Effect Of Transverse Strain Research Articles

Assessment of a new higher-order shear and normal deformation theory for the static response of functionally graded shallow shells

Abstract Static response of simply supported functionally graded (FG) shallow shells using a new higher-order shear and normal deformation theory is focused in this article. The effects of transverse strains and stresses on the bending response of FG shell are considered by the present theory. The current theory considers the impacts of transverse normal and shear deformations that meet the requirements for traction-free boundary conditions. The virtual work principle is applied to the mathematical formulation of the present theory. The simply supported doubly curved shallow shell problems under the static transverse load are analyzed using Navier’s solution technique. To verify the existing theory, the current results are, whenever possible, compared with those that have already been published. Additionally, a few benchmark results are presented in this article that will be helpful to researchers in the future.

A novel numerical approach for analyzing experimental data on critical current degradation in Nb3Sn wires caused by transverse deformations preceding heat treatment

In the framework of studies on high-field magnets for future accelerators, a specific project called ASTRACT focuses on the effect of transverse strain on the critical current of Nb3Sn wires. The first phase of the project addresses the effects of strain imposed on Nb3Sn wires before heat treatment and the development of a procedure to directly compare critical current measurements with values extracted from magnetization cycles. A Nb3Sn RRP-Ti wire was deformed to different values of transverse strain (10%, 15%, 20%, and 25%), and long samples were collected for transport measurements at 4.2 K, in a background field ranging from 10 to 14 T. Short samples were used for magnetization measurements (VSM technique). Additionally, SEM images of the cross-section were collected at different longitudinal positions along the wire for each strain value. This paper proposes a method based on SEM image analysis and magnetization measurements analysis to study the effect of bundle deformation on transport properties. The procedure requires morphological information provided by SEM images after appropriate numerical processing. Verification through statistical comparison between the Ic transport and VSM data is also conducted. Direct critical current measurements showed no degradation due to deformation up to 25%. The method introduced, independent of transport data, can reach the same conclusions by considering the real shape of the bundles.

Study of the transverse strain effect on the Fiber Bragg Grating Sensor (FBGS) response with polyimide coating under experimental biaxial tests

The aim of this research work is to study the behaviour of Fiber Bragg Grating (FBG) sensors to interpret their response more accurately in a structural monitoring system. In the presence of a complex stress state, a structure is subjected to strain fields in multiple directions simultaneously and the sensors used for its structural monitoring are affected as well. However, the traditional procedure to calibrate FBG sensors consists of uniaxial tensile tests to calculate a strain sensitivity factor (K) that relates the sensor response to the strain measured during the test. In this study, a polyimide coated FBG sensor is embedded in a cruciform composite specimen to analyse its response to biaxial strain states. The experimental methodology has consisted of carrying out a campaign of biaxial tests on this specimen in which the longitudinal strain (εx) has been kept constant and the transverse strain (εy) has been varied by means of a triaxial testing machine to reproduce different plane stress states. Biaxial tests have allowed to study experimentally the influence of the εy on the longitudinal measurement of the FBG sensor and therefore on the calibration procedure. Finally, the experimental results obtained in both uniaxial and biaxial tests have been compared to the strain-optic theory.

Electro-mechanical behaviour of graphene-based geotextiles for pavement health monitoring

Smart geosynthetics have attracted significant interest for potential applications in geotechnical structures owing to their conductive properties. This paper presents an analysis of the electro-mechanical response of graphene-based geotextiles for application in pavements. Experimental and numerical studies were conducted on a commercially available graphene-coated geotextile to understand its response to induced strains. The material was subjected to tensile loading with the effect of transverse strains also being tested, utilizing Digital Image Correlation (DIC). Experimental results indicated a significant electro-mechanical behaviour in the geotextile, with the relative resistance change being non-linear with applied strain. Existing analytical solutions could not predict the observed behaviour; hence, a multi-physics numerical model was developed using concepts of piezoresistivity to capture the non-linear behaviour. The numerical model was calibrated using the experimental data and then validated with experimental data from tests conducted for different specimen sizes. The model could capture the non-linear electro-mechanical behaviour and the electrical response due to axial and transverse strains in the material. This study is expected to serve as a basis for using graphene-based geotextiles for structural health monitoring (SHM) purposes in geotechnical structures, such as in roads.

