Longitudinal Shear Modulus Research Articles

Minimum energy combined and separated bounds on elastic constants of transversely-isotropic composites

The considered linearly-elastic transversely-isotropic composite (TIC) is composed of n isotropic, or more generally, transversely-isotropic components sharing the materials’ common symmetry axis with that of the macroscopic material. Using the basic minimum energy and complementary energy principles with certain free-parameter-dependent mixed-longitudinal-transverse-mode strain and stress trial fields, various combination bounds involving some sets of the macroscopic (effective) mixed-mode elastic constants of the composite, which are inter-connected via the constitutive relations, have been established. Choosing the appropriate parameter values of/or optimizing over the free parameters in those inequalities, the separated bounds on the major effective mixed-transverse-longitudinal-mode elastic constants, including the transverse bulk modulus Keff, the longitudinal Young modulus Eeff, and the longitudinal Poisson’s ratio νeff, are derived, beside the classical arithmetic and harmonic average bounds on the pure-mode ones — the transverse shear (μeff) and longitudinal shear (μ̄eff) moduli. The separated bounds on 4 remaining effective mixed-mode elastic constants are also obtained. The illustrative numerical comparisons of the bounds, in the two component case, with those for the special subclass of unidirectional transversely-isotropic composites (UTIC), having the unidirectional cylindrical boundaries between the component materials parallel to their symmetry axis, and the exact coated-cylinder assemblage and laminate models are presented. The extreme models cover substantial parts between the bounds for TIC; however the laminate models lie outside the bounds for the subclass UTIC.

Measurement of maize stalk shear moduli.

Maize is the most grown feed crop in the United States. Due to wind storms and other factors, 5% of maize falls over annually. The longitudinal shear modulus of maize stalk tissues is currently unreported and may have a significant influence on stalk failure. To better understand the causes of this phenomenon, maize stalk material properties need to be measured so that they can be used as material constants in computational models that provide detailed analysis of maize stalk failure. This study reports longitudinal shear modulus of maize stalk tissue through repeated torsion testing of dry and fully mature maize stalks. Measurements were focused on the two tissues found in maize stalks: the hard outer rind and the soft inner pith. Uncertainty analysis and comparison of multiple methodologies indicated that all measurements are subject to low error and bias. The results of this study will allow researchers to better understand maize stalk failure modes through computational modeling. This will allow researchers to prevent annual maize loss through later studies. This study also provides a methodology that could be used or adapted in the measurement of tissues from other plants such as sorghum, sugarcane, etc.

Identifying significant factors affecting plate stiffness of innovative CLT using Random Forest analysis

Abstract Innovative cross-laminated timber (CLT) is a relatively new engineered timber product. It is a new version of CLT having large gaps between lateral lamellas. Since it is a new material, the mechanical performance of this innovative material is not studied yet despite these advantages. This paper explores the factors that influence membrane, bending, shear, and torsional stiffness in innovative CLT and their implications, acknowledging the significance of knowing the plate stiffness of these innovative materials in predicting their behaviour and promoting their use in construction as bio-based materials. Using a large database of plate stiffness moduli derived from finite element computations and incorporating microstructural characteristics such as layer thicknesses, board width, gap width, longitudinal modulus of elasticity, longitudinal shear modulus, and rolling shear modulus of timber, Random Forest analysis was employed to study the significance of factors affecting plate stiffness in innovative CLT. Our results show that the gap affects the membrane, shear, and torsional stiffness for innovative CLT. However, the trans-versal layer thickness primarily controls the bending stiffness.

Testing of wood shear modulus based on cantilevered square plate torsional vibration method

ABSTRACT The application of the energy method has proposed a dynamic testing method for the shear modulus in two mutually perpendicular directions on the principal surface of wood using a cantilevered square plate torsional vibration method. In the study, this method was applied to measure the shear modulus of larch wood in the LT and TL directions, as well as the longitudinal and transverse shear modulus of Laminated Veneer Lumber (LVL) sheets. The validity of the results was confirmed through experimental verification using the asymmetric four-point bending beam method, the free plate torsional vibration method, and the free square plate torsional mode method. Simulation calculations of the principal shear modulus for six species of trees with width-to-thickness ratios ranging from 10 to 25 were also conducted using this method. The conclusions drawn suggest that a width-to-thickness ratio of 15 for the cantilevered square plate provides sufficient accuracy for testing the principal shear modulus of wood. Furthermore, the difference in shear modulus between two mutually perpendicular directions on the principal surface of wood is dependent on the width-to-thickness ratio of the cantilevered square plate, indicating that this method outperforms other dynamic methods for testing wood shear modulus.

