Uniaxial Model Research Articles

In-plane Uniaxial Anisotropy and Magnetization Reversal Mechanism of FeCo Films by Strip Pattern

Strip-like FeCo films were patterned by a traditional lithograph process from intrinsically isotropic continuous FeCo films. The strip-patterned FeCo film shows a strong in-plane uniaxial magnetic anisotropy with easy axis along the length direction of the strip. The angular dependences of remanence ratio, switching field, and coercivity indicate that the magnetization reversal mechanism of the strip-patterned FeCo film is coherent rotation and domain wall depinning when the applied field is near the hard axis and easy axis, respectively. The consistency of the experimental hysteresis loops of the strip-patterned FeCo film and calculated hysteresis loops with a simple in-plane uniaxial anisotropy model indicates that the strip-patterned FeCo film behaves as a single domain. The absence of the domain wall and the strong in-plane anisotropy field make the strip-patterned FeCo films have much potential for high-frequency application.

Mechanical properties and constitutive equations of concrete containing a low volume of tire rubber particles

Uniaxial compressive tests were conducted for a low-volume tire rubber concrete (RC) with different rubber volume content levels and particle sizes (five of each). The influence of rubber content and particle size on the mechanical properties of RC was investigated, including axial compressive strength, elastic modulus, peak strain, ultimate strain, appearance of visible cracks and failure pattern of specimens. The mechanical analysis of test results was conducted based on uniaxial compressive stress–strain curves. Uniaxial compressive constitutive models of low-volume rubber concrete were established that included axial compressive strength, peak strain and constitutive parameters a and b. There was obvious regularity between constitutive parameters a and b, rubber content and rubber particle size. Moreover, the physical meanings of constitutive parameters a and b were given, and the established constitutive models were evaluated by tests. The test results demonstrate that the constitutive models have not only good predicting ability and high accuracy but also nice applicability within the limit of 50kg/m3 rubber content. The constitutive models were then improved by introducing the sand rate reduction factor k to reflect the influence of rubber additives. The improved constitutive models are able to predict the performance of concrete with low amounts of rubber.

Uniaxial tensile behaviour modelling of natural-fiber-reinforced viscoplastic polymer using normalized stress–strain curves

The monotonic uniaxial tensile behaviour of hemp-fiber-reinforced high density polyethylene (HDPE) was investigated at different values of hemp fiber volume fraction (vf) and strain rate ([Formula: see text]). A normalized stress–strain family of curves was generated. An exponential normalized monotonic model was developed. A general uniaxial monotonic model was developed from the normalized model to simulate the stress–strain relationship at different values of [Formula: see text] and vf. A modified Harris mechanistic model and a linear model were proposed to incorporate the effect of vf and the absorbed moisture into the developed model.

An improved method for numerically modeling the minimum horizontal stress magnitude in extensional stress regimes

The minimum horizontal stress magnitude, Shmin, is a crucial input parameter for a variety of subsurface engineering applications. Several methods, such as the general poro-elastic model, the uni-axial strain model and the concept of frictional equilibrium can be used to simulate Shmin, whereby the general poro-elastic model is most commonly used due to its capability to account for tectonic strain in order to match existing stress measurements. If stress measurement data is unavailable this paper introduces a pre-stressing procedure for 3D numerical Mechanical Earth Models that combines the poro-elastic model with the frictional equilibrium model to provide lower bounds for Shmin in extensional stress regimes. Assuming common friction coefficients of μ in the range of 0.57 to 1, the necessary horizontal strain can be calculated to limit horizontal stress magnitudes of the whole model domain or of only certain calibration layers by frictional failure. For layers with Poisson׳s ratios smaller or larger than 0.25, Shmin magnitudes being too low or too high (as predicted by the uni-axial strain model) can thus be prevented. The presented concept is tested for two case studies and the modeling results show that the combination of the poro-elastic model with the frictional equilibrium model can provide a good match to the measured data, even if it is assumed that the calibration data is not available. It is concluded that the combination of the two deformation mechanisms can produce a more physically appealing stress profile and hence may more accurately simulate the sense and relative magnitude of layer-to-layer stress contrasts. In addition, the numerical modeling approach presented can match observations on the near surface variation of the ratio k=Shmean/Sv.

