computational results were compared with experimental results to validate the model. Elastic modulus showed an increase of 2.79 %, 6.5 %, 9.6 %, and 12.6 % for 0.5 wt%, 1 wt%, 1.5 wt%, and 2.0 wt% CNT-ABS filaments. Similarly, for 2 wt% CNT-ABS and 0.5 wt% CNT-ABS 3D printed parts, a 20.4 % and 10.3 % increase was reported. In comparison with literature reporting a decrease of 3.35 % and an increase of 1 % in the elastic modulus for 1 wt% and 2 wt% CNT-ABS filaments, the present method reported an increase of 6.54 % and 12.6 % respectively. Moreover, for 1 wt% 3D printed part, an increase of 14.2 % compared to 1 % in the literature is reported.

PFC–FLAC coupling-based numerical simulation of triaxial test on soybean granular material

A discrete-continuous (PFC–FLAC) coupling method was used in this study to simulate laboratory triaxial tests with soybean granular material. The mesoscopic mechanical parameters of the soybean granular material were calibrated by comparing them with actual laboratory test results, and the validity of the modeling method was verified. Subsequently, the particle motion law and mechanical mechanism of the soybean granular materials were analyzed based on the particle displacement field, velocity field, and force chain network. The results showed that the coupled PFC–FLAC method could better describe the macroscopic stress–strain relationship, deformation damage characteristics, and shear strength mechanical indexes of soybean granular materials. With increasing confining pressure (50–200 kPa), the bulging deformation of the specimens changed from uniform to concentrated but uneven. The particle contact number and maximum particle contact stress increased by 19.3 and 48%, respectively. Additionally, variations of the macroscopic properties of the specimens with microscopic parameters were revealed. Under the same conditions, the change in the peak stress of the specimen was proportional to the interparticle friction coefficient. Moreover, the slope of the stress–strain curve increased gradually with an increase in the effective modulus.

Effect of Materials Parameters on the Shape of Face-On Lamellae in Semi-Conducting Polymers: Insights From Qualitative Theory.

Polymer semiconductors frequently form crystals or mesophases with lamellae, that comprise alternating layers of stacked backbones and side chains. Controlling lamellar orientation in films is essential for obtaining efficient charge carrier transport. Herein, lamellar orientation is investigated in an application-relevant setup: lamellae assembled on a substrate that strongly favors face-on orientation, but exposed to a film surface that promotes orientation along an "easy" direction, other than face on. It is assumed that the face-on order propagates from the substrate, but the lamellae bend to reduce their surface energy. A qualitative free-energy model is developed. The deformation is investigated as a function of film thickness, effective Young modulus, anchoring coefficient, and easy direction at the free surface. The calculations highlight the importance of elastic constants - lamellae can substantially deform already when Young moduli are only an order of magnitude smaller than the values that are reported for crystals. Softer Young moduli are expected when lamellar assembly occurs in a non-solidified mesophase that can be an equilibrium or (more speculatively) a transient state prior to crystallization. The alternative scenario of a two-layered film is also evaluated, where edge-on and face-on grains form, respectively, at the free surface andsubstrate.

A modified Gibson-Ashby model for functionally graded lattice structures

The current paper extends the classic Gibson-Ashby model of cellular solids for repetitive graded lattices. Three well-known porous unit cells, i.e., simple cubic (SC), body-centered cubic (BCC), and their combination (BCC＋), are considered and the corresponding graded lattices are geometrically defined by functional variation in the diameters of the ligaments based on a power law. The analytical expressions for the relative elastic modulus of the cells, which vary along the graded direction, are provided by structural analysis of the representative beam framework containing tapered beams using the Euler–Bernoulli theory. After that, continuous approximation functions for variation of the relative density and the relative elastic modulus are presented by curve fitting over the analytical expressions along the graded direction. Then, the graded lattices are considered to be fully homogenized and as a homogeneous media, the exact expressions for the effective relative density and the effective relative modulus are presented. The modified version of the Gibson-Ashby model is proposed to relate the effective relative modulus to the effective relative density by introducing a correction factor to the classic model. It is shown that the classic Gibson-Ashby model with the coefficients fitted on uniform lattices, is not accurate for relating the effective properties of the graded lattices. The proposed model, presented as an analytical expression with fitting parameters and a correction factor, serves as a useful guideline for designing optimized functionally graded lattice structures, accommodating a wide range of geometric variations.

