Uniaxial Model Research Articles

Simulation of distortional hardening by generalizing a uniaxial model of finite strain viscoplasticity

In this paper we generalize a uniaxial model of finite strain viscoplasticity (proposed by Shutov and Kreißig) using the so-called concept of representative directions. As a result, a new three-dimensional phenomenological material model is obtained. The original model takes the nonlinear isotropic and kinematic hardening into account, but it does not cover the distortional hardening. Using a series of numerical computations we show that the isotropic and kinematic hardening is completely retained during the process of generalization. Moreover, the distortional hardening effects are automatically induced by the concept itself. This is demonstrated by simulating combined tension–torsion tests on thin-walled tubular specimens. Furthermore, the generalized material model is validated by a comparison with real experimental data concerning the shape of the yield surface. A good correspondence between the simulation results and the measurements is observed.

Modelling of high-temperature inelastic behaviour of the austenitic steel AISI type 316 using a continuum damage mechanics approach

A conventional material behaviour model can be extended to taking into account varying thermo-mechanical loading conditions in wide stress range. The motivation for developing this model is given by the well documented failure case study of high-temperature components at unit 1 of the Eddystone fossil power plant (Pennsylvania, USA), which have operated for 130,520 h in creep–fatigue interaction conditions. The developed model basis is a creep constitutive law in the form of hyperbolic sine stress response function originally proposed by Nadai (1938). The constitutive law is extended to assume the damage process by the introduction of scalar damage parameter and appropriate evolution equation according to Kachanov–Rabotnov concept. The research task is the introduction into the constitutive model of a few additional material state variables, able to reflect hardening and recovery effects under cyclic loading conditions. The first variable is represented by the relatively fast saturating back-stress [Formula: see text] describing kinematic hardening. The second variable is represented by the relatively slow saturating parameter [Formula: see text] describing isotropic hardening. Evolution equations for [Formula: see text] and [Formula: see text] are formulated in a modified form originally proposed by Chaboche and based on the Frederick–Armstrong concept. The uniaxial modelling results are compared with cyclic stress–strain diagrams and alternative experimental data in the form of creep curves, tensile stress–strain diagrams, relaxation curves, etc., for the austenitic steel AISI type 316 at 600 °C in a wide stress range.

A formulation of the Eurocode 2 concrete model at elevated temperature that includes an explicit term for transient creep

The first objective of this paper is to highlight the capabilities and limitations of concrete uniaxial constitutive models at elevated temperatures for thermo-mechanical behavior modeling, depending on the implicit or explicit consideration of transient creep strain in the model. The characteristics inherent to the two types of models are described and compared. It appears that one of the major limitations of implicit models concerns the unloading stiffness. Based on numerical analysis performed on loaded concrete columns subjected to natural fire, it is shown that the stress–temperature paths experienced by structural concrete are varied and complicated and that concrete material models cannot handle properly these complex situations of unsteady temperatures and stresses without explicit consideration of transient creep.The second objective of the paper is to propose a new formulation of the Eurocode 2 concrete material model that contains an explicit term for transient creep. The new model is implemented in the software SAFIR and validated against experimental data of the mechanical strain developed by concrete cylinders under different unsteady temperatures and loads. It is shown that the actual material behavior is better matched with the new explicit model than with the current implicit Eurocode 2 model. Finally, a comparison is given between experimental and computed results on a centrally loaded concrete column submitted to heating–cooling sequence.