Large displacement models for composites based on Murakami's Zig-Zag Function, Green-Lagrange Strain Tensor, and Generalized Unified Formulation

Abstract Murakami's Zig-Zag Function in conjunction of Green-Lagrange Strain- and Second-Piola Kirchhoff Stress-tensors and Generalized Unified Formulation are introduced for the first time to present a class of Zig-Zag theories for composite structures. Transverse strain effects are retained and modeled, making the present approach also suitable for thick structures. Each displacement variable is independently represented with user-selected order of expansion. The stress recovery is achieved with a special procedure in which combination of deformation gradient and Second-Piola Kichhoff transverse stresses are integrated along the thickness of the undeformed geometry. Comparison with available data and commercial codes indicate the effectiveness of the proposed framework for variable kinematics Zig-Zag theories in the presence of large displacements.

A generalized approach on bending and stress analysis of beams with piezoelectric material bonded

The modeling and analysis of piezoelectric cantilevers are critically important in the design of micro intelligent systems, where piezoelectric beams serve as major components in micro sensors, actuators or energy harvesters. In this paper, we propose an analogy modeling method for the unimorph and bimorph piezoelectric beams, which helps to improve the accuracy of the neutral plane location of piezoelectric beams with different thickness ratios and total thicknesses. In particular, the strains of each layer are obtained by employing the analogy modeling method with the consideration of the transverse strain effect, where the force balance and moment balance equations of the final state of piezoelectric beams are derived under electric fields to reveal the relationship between the external deflection and the internal stress distribution of piezoelectric beams. To verify the effectiveness of the proposed approach, the bending characteristics of unimorph and bimorph piezoelectric beams (PZT-5A) are comprehensively tested under various electric fields, where theoretical values agree well with experiments and simulations. Compared with existing results, the proposed method provides a more general and accurate approach to characterize the properties of deflection and internal stress distribution for piezoelectric beams, which can be better used to study the stress of the adhesive layers, the geometric dimension optimization and the dynamics of piezoelectric beams in micro sensor or actuator applications.

Numerical modeling of the capillary in the Bragg grating area, ensuring uniaxial stress state of embedded fiber-optic strain sensor

In this paper, the possibility of providing a uniaxial stress state of FOSS based on the use of a capillary tube in the area of the Bragg grating is studied. The capillary tube, which consists of the additional external coating and a cavity between the coating and the optical fiber, protects the Bragg grating from the effects of transverse strain. This allows to use a direct relation between the measured value of the Bragg wavelength shift and the longitudinal strain. With the help of numerical simulation, the geometric and mechanical parameters of the capillary tube have been studied. Numerical calculations showed a slight effect of the elastic modulus of the capillary coating on the cavity size under load. However, the presence of a cavity in the capillary leads to an increase in stress concentration, which must be considered when designing a capillary tube for a particular application. The obtained results confirmed the effectiveness of the structural scheme of the capillary in the area of FOSS embedded into the controlled material.

Effect of transverse strains and angular distortions on the nanoscale elastic behavior of platelet nanocomposites

In order to correctly predict the macroscale elastic behavior of nanocomposite macroscale structures, an accurate nanoscale model must be available for subsequent homogenization. In this work, we demonstrate that the accuracy of that nanoscale model greatly depends on the consideration of transverse strains and angular distortions, which are not frequently taken into account, but have a significant influence on the cohesive mechanisms at the nanofiller-matrix interface. We use a nanoscale cohesive model to qualitatively and quantitatively analyze the effect of transverse shear and angular distortion on the interfacial stress transfer mechanisms. While the effect of the transverse strain is less significant, results show that angular distortion greatly affects the interfacial damage pattern. It appears to shift the interfacial shear stress distribution to one of the interface ends, which consequently also modifies the interfacial longitudinal stress distribution and its mean value, resulting in reduced nanocomposite stiffnesses. The effect should be taken into account as shear and transverse strains may be present at the macroscale if, for instance, nanofiller misalignment or stress concentrators exist. We also provide design maps representing damage onset for different 2D multiaxial strain states in graphene-epoxy nanocomposites, so that the strain state limit can be inferred for the given nanocomposite properties. A substantial reduction in the allowable strains can be observed.