A fast Fourier transform-based solver for elastic micropolar composites

This work presents a spectral micromechanical formulation for obtaining the full-field and homogenized response of elastic micropolar composites. The algorithm relies on a coupled set of convolution integral equations for the micropolar strains, where periodic Green’s operators associated with a linear homogeneous reference medium are convolved with functions of the Cauchy and couple stress fields that encode the material’s heterogeneity, as well as any potential material nonlinearity. Such convolution integral equations take an algebraic form in the reciprocal Fourier space that can be solved iteratively. In this vein, the fast Fourier transform (FFT) algorithm is leveraged to accelerate the numerical solution, resulting in a mesh-free formulation in which the periodic unit cell representing the heterogeneous material can be discretized by a regular grid of pixels in two dimensions (or voxels in three dimensions). For verification, the numerical solutions obtained with the micropolar FFT solver are compared with analytical solutions for a matrix with a dilute circular inclusion subjected to plane strain loading. The developed computational framework is then used to study length-scale effects and effective (micropolar) moduli of composites with various topological configurations.

Investigating the mechanical performance of graphene reinforced polymer nanocomposites via atomistic and continuum simulation approaches

Graphene, having exceptional mechanical properties, is expected to improve the overall mechanical performance of polymer nanocomposites when inserted as a nanofiller. In this work, the mechanical properties of graphene-based cis-1,4-polybutadiene glassy polymer nanocomposites are investigated via a hierarchical multiscale approach, combining atomistic simulations and continuum mechanics. The global mechanical properties of the graphene-based polymer nanocomposites are computed via a rich enough set of remote applied deformations. On a localized level, the effective Young's modulus and Poisson's ratio are calculated in both the interphase and polymer matrix regions where the former shows greater rigidity. Finally, the properties of the different phases forming the heterogeneous polymer nanocomposite are used to develop a continuum three-phase micromechanical finite element model for predicting the overall mechanical behavior of the structure, which are found to be in very good agreement with the results from the atomistic MD simulations.

Lightweight soundproofing meta-panel for two separate broadband noises

We propose a lightweight soundproofing meta-panel, with a multi-scale lattice structure sandwiched between thin membranes, effectively suppressing two separate broadband noises. By adjusting the geometrical parameters, the meta-panel is designed to induce negative effective mass density and negative effective bulk modulus for two distinct target frequency bands: 100–500 Hz and 1000–1500 Hz, thereby achieving high transmission loss that outperforms the mass density law. A meta-panel sample is fabricated via 3D printing technology and we evaluate its sound insulation performance by measuring transmission loss and insertion loss in an impedance tube and an anechoic chamber. Experimental measurements show that the meta-panel can exhibit excellent insulation performance while being significantly lighter in weight (about 5%) compared to a steel plate, and furthermore, it effectively suppresses low-frequency road noise and high-frequency motor noise from an actual electric car.

The influence of Bi nonstoichiometry on the depolarization temperature in lead-free piezoelectric Na0.5Bi0.5+xTiO3+1.5x

The influence of Bi-nonstoichiometry of Na0.5Bi0.5+xTiO3+1.5x (NBT) on the depolarization temperature Td was investigated by in-situ direct piezoelectric measurements (d33) and Resonant Piezoelectric Spectroscopy (RPS). For the latter measurements, the converse piezoelectric effect was used to determine the temperature dependence of the piezoelectric effect and elastic modulus. The composition x = 0.01 shows Td = 137 °C, whereas in x = 0 and x = 0.015 Td = 177 °C. The composition with x = 0 has defects, such as oxygen/bismuth vacancies, related to the loss of Bi2O3 that occurs during high temperature sintering, such as oxygen/bismuth vacancies. At x = 0.01, these defects are minimized via the compensation of Bi2O3 loss, whereas x = 0.015 contains excess Bi2O3. This indicates that minimization of defects decreases Td, while higher Td values are attributed to the shift of the transition temperature between the rhombohedral and the intermediate phases.