Experimental and numerical investigation on the elastic properties of luffa–cenosphere‐reinforced epoxy hybrid composite

AbstractEstimating the elastic characteristics of natural fiber‐reinforced polymer composites such as luffa fiber reinforced with epoxy is challenging. The structure of luffa cylindrica is complex, like a three‐dimensional natural fibrous mat, netting‐like structure. The multiscale modeling of such structures is the challenge to be addressed. The prime objective of this work is to determine the specific elastic properties of luffa–cenosphere‐reinforced epoxy (LCE) composite, considering the effect of filler volume fractions. Furthermore, multiscale modeling techniques, such as representative volume elements (RVEs) of finite element techniques with chopped, unidirectional, plain, and twill weaving fiber arrangements, were employed. The longitudinal modulus, transverse modulus, shear modulus, and Poisson's ratio were predicted through these modeling approaches. However, experimental and analytical methodologies, including the rule of mixture and Halpin–Tsai, were considered to validate the finite element analysis results. The elastic characteristics of LCE composite were therefore shown to be enhanced by increasing filler volume fraction. However, the cenosphere's 20% volume fraction has the highest elastic properties as determined by analytical, experimental, and computational models. Analytical and finite element simulation results were compared with the experimental results, and based on the findings, the most suitable (unidirectional, chopped, plain, and twill weaving) RVE was identified for finite element modeling of LCE composite for the evaluation of elastic properties. Results from practical approaches and the RVE twill weaving model showed good agreement, with less than 1% error, compared to the other analytical and finite element methods.Highlights NFCs are gaining ground in polymer composites. Overcoming challenges in modeling of luffa fiber inside epoxy matrix. The study uses multiscale modeling with diverse fiber arrangements. Experimental and analytical methods used to confirm FEA results. Increased cenosphere volume fraction boosts LCE composite properties.

Effective mechanical properties of frozen hydrogel with ice inclusions

Hydrogel exhibits attractive mechanical properties that can be regulated to be extremely tough, strong and resilient, adhesive and fatigue-resistant, thus enabling diverse applications ranging from tissue engineering scaffolds, flexible devices, to soft machines. As a liquid-filled porous material composed of polymer networks and water, the hydrogel freezes at subzero temperatures into a new material composed of polymer matrix and ice inclusions: the frozen hydrogel displays dramatically altered mechanical properties, which can significantly affect its safety and reliability in practical applications. In this study, based upon the theory of homogenization, we predicted the effective mechanical properties (e.g., Young's modulus, shear modulus, bulk modulus and Poisson ratio) of a frozen hydrogel with periodically distributed longitudinal ice inclusions. We firstly estimated its longitudinal Young's modulus, longitudinal Poisson ratio and plane strain bulk modulus using the self-consistent method, and then its longitudinal and transverse shear modulus using the generalized self-consistent method; further, the results were employed to calculate its transverse Young's modulus and transverse Poisson ratio. We validated the theoretical predictions against both finite element (FE) simulation and experimental measurement results, with good agreement achieved. We found that the estimated transverse Poisson ratio ranges from 0.3 to 0.53 and, at low volume fraction of ice inclusions, exhibits a value larger than 0.5 that exceeds the Poisson ratios of both the polymer matrix and the ice inclusion (typically 0.33–0.35). Compared with other homogenization methods (e.g., the rule of mixtures, the Halpin-Tsai equations, and the Mori-Tanaka method), the present approach is more accurate in predicting the effective mechanical properties (in particular, the transverse Poisson ratio) of frozen hydrogel. Our study provides theoretical support for the practical applications of frozen liquid-saturated porous materials such as hydrogel.