Strain-rate sensitivity of the lateral collateral ligament of the knee

The material properties of ligaments are not well characterized at rates of deformation that occur during high-speed injuries. The aim of this study was to measure the material properties of lateral collateral ligament of the porcine stifle joint in a uniaxial tension model through strain rates in the range from 0.01 to 100/s. Failure strain, tensile modulus and failure stress were calculated. Across the range of strain rates, tensile modulus increased from 288 to 905MPa and failure stress increased from 39.9 to 77.3MPa. The strain-rate sensitivity of the material properties decreased as deformation rates increased, and reached a limit at approximately 1/s, beyond which there was no further significant change. In addition, time resolved microfocus small angle X-ray scattering was used to measure the effective fibril modulus (stress/fibril strain) and fibril to tissue strain ratio. The nanoscale data suggest that the contribution of the collagen fibrils towards the observed tissue-level deformation of ligaments diminishes as the loading rate increases. These findings help to predict the patterns of limb injuries that occur at different speeds and improve computational models used to assess and develop mitigation technology.

Modeling of the temperature-dependent ideal tensile strength of solids

To reveal the fracture failure mechanisms of single crystals at elevated temperatures, a new temperature-dependent ideal tensile strength model for solids has been developed, based on the critical strain principle. At the same time, the uniaxial tensile strength model, based on the critical failure energy density principle for isotropic materials that was presented in the previous study, is generalized to multi-axial loading and to cubic single crystals. The relationship between the two models is discussed, and how to obtain the material properties needed in the calculations is summarized. The two well-established models are used to predict the temperature-dependent ideal tensile strength of W, Fe and Al single crystals. The predictions from the critical strain principle agree well with the predictions from the critical failure energy density principle. The theoretical values from the critical strain principle at 0 K is in reasonable agreement with the ab initio results. The study shows that the temperature dependence of the ideal tensile strength is similar to that of Young’s modulus; that is, the ideal tensile strength firstly remains approximately constant and then decreases linearly with the temperature. The fracture failure for single crystals at elevated temperatures has been identified, for the first time, as a strain-controlled criterion.

A Numerical Investigation on Time-Dependent Failure of Tunnels Based on the Long-Term Strength Characteristics of Rocks

How to establish the proper rheological model to describe and simulate the relationship between rock mechanic characteristics and time is one of the difficulties in the tunnel long-term stability analysis. In this paper, a numerical model to replicate the time-dependent deformation of rock mass was presented. In the model, the time-dependent deformation is described in terms of degradation of intrinsic physical and mechanical properties of rock and accumulation of mesoscopic damage inside the rock. Based on the model, uniaxial numerical experimentation and tunnel numerical model test are numerically constructed and investigated respectively. The model well reflects the initial creep, steady creep of rock and accelerated creep, which preliminary prove the validity of the proposed model. The results of the tunnel numerical model test show that the displacement curves from the numerical simulation were generally consistent with those from physical model tests. Furthermore, the macroscopic failure modes and local mesoscopic damage evolution of the tunnels were simulated.