Design of a PVDF-MFC Force Sensor for Robot-Assisted Single Cell Microinjection

Robot-assisted cell microinjection is an important approach to modern biological applications. Micro-force sensor is a crucial device to facilitate a precise injection of biological cells. Majority of existing film-based force sensors are designed as a cantilever structure for cell injection application. However, such kind of force sensor has inherent disadvantages in terms of unstable transmission of injection force, bigger puncturing wound, and operation inaccuracy. In this paper, a novel 1-D force sensor is designed by using polyvinylidene fluoride (PVDF) and macro fiber composite (MFC) films as fixed-guided beams to construct a multistage compound parallelogram flexure mechanism. It enables both capabilities of force sensing and stable cell holding. A prototype is fabricated, calibrated, and applied to crab egg embryo injection. The transverse strain effect of the fixed-guided sensing beams has been quantitatively measured by experiments. Comparison investigation reveals the great potential of MFC film over PVDF film for force sensing in cell microinjection application. The MFC force sensor offers the resolution, sensitivity, and measuring range of 0.80 mN, 1.23 mV/mN, and 100 mN, respectively. Microinjection experiments demonstrate that the developed force sensor faithfully reveals the process of cell injection and measures the puncturing force of 27 mN for crab eggs in real time.

Patch antenna sensor rosettes for surface strain measurement

Passive (battery-free) wireless patch antenna sensors have been developed in recent years for strain sensing, to provide convenient and low-cost instrumentation. Despite past efforts, current analytical and experimental studies have mainly focused on performance in single-axial measurement, which is simple and unrealistic from typically encountered arbitrary plane stress fields. This paper presents strain sensor rosettes made of folded patch antennas and slotted patch antennas for measuring an arbitrary surface strain (plane stress) field. The transverse strain effect of both sensors is discussed and has been validated through laboratory experiments. Multiphysics coupled simulation is conducted to describe accurately the mechanical and electromagnetic behaviours of antenna sensors. Resonance frequency shifts of the antenna sensors are used to derive the three strain components in an arbitrary plane stress scenario – that is, two normal and one shear strain components. Both numerical studies and experimental validations have been performed.

Elasticity solution of two-layer beam with a viscoelastic interlayer considering memory effect

The elasticity solution of a simply supported beam, composed of two same elastic layers adhesively bonded by a thin viscoelastic interlayer, subjected to time-dependent load is studied. The tangential and transverse strains in the interlayer are considered simultaneously. The viscoelasticity of the interlayer is described by the standard linear model, which considers the memory effect of strains. An analytical method is developed to obtain the stress and displacement fields in the beam. The present method gives the exact stress and displacement distributions in the beam, which cannot be predicted by the approximate theories such as the one-dimensional Euler–Bernoulli theory. The comparison study indicates that the present results have a good agreement with the two-dimensional finite element solutions. However, there is considerable difference between the present solution and the Euler–Bernoulli solution for thick beams. It is shown that the effect of transverse strains of the interlayer on displacements and stresses cannot be neglected for thick beams and the common quasi-elastic interlayer model is unserviceable for beams with viscoelastic interlayer with the repeatedly loading-unloading path. Finally, the effects of interlayer thickness and viscoelastic properties on displacements and stresses of the beam are discussed in detail.