Elastic and inelastic behavior of boron nitride nanocones at finite strains

This research is carried out to characterize the mechanical behavior of boron nitride nanocones (BNNCs) via molecular dynamics (MD) simulations using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). The calculations of atomic interactions are performed based on the Tersoff-type potential function. The five elastic moduli are determined by applying four mechanical loadings i. e. uniaxial stretching, axial twist, plane-strain biaxial tension, and in-plane shear. It is found that all elastic constants depend on the apex angle of BNNCs, whereas wider ones have lower Young's and longitudinal shear moduli. In contrast, as the apex angle of the nanocones increases, their plane-strain bulk moduli and in-plane shear constants increase. In addition, Poisson's ratio decreases with an increase in the apex angle and length of the BNNCs. Moreover, the shorter and sharper BNNCs, the higher values of strain at which they fail under uniaxial tensile and axial twist loadings.

Measuring elastic parameters of transversely isotropic materials by cylindrical indentation

Based on the cylindrical indentation experiments, a novel model for characterizing the elastic mechanical property of transversely isotropic materials has been established. The cylindrical indentation of transversely isotropic materials was theoretically and dimensionally analyzed. Three-dimensional (3D) indentation experiments that encompass the wide range of transversely isotropic material parameters were simulated by finite element. The effect of each parameter (transversely isotropic Young’s modulus, EP , longitudinal Young’s modulus, EL , longitudinal shear modulus, GL , and loading orientation angle, α) on the normalized indentation modulus was investigated. Then, the dimensionless analytical relationship between indentation moduli and elastic parameters was obtained at three different indentation orientations . Several groups of transversely isotropic materials were selected as input parameters to carry out numerical indentation experiments for the error analysis. The sensitivity of the calculated elastic parameters to the experimental data was analyzed. Simultaneously, the technique was used in the particular case of a Zinc single-crystal material, and the accuracy of these derived formulas was verified. The good agreement shows that the proposed method is reliable and could be applied to characterize the elastic parameters of transversely isotropic materials.

A stress disturbance barrier on a circular torque tube blocking the end effects

AbstractKnowing that the end effects arising from the end torsional loads will disturb the stress distribution in a torque tube, this paper develops a means of blocking the stress disturbances from the end where a torsional load is applied, such that the stress distributions of the Saint-Venant torsion can be maintained. The stress disturbance barrier (SDB) as an end effect shielding barrier is considered installed on an end of a circular toque tube whose material property can be with the cylindrical orthotropy. In general, the SDB is comprised of two layers: the front layer and the blocking layer. The front layer, which is optional and directly contacted with the external load, is for enhancing the durability, while the blocking layer situated between the front layer and the torque tube body is mainly for blocking the stress disturbances. The analysis is based on the state-space formalism, whose uncoupling feature on cylindrically orthotropic materials is beneficial for the further extension of the research. It is found that the parameters crucial to determine an effective SDB with a given thickness are the cylindrical orthotropy parameter and the longitudinal shear modulus. The approach of how to determine the proper material constants for having an effective SDB is clearly provided. As shown by the numerical results presented in the examples, an effective SDB of this research can fully block the stress disturbances from the external torsional loads that can be mathematically expanded by power series.

Parametric Analysis of SV Mode Shear Waves in Transversely Isotropic Materials Using Ultrasonic Rotational 3-D SWEI.