Implementation and verification of a mechanistic permanent deformation model (shift model) to predict rut depths of asphalt pavement

The shift model is implemented in the layered viscoelastic asphalt pavement analysis for critical distresses (LVECD) program to predict the rut depth of asphalt pavements. The rut depth measurements taken at the National Center for Asphalt Technology (NCAT) test track and the Federal Highway Administration Accelerated Facility (FHWA ALF) test sections are evaluated using the model. The model can successfully evaluate rut depth, which proves the capability of the model implemented in the LVECD program. The slight over-prediction of the NCAT sections can be explained by ageing in the field that increases the pavement's resistance to rutting. The simulation results support the hypothesis that triaxial stress sweep tests with confinement can represent the permanent deformation behaviour of asphalt concrete in the field. In this regard, excessive shear flow may be the reason for the under-prediction of the FHWA ALF mixtures. For better predictions, a correction factor (i.e. a transfer function) is suggested, which is quantified via the ratio of shear stress to shear resistance. After applying individual transfer functions, the permanent deformation model in the LVECD can evaluate the growth of the rut depth. Therefore, even though the shift model is a uniaxial model, the model can predict the rut depth of asphalt concrete by employing the transfer function.

Constitutive modelling of the amplitude and frequency dependency of filled elastomers utilizing a modified Boundary Surface Model

A phenomenological uniaxial model is derived for implementation in the time domain, which captures the amplitude and frequency dependency of filled elastomers. Motivated by the experimental observation that the frequency dependency is stronger for smaller strain amplitudes than for large ones, a novel material model is presented. It utilizes a split of deformation between a generalized Maxwell chain in series with a bounding surface plasticity model with a vanishing elastic region. Many attempts to capture the behaviour of filled elastomers are found in the literature, which often utilize an additive split between an elastic and a history dependent element, in parallel. Even though some models capture the storage and loss modulus during sinusoidal excitations, they often fail to do so for more complex load histories. Simulations with the derived model are compared to measurements in simple shear on a compound of carbon black filled natural rubber used in driveline isolators in the heavy truck industry. The storage and loss modulus from simulations agree very well with measurements, using only 7 material parameters to capture 2 decades of strain (0.5–50% shear strain) and frequency (0.2–20Hz). More importantly, with material parameters extracted from the measured storage and loss modulus, measurements of a dual sine excitation are well replicated. This enables realistic operating conditions to be simulated early in the development process, before an actual prototype is available for testing, since the loads in real life operating conditions frequently are a combination of many harmonics.

Modeling of smart concrete beams with shape memory alloy actuators

In the present work, a computational strategy for the modeling of reinforced concrete beams with SMA actuators for cracks repair is developed. In particular, for the concrete, an original transition damage–fracture technique is proposed in order to simulate the microcrack arising, their coalescence and, finally, the macrocrack development. Microcracks are modeled adopting a nonlocal damage and plasticity approach, which is able to consider the tensile and compressive damaging, accumulation of irreversible strains and the unilateral phenomenon. Macrocracks are modeled using a cohesive zone interface which accounts for the mode I, mode II and mixed mode of damage, the unilateral contact and the friction effects. The interface models the transition from the continuum damage (simulating the presence of microcracks) to fracture. A uniaxial SMA model able to reproduce both the pseudo-elastic behavior and the shape memory effect is adopted for the reinforcing SMA bars.Finite element simulations are developed in order to reproduce the behavior of smart concrete beams subjected to three-point bending experimental tests available in literature (Kuang and Ou, 2008, Daghia et al., 2011). The construction phases of the beam are simulated and the loading history, consisting in three-point bending tests, are reproduced; in particular, the repairing phase due to pseudo-elastic behavior and shape memory effect is reproduced. Numerical results are compared with experimental data to validate the computational strategy.

True Stress and Shakedown Analysis of Pressure Vessel which under Cyclic Loading to Plastic Deformation

The aim of this study is to discuss the plastic shakedown and true stress of the cyclically loaded pressure vessel. A thin-walled cylinder pressure vessel is made according to actual working state and a water pressure test system is built. The vessel is loaded to different strain levels of plastic deformation first. Then it is loaded cyclically to shakedown state. The relationship between plastic strain and shakedown range is given based on numerous experiments. The constitutive model of the true stress-true strain of the vessel is obtained. The experimental results show that the ratcheting obviously occurred when the vessel is cyclically loaded to plastic deformation. The true stress-strain constitutive model which is presented in this paper can show appropriately the constitutive relation of the vessel when it is under multi-axial stress state. The application of uniaxial shakedown constitutive model has been demonstrated in this study.