Measurement and analysis of winding stresses in dry-wound pancake coils considering nonlinear compressive behaviors

Considering coil stress management, conductor thermal stability, and susceptibility to delamination, the dry-winding approach has been gradually applied and tested in high-temperature-superconducting coils wound with REBa2Cu3O (REBCO) coated conductors (CCs). In dry-wound coils, the winding tension can be a useful tool for managing the mechanical stresses and maintaining the structural stability. It is also related to the contact resistivity characteristics of no-insulation and metal-as-insulation coils. In this paper, we present a study on the winding stresses in dry-wound pancake coils considering nonlinear compressive behaviors in the radial direction. Coils wound with stainless-steel (SS) tapes and REBCO CCs were prepared, respectively, with various sizes (90–140 turns) and winding tensions (26–61 MPa). The radial pressure was obtained by applying the pressure measurement films, which cover a pressure range up to 50 MPa. A relatively moderate radial pressure buildup was observed in coils wound with SS tapes, indicating that the effective radial modulus of the coil as an entity is considerably lower compared to the tensile modulus in the azimuthal direction. This is consistent with the nonlinear stress–strain relationship of stacked thin sheets under transverse compression, which can be further explained by the contact behaviors between two rough surfaces. The average radial pressure in CC coils shared similar characteristics as that in SS coils, whereas the radial stress along the conductor edges were significantly higher compared to the middle. Cross-sectional microscopy of the CCs suggests that this can be primarily attributed to the thickness variations across the conductor width. These results suggest that the microscopic rough-surface contact and thickness variation of the wound tape play a critical role in the coil stiffness as well as the winding stress distributions.

Informatics guided FE design of bioactive titanium alloy/composite multi-layered dental implants

A dental implant with three distinct layers, of titanium alloy at core, porous titanium alloy at the intermediate layer and titanium alloy hydroxyapatite composite at the outer layer, is designed to achieve low elastic modulus and adequate strength with bioactive surface. Artificial Neural Network (ANN) along with Rule of Mixture (ROM) is used to generate the objective functions for the Genetic Algorithm (GA) based multi-objective optimization for achieving the optimal designs, which are validated using Finite Element Analysis (FEA) simulations. The composition and processing parameters are correlated with the yield strength and elastic modulus of titanium alloy using ANN. The ANN models are generated to express the strength and effective modulus of the implant using ROM. To determine the optimal composition of titanium alloys, porous layers, and composite layers for a three-layer dental implant, multi-objective genetic algorithm is employed. The Pareto optimal solutions provide the guidelines for designing the implant. A few selected non-dominated solutions are used for studying the actual stress distribution at the bone-implant interface using FEA, and showed significant improvements compared to conventional implants.

Surface wrinkling of a film on an anisotropic substrate

This paper presents analytical solution for wrinkling of thin film bonded to anisotropic substrate by complex function method and linear perturbation analysis, which is verified by FEM. Effect of material parameters along principal axes on critical strain is illustrated. Furthermore, due to effective modulus determined by Voigt assumption, a fiber-reinforced substrate is considered, and results indicate that both Young’s modulus perpendicular to wrinkling direction and in-plane shear modulus have significant influence on wrinkling onset point. The most effective fiber layout in resisting wrinkling is at about 45°inclined to wrinkling direction and arranging at the upper area of the substrate.

Determination of elastic characteristics for a package of monolayers thin-walled plates from composite fibrous materials