Ultrasonic rotational 3-D shear wave elasticity imaging (SWEI) has been used to induce and evaluate multiple shear wave modes, including both the shear horizontal (SH) and shear vertical (SV) modes in in vivo muscle. Observations of both the SH and SV modes allow the muscle to be characterized as an elastic, incompressible, transversely isotropic (ITI) material with three parameters: the longitudinal shear modulus μL , the transverse shear modulus μT , and the tensile anisotropy χE . Measurement of the SV wave is necessary to characterize χE , but the factors that influence SV mode generation and characterization with ultrasonic SWEI are complicated. This work uses Green's function (GF) simulations to perform a parametric analysis to determine the optimal interrogation parameters to facilitate visualization and quantification of SV mode shear waves in muscle. We evaluate the impact of five factors: μL , μT , χE , fiber tilt angle [Formula: see text], and F-number of the push geometry on SV mode speed, amplitude, and rotational distribution. These analyses demonstrate that the following hold: 1) as μL increases, SV waves decrease in amplitude so are more difficult to measure in SWEI imaging; 2) as μT increases, the SV wave speeds increase; 3) as χE increases, the SV waves increase in speed and separate from the SH waves; 4) as fiber tilt angle [Formula: see text] increases, the measurable SV waves remain approximately the same speed, but change in strength and in rotational distribution; and 5) as the push beam geometry changes with F-number, the measurable SV waves remain approximately the same speed, but change in strength and rotational distribution. While specific SV mode speeds depend on the combinations of all parameters considered, measurable SV waves can be generated and characterized across the range of parameters considered. To maximize measurable SV waves separate from the SH waves, it is recommended to use an F/1 push geometry and [Formula: see text].

Numerical Analysis of Micro-Residual Stresses in a Carbon/Epoxy Polymer Matrix Composite during Curing Process.

The manufacturing process in thermoset-based carbon fiber-reinforced polymers (CFRPs) usually requires a curing stage where the material is transformed from a gel state to a monolithic solid state. During the curing process, micro-residual stresses are developed in the material due to the different chemical–thermal–mechanical properties of the fiber and of the polymer, reducing the mechanical performance of the composite material compared to the nominal performance. In this study, computational micromechanics is used to analyze the micro-residual stresses development and to predict its influence on the mechanical performance of a pre-impregnated unidirectional CFRP made of T700-fibers and an aeronautical grade epoxy. The numerical model of a representative volume element (RVE) was developed in the commercial software Abaqus® and user-subroutines are used to simulate the thermo-curing process coupled with the mechanical constitutive model. Experimental characterization of the bulk resin properties and curing behavior was made to setup the models. The higher micro-residual stresses occur at the thinner fiber gaps, acting as triggers to failure propagation during mechanical loading. These micro-residual stresses achieve peak values above the yield stress of the resin 55 MPa, but without achieving damage. These micro-residual stresses reduce the transverse strength by at least 10%, while the elastic properties remain almost unaffected. The numerical results of the effective properties show a good agreement with the macro-scale experimentally measured properties at coupon level, including transverse tensile, longitudinal shear and transverse shear moduli and strengths, and minor in-plane and transverse Poisson’s ratios. A sensitivity analysis was performed on the thermal expansion coefficient, chemical shrinkage, resin elastic modulus and cure temperature. All these parameters change the micro-residual stress levels and reduce the strength properties.

Mechanical and radiation shielding properties of CuO doped TeO2–B2O3 glass system

A series of borotellurite glass system doped with copper oxide was synthesized using the method of melt quenching. The density of the glass decreases whereas its molar volume increases in respect to copper oxide concentration. The amorphous nature of prepared glasses was proven with the utilisation of XRD spectra. Meanwhile, the glass samples' elastic properties are determined from the measurement of longitudinal and shear velocities using ultrasonic technique. The longitudinal modulus, shear modulus, bulk modulus and Young's modulus has shown an irregular trend that fluctuates within certain limits. Moreover, the FLUKA Monte Carlo code is implemented to determine the shielding features at gamma energy of 0.3565, 0.6616, 0.8348 and 1.3325 MeV. Linear attenuation coefficients acquired from FLUKA and XCOM are found to be in good agreement with relative difference <1%. The glass sample B2O3TeO2CuO1 (with highest percentage of TeO2) is found to be the best shielding glass material in this study.

A New Failure Theory and Importance Measurement Analysis for Multidirectional Fiber-Reinforced Composite Laminates with Holes.

In this paper, a failure theory for the multidirectional fiber-reinforced composite laminate with a circular hole is developed. In this theory, the finite fracture mechanics method is combined with the improved Puck’s failure theory including the in situ strength effect. It can predict the notched strength by only basic material properties of unidirectional laminas, geometries and stacking sequence of the laminate. In advance mechanical properties of the laminate are unnecessary. The notched laminates with different material types and stacking sequences are taken as examples to verify this failure theory, and predicted results are in good agreement with experiments. Based on the developed failure theory, importance measurement of uncertain material properties to the notched strength is analysed. Results show that notched strength increases with increasing longitudinal tensile strength and in-plane shear modulus for the laminate with an arbitrary hole diameter. However, it decreases with increasing transverse modulus.