High elastic modulus nanoparticles: a novel tool for subfailure connective tissue matrix damage

Subfailure matrix injuries such as sprains and strains account for a considerable portion of ligament and tendon pathologies. In addition to the lack of a robust biological healing response, these types of injuries are often characterized by seriously diminished matrix biomechanics. Recent work has shown nanosized particles, such as nanocarbons and nanocellulose, to be effective in modulating cell and biological matrix responses for biomedical applications. In this article, we investigate the feasibility and effect of using high stiffness nanostructures of varying size and shape as nanofillers to mechanically reinforce damaged soft tissue matrices. To this end, nanoparticles (NPs) were characterized using atomic force microscopy and dynamic light scattering techniques. Next, we used a uniaxial tensile injury model to test connective tissue (porcine skin and tendon) biomechanical response to NP injections. After injection into damaged skin and tendon specimens, the NPs, more notably nanocarbons in skin, led to an increase in elastic moduli and yield strength. Furthermore, rat primary patella tendon fibroblast cell activity evaluated using the metabolic water soluble tetrazolium salt assay showed no cytotoxicity of the NPs studied, instead after 21 days nanocellulose-treated tenocytes exhibited significantly higher cell activity when compared with nontreated control tenocytes. Dispersion of nanocarbons injected by solution into tendon tissue was investigated through histologic studies, revealing effective dispersion and infiltration in the treated region. Such results suggest that these high modulus NPs could be used as a tool for damaged connective tissue repair.

Effects of ternary mixed crystal and size on optical phonons in wurtzite nitride core-shell nanowires

Within the framework of dielectric continuum and Loudon's uniaxial crystal models, existence conditions dependent on components and frequencies for optical phonons in wurtzite nitride core-shell nanowires (CSNWs) are discussed to obtain dispersion relations and electrostatic potentials of optical phonons in InxGa1−xN/GaN CSNWs. The results show that there may be four types of optical phonons in InxGa1−xN/GaN CSNWs for a given ternary mixed crystal (TMC) component due to the phonon dispersion anisotropy. This property is analogous to wurtzite planar heterojunctions. Among the optical phonons, there are two types of quasi-confined optical (QCO) phonons (named, respectively, as QCO-A and QCO-B), one type of interface (IF) phonons and propagating (PR) phonons existing in certain component and frequency domains while the dispersion relations and electrostatic potentials of same type of optical phonons vary with components. Furthermore, the size effect on optical phonons in CSNWs is also discussed. The dispersion relations of IF and QCO-A are independent of the boundary location of CSNWs. Meanwhile, dispersion relations and electrostatic potentials of QCO-B and PR phonons vary obviously with size, especially, when the ratio of a core radius to a shell radius is small, and dispersion relation curves of PR phonons appear to be close to each other, whereas, this phenomenon disappears when the ratio becomes large. Based on our conclusions, one can further discuss photoelectric properties in nitride CSNWs consisting of TMCs associated with optical phonons.

An enhanced concept of rheological models to represent nonlinear thermoviscoplasticity and its energy storage behavior, part 2: spatial generalization for small strains

The paper provides the spatial formulation of the enhanced concept of rheological models (Brocker and Matzenmiller in Cont Mech Thermodyn 25(6):749–778, 2013) for small deformations and the graphical representation of the rheological network for three-dimensionalmaterial behavior. The rheological components are redefined as tensor-valued elements, and afterward, they are assembled into a network of thermoviscoplasticity with volumetric–deviatoric split. The related constitutive equations are derived analogously as in the uniaxial model in Brocker and Matzenmiller (Cont Mech Thermodyn 25(6):749–778, 2013), providing the von-Mises yield function of metal plasticity and the associated flow rule in a natural way.