Transverse strain effects on the thermal expansion measurement of composite structure using fiber Bragg grating sensors: Experimental validation

When transverse strain is much larger than the longitudinal one, conventional fiber Bragg grating measurement model presents significant errors in the longitudinal strain measurement. The present authors presented a fiber Bragg grating measurement model to consider transverse strain effects and numerically demonstrated the effectiveness of the model. This article experimentally validates the fiber Bragg grating measurement model by measuring thermal expansion of anisotropic composite specimens and an isotropic invar specimen. The longitudinal thermal expansion of the specimens is measured by using fiber Bragg grating sensors and compared with a reference measurement result using an optical interferometer. The proposed fiber Bragg grating model shows good agreement with the reference measurement for the longitudinal strain while large discrepancy (~22%) is observed according to the conventional one-dimensional fiber Bragg grating model.

Partially Zig-Zag Advanced Higher Order Shear Deformation Theories Based on the Generalized Unified Formulation

The Generalized Unified Formulation (GUF) is a multi-theory and a multi-fidelity architecture for the generation of a virtually infinite class of Advanced Higher Order Shear Deformation Theories (AHSDT) or Zig-Zag theories or Layer-Wise (LW) theories with any order of expansion for each of the primary variables. This work will present, for the first time in the literature, an extension of GUF to address problems in which every single variable can have either an Equivalent Single Layer (ESL) or a Zig-Zag-enhanced ESL description [Partially Zig-Zag Advanced Higher Order Shear Deformation Theories (PZZAHSDT)]. Applications to the case of thick sandwich structures are presented: starting from a baseline fourth-order AHSDT which also includes the transverse strain effects, all the possible types of PZZAHSDT are generated and compared with the baseline and with a fourth-order fully Zig-Zag theories.

Transverse Strain Effects on the Measurement of the Thermal Expansion of Composite Structure Using Surface-Mounted Fiber Bragg Grating Sensors

The effects of transverse strain on the wavelength shifts of surface-mounted fiber Bragg grating (FBG) sensors are investigated. A new FBG model including the concept of strain transmissibility coefficients along the longitudinal and transverse directions of the sensors is proposed. The finite element method is applied to obtain the strain transmissibility coefficients between the FBG sensor and surface of the base structure. The wavelength shifts of each FBG sensor are calculated with respect to the assumed thermal strain condition of the base structures; the estimated strains by the proposed FBG model are compared with the results from conventional FBG model. The numerical results show that the surface strains of the composite structure can be predicted well using the proposed FBG model, while the conventional FBG model results in a larger error when the transverse strain of the base structure is much larger than longitudinal strain of the base structure, as in composite structures under thermal loadings.

Improved constitutive equations of piezoelectric monomorphs: Application to the preliminary study of an original traveling-wave peristaltic pump

This article establishes the constitutive equations of a piezoelectric monomorph by separating the effects of the piezoelectric action from the effects of the external loads and by considering in both cases a static equilibrium of forces and moments. Unlike previous studies, our model explicitly incorporates the effects of transverse strains and electric field gradients in order to approach more faithfully the real strains and stresses in the monomorph. This model, which can be easily generalized to other types of benders and applied to complex study cases is used in this paper to analyse the impact of the characteristic parameters of an original traveling-wave peristaltic pump on its performance.

Fibre Bragg grating transverse strain sensing using reflections at twice the Bragg wavelength

The effect of transverse strain on a fibre Bragg grating fabricated using a phase mask with 536 nm pitch has been investigated through the study of its reflection spectra at twice the Bragg wavelength near 1552 nm. At this wavelength the reflection spectrum consists of two narrow closely spaced peaks that arise from the interleaved refractive index modulations along the fibre core having the periodicity of the phase mask and produces a type of π-phase-shifted grating. The response of these peaks to transverse strain is similar to that observed previously at the Bragg wavelength, and also at two thirds of the Bragg wavelength for peaks that are also due to the same complex refractive index structure. The attractions of using this grating for multi-parameter sensing are discussed.