A molecular dynamics study on the mechanical properties of defective CNT/epoxy nanocomposites using static and dynamic deformation approaches

Abstract In this paper, the mechanical behavior of epoxy polymer nanocomposite with continuous single-walled carbon nanotubes (SWCNT) with and without vacancy defects has been investigated based on two approaches of deformation, molecular mechanics (static) and molecular dynamics. In this regard, molecular simulation has been performed on the basis of the compass force field. In order to validate the research steps, the results obtained for pure epoxy polymer were compared with similar molecular dynamic simulations, which confirmed the simulation process. The research process proposed a method for controlling the symmetry of the system during equilibration with an asymmetric barostat. The Souza-Martins barostat was also used to apply loading and deformation control over a constant strain rate range. The results showed that in both deformation approaches (with and without calculating the contribution of kinetic energy), the presence of defects improved the transverse tensile and shear moduli, while the longitudinal tensile modulus decreased. Also, the improvement and decrease of the longitudinal tensile modulus and longitudinal shear modulus of the nanocomposite in comparison with the net polymer have been observed in both approaches, respectively. As a general result, it was observed that the contribution of kinetic energy has a major effect on the mechanical properties of pristine and defective nanocomposites.

Non-Invasive Full Rheological Characterization via Combined Speckle and Brillouin Microscopy

Rheology serves to measure the deformation and flow of materials. Its associated quantities, for example, the Young&#x2019;s modulus, shear modulus, bulk modulus, or longitudinal modulus, are important in the biomedical field, in particular for soft materials, to characterize the response of materials to external force. Usually, mechanical probes, in particular rheometers or atomic force microscopy, are used to characterize these quantities. In the last decade, optical measurements have been derived to obtain these quantities even in small sample volumes. However, usually only one quantity is evaluated using optical techniques, such as Brillouin microscopy, which does not allow a full rheological characterization. The latter requires measuring at least two quantities, which allows for calculating all further rheological properties. In this paper, we aim to close this gap by combining two optical rheology methods, Brillouin microscopy to measure the longitudinal modulus and Laser Speckle Rheology for the shear modulus. We built an optical setup that allows the non-contact and hence non-destructive and non-invasive measurement of both quantities simultaneously in the same sample using a 780 nm, narrow linewidth (&#x007E;50 kHz) laser system. We evaluate our approach using defined samples of glycerol and polydimethylsiloxane and we demonstrate image acquisition using the combined setup. We also investigate porcine corneae, as biological samples, and demonstrate direct measurement of longitudinal modulus and shear modulus and calculation of Young&#x2019;s modulus, bulk modulus, and the Poission ratio, which are all in good agreement with published quantities. In the future, our approach allows for full characterization of the rheology of biological specimens.

Full Characterization of in vivo Muscle as an Elastic, Incompressible, Transversely Isotropic Material Using Ultrasonic Rotational 3D Shear Wave Elasticity Imaging.

Using a 3D rotational shear wave elasticity imaging (SWEI) setup, 3D shear wave data were acquired in the vastus lateralis of a healthy volunteer. The innate tilt between the transducer face and the muscle fibers results in the excitation of multiple shear wave modes, allowing for more complete characterization of muscle as an elastic, incompressible, transversely isotropic (ITI) material. The ability to measure both the shear vertical (SV) and shear horizontal (SH) wave speed allows for measurement of three independent parameters needed for full ITI material characterization: the longitudinal shear modulus μL , the transverse shear modulus μT , and the tensile anisotropy χE . Herein we develop and validate methodology to estimate these parameters and measure them in vivo, with μL = 5.77±1.00 kPa, μT = 1.93±0.41 kPa (giving shear anisotropy χμ = 2.11±0.92 ), and χE = 4.67±1.40 in a relaxed vastus lateralis muscle. We also demonstrate that 3D SWEI can be used to more accurately characterize muscle mechanical properties as compared to 2D SWEI.