Compaction of a double-layered metal foam block impacting a rigid wall

The propagation of compaction waves in layered metal foam materials subjected to impact loading is analysed in order to examine the mechanism of compaction and reveal the phenomena that develop at the interface between the foam layers. The analysis is focused on double-layered configurations in which the individual materials exhibit strain hardening in the quasi-static regime of loading.Complex patterns of compaction due to impact are revealed depending on the foam quasi-static stress–strain characteristics, sequence of layers and impact velocity. The compaction of the individual foam layers under an increasing and decreasing velocity is distinguished. It is established that either a strong discontinuity wave or a simple compression wave can start propagating from the layers interface inside the distal layer depending on the material properties. It is shown that a secondary compaction of the proximal foam layer is possible to occur due to the propagation of the reflected wave from the layers interface when a particular layer sequence is arranged. This can lead to a significant stress increase at the interface.The present analysis is based on uniaxial models of compaction in which the compacted strains are not predefined but are obtained as a part of the solution being functions of the velocity variation. The proposed analytical models are verified by numerical simulations considering aluminium based foam Cymat with densities 253 and 570kg/m3 and Alporas with density 245kg/m3. The influence of the elastic material properties is briefly discussed.

Role of multiaxial state of stress on cracking of RC ties

This paper aims to investigate the role and effect of stress diffusion and bond deterioration in the analysis of reinforced concrete ties. Although tension ties seem to be basically in a uniaxial state of stress, after the onset of cracking the problem presents a multiaxial diffusion of stresses. In this paper, a uniaxial 1D numerical model has been compared with more sophisticated 2D and 3D Finite Element (FE) models, in order to investigate the different level of accuracy and information that can be attained considering or not the multiaxial state of stress. The obtained results show that the contribution of stress diffusion in concrete blocks between cracks has a certain importance for the evaluation of the global and local behavior of investigated tension ties, but it does not alter completely the response. Furthermore, the inclusion of damage in the bond–slip law due to the presence of “cone” cracks improves the description of the element behavior especially in the stabilized cracking stage. The same applies if thin secondary cracks are taken into account.

Feasibility of tension braces using Cu-Al-Mn superelastic alloy bars

SUMMARY This paper investigates the feasibility of tension braces using Cu–Al–Mn superelastic alloy bars as energy dissipating and self-centering elements for steel frames by performing 1/3 scale shaking table tests. The difficulty with conventional steel tension braces lies in pinching or significant deterioration of stiffness and strength under cyclic loading. When a steel frame with conventional tension braces is subjected to intense earthquakes, pinching may lead to a large residual drift and/or instability. To overcome the difficulty, this paper examines the effectiveness of Cu–Al–Mn superelastic alloy bars, facilitated by their large recovery strain, low material cost, and high machinability, as a partial replacement of steel bars in tension braces. In the shaking table tests, a 1/3 scaled 1-bay, 1-story steel frame with the present tension braces is subjected to quasi-static cyclic loading and dynamic harmonic ground motions of 6 Hz. Both the static and dynamic test results demonstrate the effectiveness of the present braces in avoiding pinching under the ductility ratio up to 3. The dynamic test results also demonstrate the capability of the present tension braces in reducing the peak response acceleration within the base shear capacity. To study the rate dependence of the frame response, further, time-history analyses are performed by using a SDOF model based on a uniaxial rate-independent model, calibrated with the quasi-static tests. A comparison of the analytical results with the dynamic test results demonstrates that the rate dependence of the frame response is negligible up to the loading frequency of 6 Hz. Copyright © 2014 John Wiley & Sons, Ltd.