An analytical method for calculating the equivalent elastic characteristics of anisotropic multilayer plates made of composite fibrous materials is laid out. The main assumptions taken into consideration when calculating elastic moduli and Pousson's coefficients are that fibers are elastic materials with orthotropic mechanical characteristics that deform together when multilayer plates are loaded. Analytical methods for calculating effective modulus of elasticity most common in practical applications of applied mechanics are laid out in the list of cited publications. These include the rules of the mixture, the model proposed by Hill and Khashin, the model of Kilchinsky, the methods of Vanin and L.P. Khoroshun. Numerical methods for determining the elastic mechanical properties of reinforced unidirectional and layered composite materials are based on information technologies of finite-element modeling of representative volumes of composite materials and solving a number of boundary value problems for them. For the constructions of thin-walled plates with composite fibrous materials, traditional calculation schemes are used, for which the plane stress state is typical. The stress-strain relationship for a monolayer of plates loaded at an arbitrary angle is presented in the form of Hooke's law for aniotropic materials. Deformations of a package of monolayers with composite fibrous materials in a plane elastic-deformed state are determined, as for a monolayer, by four independent elastic constants. With the use of a universal calculation model based on the equations of applied mechanics, the results of the calculations of elastic moduli and Poisson's coefficients were obtained for a package of monolayers of thin-walled plates with composite fibrous materials made of carbon fiber and carbon fiber. Research results are presented in an analytical and graphic form. The influence of the construction structure of composite fibrous materials of thin-walled plates on its mechanical properties and their dependence on the angle of the force load vector is presented. The research results can be used to determine the rational mechanical properties of multilayer composite plates, taking into account their structural and technological purpose in various industries.

A high resolution inversion method for fluid factor with dynamic dry-rock VP/VS ratio squared

As an important indicator parameter of fluid identification, fluid factor has always been a concern for scholars. However, when predicting Russell fluid factor or effective pore-fluid bulk modulus, it is necessary to introduce a new rock skeleton parameter which is the dry-rock VP/VS ratio squared (DVRS). In the process of fluid factor calculation or inversion, the existing methods take this parameter as a static constant, which has been estimated in advance, and then apply it to the fluid factor calculation and inversion. The fluid identification analysis based on a portion of the Marmousi 2 model and numerical forward modeling test show that, taking the DVRS as a static constant will limit the identification ability of fluid factor and reduce the inversion accuracy. To solve the above problems, we proposed a new method to regard the DVRS as a dynamic variable varying with depth and lithology for the first time, then apply it to fluid factor calculation and inversion. Firstly, the exact Zoeppritz equations are rewritten into a new form containing the fluid factor and DVRS of upper and lower layers. Next, the new equations are applied to the four parameters simultaneous inversion based on the generalized nonlinear inversion (GNI) method. The testing results on a portion of the Marmousi 2 model and field data show that dynamic DVRS can significantly improve the fluid factor identification ability, effectively suppress illusion. Both synthetic and filed data tests also demonstrate that the GNI method based on Bayesian deterministic inversion (BDI) theory can successfully solve the above four parameter simultaneous inversion problem, and taking the dynamic DVRS as a target inversion parameter can effectively improve the inversion accuracy of fluid factor. All these results completely verified the feasibility and effectiveness of the proposed method.

Reinforcing Tissue‐Engineered Cartilage: Nanofibrillated Cellulose Enhances Mechanical Properties of Alginate Dialdehyde–Gelatin Hydrogel

Cartilage tissue engineering offers a promising option for treating osteochondral defects. Alginate dialdehyde–gelatin (ADA–GEL) hydrogel has been explored as promising material for soft tissue scaffolds; however, its low stiffness has posed a constraint to load bearing applications. Herein, this limitation is addressed by introducing nanofibrillated cellulose (NFC) into the ADA–GEL matrix. The effect of NFC on the physicochemical properties of hydrogels is evaluated. Fourier transform infrared spectra demonstrate no chemical interaction between NFC and ADA–GEL, while scanning electron microscopy pictures reveal NFC fibers embedded in the hydrogel matrix, thus confirming the fiber‐reinforced composite hypothesis. NFC‐reinforced ADA–GEL (AG‐N) composite hydrogels exhibit increased stiffness, with a maximum compressive effective modulus of 19.6 ± 3.0 kPa at 25% w/w NFC content. ATDC5 cell viability and proliferation as well as chondrogenic differentiation are assessed using immunohistochemical staining for sulfated glycosaminoglycans and collagen type II. A possible application of AG‐N hydrogels as an osteochondral plug is also proposed, with polyetheretherketone as the subchondral bone anchor part. The mechanical properties of the resulting osteochondral device highlight its potential as a promising biomaterial for treatment of osteochondral defects. These findings provide valuable insights into the development of AG‐N hydrogels for load‐bearing tissue engineering applications.