Non-destructive mechanical characterisation of thin-walled GFRP beams through dynamic testing and model updating

This work deals with a non-destructive approach based on dynamic testing combined with model updating techniques through finite element modelling and optimisation processes to characterise the main elastic constants of a thin-walled glass fibre reinforced polymer (GFRP) C-channel beam. The experimental modal analysis identified nine vibration modes encompassing global modes predominated by coupled flexural-torsional behaviour as well as local flexural ones related to the flanges of the beam. The longitudinal elasticity and in-plane shear moduli were less sensitive to the number of modes, indicating that only the first three modes were enough to obtain a good estimate of these parameters. In contrast, the transverse modulus of elasticity was more affected over the nine modes and the optimisation process became imperative to seek the optimal value. As corroborated by destructive tests, the non-destructive procedure gives an alternative approach for the mechanical characterisation of GFRP members, which can be advantageous for low-cost in situ quality control.

Semi-analytical constitutive model of cracked plies based on linear elastic fracture mechanics

Matrix microcracking of laminated composites lead to stiffness degradation. Microscopic critical stresses are defined according to the linear elastic fracture mechanics and are found to be independent of the crack density. The microscopic critical stresses are constant as long as the material and the thickness of the cracked plies are constant, and can be used to obtain the semi-analytical expression of the equivalent transverse moduli and in-plane shear moduli of the cracked plies versus the crack density. The equivalent longitudinal moduli and in-plane shear moduli of [0/±θ4/01/2]S laminates are obtained by using the semi-analytical model and the classical laminate theory, and are compared with the available experimental data and conventional finite element analysis (FEA) results.

Inclined composite guardrails/safety barriers – Numerical and experimental evaluation of their transverse stiffnesses and compliance with standards

Three-point flexure and axial torsion tests were undertaken to establish the longitudinal elastic flexural and in-plane shear moduli of pultruded GFRP tubes. They were used to define one-dimensional two-node beam elements for modelling single- and two-bay inclined guardrails with inclinations up to 60°. Subsequently, three-dimensional FE models were developed to analyse more accurately single- and two-bay 30° inclined guardrails. The results from these analyses were compared with those of full-scale load tests on 30° inclined guardrails subjected to transverse normal preload, usability, and ultimate loads applied to the handrails. It is shown that the analysis results based one-dimensional elements significantly underestimate the mean handrail deflections and over-estimate the guardrails’ transverse stiffness. By contrast, using three-dimensional elements in the FE models give more accurate predictions, with mean handrail deflections 9% and 14–16% lower than single- and two-bay test values respectively. The corresponding percentages for mean transverse stiffnesses are 10% and 12.5 – 14.3% higher respectively. It was also observed that the responses of the guardrails were linear, the residual deflections on unloading were less than permitted for the preload, usability and ultimate loads. Furthermore, neither the single- nor the two-bay 30° inclined guardrails sustained any damage.

Prediction of elastic properties of unidirectional carbon/carbon composites using analytical and numerical homogenisation methods

ABSTRACT Carbon/carbon composites are being used increasingly in the field of Space, Aviation; Air craft breaks discs, High temperature applications. They can withstand a very high temperature up to 3315°C. They have distinct advantage of strength over graphite fibre. They are lighter to graphite fibres. Elastic properties of the carbon/carbon composites are important for design considerations. They can be evaluated through analytical, numerical or experimental methods. Experimental methods are expensive and are not feasible to be performed at the design stage. Analytical methods are complex and difficult to implement. Numerical methods through Finite Element Modelling (FEM) are useful tools for evaluation of elastic properties of composite materials. The present work is aimed at review and comparison of various analytical models and numerical finite model for evaluation of elastic properties. The elastic properties of unidirectional carbon/carbon composites are evaluated using analytical models and numerical finite element model using ABAQUS with EasyPBC plugin. Elastic modulus in longitudinal and transverse direction show good agreement in all methods. Major Poisson’s ratio and transverse Young’s modulus are also in agreement. Longitudinal shear modulus obtained by rule of mixtures is on lower side while that obtained by other models are on higher side when compared to numerical model.