Constitutive Relation of Engineering Material Based on SIR Model and HAM

As an epidemic mathematical model, the SIR model represents the transition of the Susceptible, Infected, and Recovered. The profound implication of the SIR model is viewed as the propagation and dynamic evolutionary process of the different internal components and the characteristics in a complex system subject to external effect. The uniaxial stress-strain curve of engineering material represents the basic constitutive relation, which also represents the damage propagation in the units of the damaged member. Hence, a novel dynamic stress-strain model is established based on the SIR model. The analytical solution and the approximate solution for the proposed model are represented according to the homotopy analysis method (HAM), and the relationship of the solution and the size effect and the strain rate is discussed. In addition, an experiment on the size effect of confined concrete is carried out and the solution of SIR model is suitable for simulation. The results show that the mechanical mechanism of the parameters of the uniaxial stress-strain model proposed in this paper reflects the actual characteristics of the materials. The solution of the SIR model can fully and accurately show the change of the mechanical performance and the influence of the size effect and the strain rate.

In vitro uniaxial stretch model for evaluating the effect of strain along axon on damage to neurons

Diffuse axonal injury (DAI), a major component of traumatic brain injury, is associated with rapid deformation of brain tissue resulting in the stretching of neuronal axons. Focal axonal beading, which is the morphological hallmark of DAI pathology, leads to the disconnection of neurons from tissues and results in cell death. Our goal is to achieve a better understanding of neuronal tolerance and help predict the pathogenesis of DAI from mechanical loading to the head. In the present study, we developed an experimental model that subjected cultured neurons to uniaxial stretch by controlling the direction of axonal elongation with a microfluidic culture technique and examined the effect of strains along the axon on cell damage. Neurites from PC 12 cells that differentiate into neurons with structurally axon-like cylindrical protrusions by nerve growth factor were extended at 0°, 45°, and 90° relative to the tensile direction by using a fabricated polydimethylsiloxane (PDMS) piece with microgrooves in combination with a PDMS substrate. The morphology of the same neurites was observed before and after stretching with a strain of 0.22 at a strain rate of 27 s-1. As a result, swellings along neurites oriented at 0° increased immediately following stretching and were sustained for 24 h. In contrast, swellings along neurites oriented at 45° and 90° transiently increased within 1 h following stretching. Although more ruptures were observed in neurites oriented at 0° and 90° than in those oriented at 45°, the number of neurites and cells did not differ among orientation conditions. These results suggest that the difference in strain along the axon induces axonal injuries differing in type and degree. They also suggest that the strain on the axon, rather than that on the cell-cultured substrate, is important for evaluating neuronal damage.

Tunable hydrodynamic characteristics in microchannels with biomimetic superhydrophobic (lotus leaf replica) walls

The present work comprehensively addresses the hydrodynamic characteristics through microchannels with lotus leaf replica (exhibiting low adhesion and superhydrophobic properties) walls. The lotus leaf replica is fabricated following an efficient, two-step, soft-molding process and is then integrated with rectangular microchannels. The inherent biomimetic, superhydrophobic surface-liquid interfacial hydrodynamics, and the consequential bulk flow characteristics, are critically analyzed by the micro-particle image velocimetry technique. It is observed that the lotus leaf replica mediated microscale hydrodynamics comprise of two distinct flow regimes even within the low Reynolds number paradigm, unlike the commonly perceived solely apparent slip-stick dominated flows over superhydrophobic surfaces. While the first flow regime is characterized by an apparent slip-stick flow culminating in an enhanced bulk throughput rate, the second flow regime exhibits a complete breakdown of the aforementioned laminar and uni-axial flow model, leading to a predominantly no-slip flow. Interestingly, the critical flow condition dictating the transition between the two hydrodynamic regimes is intrinsically dependent on the micro-confinement effect. In this regard, an energetically consistent theoretical model is also proposed to predict the alterations in the critical flow condition with varying microchannel configurations, by addressing the underlying biomimetic surface-liquid interfacial conditions. Hence, the present research endeavour provides a new design-guiding paradigm for developing multi-functional microfluidic devices involving biomimetic, superhydrophobic surfaces, by judicious exploitation of the tunable hydrodynamic characteristics in the two regimes.