Parametric investigation of bonded composite joints under Mode II using a new methodology based on design of experiments

ABSTRACT In the pursuit of a sustainable future with limited resources and growing environmental concerns, adhesive joining stands out as a pivotal technology for the advancement of lightweight structures. This study aims to investigate the influence of various variables on the critical strain energy release rate in mode II (GIIc) for End-Notched Flexure (ENF) bonded composite joints, employing a new methodology based on Design of Experiments (DoE) approach. Two-dimensional finite element models of the ENF bonded composite joints are developed using commercial software, with all numerical models generated via Python™ scripts linked with AbaqusⓇ. Eleven design parameters related to the specimen geometry and material properties are systematically evaluated to determine the influence of each variable on GIIc. Numerical force–displacement curves are obtained, followed by the application of the Compliance-Based Beam Method (CBBM) to estimate the critical fracture energy in mode II, represented by a numerical envelope. The influence of each parameter is assessed using the main effect (ME) metric. The top five most influential variables affecting GIIc and CBBM are identified as the adhesive’s critical strain energy release rate in mode II (GIIc), effective laminate longitudinal elastic modulus (), adhesive thickness (tA), adherent thickness (h), and pre-crack length (). Furthermore, the study highlights the epistemic uncertainty associated with the geometric variables. Despite the limitations inherent in the computational model, the Plackett-Burman method consistently proves effective in conducting sensitivity analysis of the variables in the ENF test. These findings demonstrate promising prospects for the application of this procedure in the design of composite joint structures.

In-Silico Prediction of Mechanical Behaviour of Uniform Gyroid Scaffolds Affected by Its Design Parameters for Bone Tissue Engineering Applications

Due to their excellent properties, triply periodic minimal surfaces (TPMS) have been applied to design scaffolds for bone tissue engineering applications. Predicting the mechanical response of bone scaffolds in different loading conditions is vital to designing scaffolds. The optimal mechanical properties can be achieved by tuning their geometrical parameters to mimic the mechanical properties of natural bone. In this study, we designed gyroid scaffolds of different user-specific pore and strut sizes using a combined TPMS and signed distance field (SDF) method to obtain varying architecture and porosities. The designed scaffolds were converted to various meshes such as surface, volume, and finite element (FE) volume meshes to create FE models with different boundary and loading conditions. The designed scaffolds under compressive loading were numerically evaluated using a finite element method (FEM) to predict and compare effective elastic moduli. The effective elastic moduli range from 0.05 GPa to 1.93 GPa was predicted for scaffolds of different architectures comparable to human trabecular bone. The results assert that the optimal mechanical properties of the scaffolds can be achieved by tuning their design and morphological parameters to match the mechanical properties of human bone.

Grain-Level Numerical Simulations for the Effective Elasticity of Weakly Cemented Sandstones.

Weakly cemented sandstones are characteristic of loose-bonding contacts, large porosities, and high-clay contents. This study presents a discrete element method (DEM)-based numerical study for the effective elasticity of such rocks that mainly depends on the mechanical behavior of intergranular contact regions. The DEM scheme employs a set of normal and shear springs to phenomenologically describe the mechanical behavior of intergranular finite-sized cements defined by three morphological parameters: cement thickness, bonding radius, and grain radius. Applications to two digital models established in terms of contact-bonding and distant-bonding modes, respectively, where spherical quartz grains are randomly packed together with adding cements under the specified confining pressure, are compared with the theoretical predictions by the contact-bonding and distant-bonding cement theories, which demonstrates a good agreement generally for small contact widths, small contact thicknesses, and large-magnitude moduli, especially for the effective shear modulus. Applications to a series of artificial sandstone samples made in terms of different proportions of quartz grains and clays (a mixture of epoxy and kaolinite) under loose compaction for weak cementation demonstrate a good agreement with ultrasonic measurements. Numerical investigations for the micromechanical characteristics (differential stress fields, force chains, and fabric tensors) of artificial samples subject to applied axial strains demonstrate that the strong mechanical behavior of weakly cemented sandstones tends to appear inside the cohesive aggregates of stiff grains because of their relatively large sizes with loose compaction.