A unified formulation to assess theories of multilayered plates for various bending problems

This work uses a unified formulation to compare about 40 theories for multilayered, composites and sandwich plates which are loaded by transverse pressure with various in-plane distributions (harmonic, constant, triangular and tent-like). So-called equivalent single layer models (ESLMs), which preserve the number of the unknown variables to be independent by the number of layers, as well as layer-wise models (LWMs) are considered in both framework of principle of virtual displacement (PVD) and Reissner Mixed Variational Theorem (RMVT). Murakami’s Zig-Zag Function is used to introduce zig-zag (ZZ) effects while independent assumptions for transverse stresses (both shear and normal components) are used to enforce interlaminar continuity (IC) between two adjacent layers. Linear and higher order expansions (fourth-order) are introduced for displacements and stresses in the thickness plate directions. The fundamental effects of transverse strain is evaluated for most of the considered analyses. The whole modeling has been herein written by employing a unified formulation recently proposed by the first author. As a results a large number of classical and advanced theories for laminated structures are formulated and the related governing equations are written in terms of so-called fundamental nuclei with only nine terms each. Navier-type, closed form solutions of these equations are presented for orthotropic plates by expanding the applied pressure loading in Fourier series. A number of conclusions have been traced as far as performance and limitations of compared theories is concerned. Quoted results could be used as benchmarks to assess available theories not considered in this paper as well as approximated solution techniques, such as finite element applications.

Direct numerical simulation of a three-dimensional turbulent boundary layer

The effects of transverse strain on an initially two-dimensional turbulent boundary layer are studied in a direct numerical simulation of a planar channel flow with impulsively started transverse pressure gradient. Consistent with experiments in three-dimensional boundary layers, the simulation shows a decrease in the Reynolds shear stress with increasing transverse strain. Also, the directions of the Reynolds shear stress vector and the mean velocity gradient vector were found to differ. In addition, the simulation shows a drop in the turbulent kinetic energy. Terms in the Reynolds stress transport equations were computed. The balances indicate that the decrease in turbulent kinetic energy is a result of a decrease in turbulence production, along with an increase in turbulent dissipation. Intuitive reasoning and current turbulence models would predict an increase in kinetic energy along with increases in production and dissipation rates as a result of increased mean-flow strain rate. Later in the evolution of the flow, both turbulence production and dissipation increase.

Longitudinal and transverse gauge factors of polycrystalline strain gauges

The gauge factor of strain gauges is calculated considering the longitudinal and transverse strain sensitivity of the resistivity. The general result is applied to free wire strain gauges, adhered foil strain gauges and thin film strain gauges. The relation between the gauge factor and the piezoresistive constant π l and π t is given and it is shown that the use of piezoresistive constant ϕ l and ϕ t referring to strain instead of stress simplifies the calculation substantially. A recently proposed approach based on the changes of the mobility and the number of free carriers due to stress or strain has been improved by including longitudinal and transverse strain effects. The relationship with the piezoresistive constants is shown. This approach offers a better understanding of the temperature coefficient of resistance in strain gauges on various substrates.

The effect of transverse strains in the mechanics of a solid medium

The effect of transverse strains for elastic and plastic bodies is discussed. It is shown that for plastic bodies transverse strains have the same nature as longitudinal strains — rotation of elastic elements cut out by Luders lines. For elastic bodies longitudinal (active) and transverse (passive) strains have a different nature, and the emergence of internal forces is connected with the gradients of the active but not total displacements. Accordingly the equations of state are written in the form of connections of the stresses with the active strains, and connections of the stresses with the passive strains. It is shown that the connection between stresses and strains calculated with respect to an arbitrary plane has a physical meaning only for certain (defining) planes. The strains calculated on the rest of the planes have no physical meaning; their role is reduced to an invariant description of the processes taking place on the defining planes. Therefore, for the description of the processes taking place on all planes, a single strain tensor is insufficient. It is shown that, in the case of a linearly elastic body, a tensor of the active and a tensor of the passive strains are sufficient.