Estimating the elastic modulus of landfast ice from wave observations

AbstractProgress in our understanding of wave–ice interactions is currently hindered by the lack of in situ observations and information of sea-ice properties, including the elastic modulus. Here, we estimate the effective elastic modulus of sea ice using observations of waves in ice through the deployment of three open-source geophone recorders on landfast sea ice. From observations of low-frequency dispersive waves, we obtain an estimate of the effective elastic modulus in the range of 0.4–0.7 GPa. This is lower than the purely elastic modulus of the ice estimated at 1 GPa as derived from in situ beam experiments. Importantly, our experimental observation is significantly lower than the default value currently in use in wave models. While our estimate is not representative for all sea ice, it does indicate that considerably more measurements are required to provide confidence in the development of parameterizations for this complex sea-ice property for wave models.

Mechanical modelling of viscoelastic hierarchical suture joints and their optimisation and auxeticity

It has been widely recognised that suture joints play a fundamental role in the exceptional mechanical properties of many biological structures like the cranium and ammonite fossil shells. Up to date, many efforts have been devoted to investigate suture interfaces to predict the relations between the characteristics of its two phases, the teeth and the interface layer, and the structure effective properties. However, in very few works the viscoelasticity of the suture components has been taken into account. To provide a contribution in this limitedly explored research area, this paper describes the mathematical formulation and modelling technique leading to explicit expressions for the effective properties of viscoelastic suture joints with a general trapezoidal waveform. It emerges a strong influence of the suture geometric and mechanical characteristics on the effective properties and a parametric analysis reveals that an auxetic behavior can be obtained simply by tailoring the suture parameters. The effects of adding hierarchy into the above system are also explored and closed-form relations for the effective moduli are derived. Optimal levels of hierarchy can be identified and, similarly to the non-hierarchical case, an auxetic behavior emerges for particular values of the suture parameters. Finally, an extension of the theory to the sinusoidal sutures in biology is reported. By considering the examples of the cranium and the woodpecker beak, it emerges that the first is optimised to obtain high stiffness, while the second to obtain high energy dissipation levels.

Composite slab floors made of cross laminated timber and ultra high-performance concrete: Early-age deflection, stripping time, and its implication on the structural performances

Timber-Concrete Composite floors made of Cross-Laminated Timber (CLT) and Ultra-High-Performance Concrete (UHPC) boast remarkable efficiency in lightweight and slenderness. While the rapid UHPC hardening facilitates swift construction, the optimal shoring time depends on the effect of the UHPC autogenous shrinkage on the floor deflection. This study aims to investigate the experimental deflection of CLT-UHPC floors at an early age without shoring and to develop a simplified model for predicting the optimal shoring time for TCC floors.An eco-friendly UHPC with recycled glass waste is considered in this study. Firstly, the evolution of its modulus of elasticity and compressive strength as well as the early-age shrinkage were experimentally characterized. Furthermore, the shear behavior of the notch connection was evaluated after 28 days, and it was estimated to be proportional to the stiffness of the concrete at an early age. Then, two TCC floors made of CLT-UHPC with a span of 3.6 m were cast and their deflection under the self-weight of fresh concrete was measured over the initial 28-day period in a simple supported configuration without the use of shoring. A simplified analytical model was developed to predict the TCC deflection at an early age by coupling an existing solution with the concept of Age-Adjusted Effective Modulus (AAEM). The model effectively predicted the experimental early-age deflection of the CLT-UHPC floor without the use of shoring. Finally, after 3 months, the TCC floors were tested under bending, showing a reduced structural stiffness of about 35 %, caused by concrete cracking due to restrained shrinkage. The parametric analysis with the developed analytical tool allowed for estimating the maximum span of CLT-UHPC floors without shoring or, for longer spans, the optimal time of shoring removal. This study offers valuable insights into the behavior of CLT-UHPC along, along with a robust analytical tool to optimize their design and construction of TCC floors.