Comparison of three models of actigraph accelerometers during free living and controlled laboratory conditions

The aim of this study was to compare the outputs of three commonly used uniaxial Actigraph models (Actitrainer, 7164 and GT1M) under both free-living and controlled laboratory conditions. Ten adults (mean age = 24.7±1.1 years) wore the three Actigraph models simultaneously during one of day free-living and during a progressive exercise protocol on a treadmill at speeds between 1.5 and 5.5 miles per hour (mph). During free-living the three Actigraph models produced comparable outputs in moderate, vigorous and moderate-to-vigorous physical activity (MVPA) with effect sizes typically <0.2, but lower comparability was seen in sedentary and light categories, as well as in total step counts (effect sizes often >0.30). In controlled conditions, acceptable comparability between the three models was seen at all treadmill speeds, the exception being walking at 1.5 mph (mean effect size = 0.48). It is concluded that care should be taken if different Actigraph models are to be used to measure and compare light physical activity, step counts and walking at very low speeds. However, using any of these three different Actigraph models to measure and compare levels of MVPA in free-living adults seems appropriate.

DEVELOPMENT AND APPLICATION OF STEEL-CONCRETE COMPOSITE FIBER BEAM MODEL IN ABAQUS PLATFORM

A steel-concrete composite fiber beam model is developed in this paper, which can divide the composite sections into fibers and the user-defined uniaxial hysteretic material constitutive model can be incorporated in subprogram UMAT provided by ABAQUS. The steel-concrete composite fiber beam model can be used to perform global elasto-plastic analysis of composite frames with full connections subjected to the combined action of gravity and cyclic lateral loads. The model is verified through a number of experiments showing that the composite fiber beam model developed by authors possesses good accuracy and wide applicability compared with the traditional finite element model. Although the fiber beam model neglects the slip between steel beam and concrete slab, the accuracy of global predictions of steel-concrete composite frames is not affected. So the developed steel-concrete fiber beam model possesses modelling simplicity and calculation efficiency, and is suitable for the seismic analysis of steel-concrete composite frames.

Analysis of composite frame structures with mixed elements - state of the art

The paper presents a review of the application of the newly proposed mixed finite element model for seismic simulation of different types of composite frame structures. To evaluate the performance of the element, a comparison with displacement-based and force-based models is conducted. The study revealed that the mixed model is superior to the others in terms of both speed of convergence and numerical stability, and is therefore considered the most practical approach for modeling of composite structures. In this model, the element is derived using independent force and displacement shape functions. The nonlinear response of the frame element is based on the section discretization into fibers with uniaxial material models. The interfacial behavior is modeled using an inelastic interface element. Numerical examples to clarify the advantages of the model are presented for the following structural applications: anchored reinforcing bar problems, composite steel-concrete girders with deformable shear connectors, beam on elastic foundation elements, R/C girders strengthened with FRP sheets, R/C beam-columns with bond-slip, and prestressed concrete girders. These studies confirmed that the model represents a major advancement over existing elements in simulating the inelastic behavior of composite structures.

Influence of optical-phonon scattering on electron mobility in wurtzite AlGaN/AlN/GaN heterostructures

Adopting a numerical method of solving self-consistently the Schrdinger equation and Poisson equation through taking into account the realistic heterostructure potential, which includes the influences of energy band bending and the finite thickness of barriers, and through considering the built-in electric field induced by spontaneous and piezoelectric polarization, the eigenstates and eigenenergies of electrons in two-dimensional electron gas (2DEG) are obtained for wurtzite AlxGa1-xN/AlN/GaN heterostructures with an inserted AlN layer. Based on the continuous dielectric model and the Loudon's uniaxial crystal model, optical-phonon modes and their ternary mixed crystals effect are discussed using the transfer matrix method. Furthermore, the Lei-Ting balance equation is extended in order to investigate the distribution of 2DEG and its size effect as well as ternary mixed crystals effect on electron mobility, which under the influence of each branch of optical-phonon modes are analyzed at room temperature. The results show that the increases of the thickness of inserted AlN layer and the Al component of AlxGa1-xN in the barrier enhance the built-in electric field in the GaN layer, leading 2DEG to be much closer to the interface of a heterostructure. In addition, it can also be found that the scattering from the interface phonons is stronger than from other optical-phonons, the interface phonons play a dominant role in the total mobility. A higher electron mobility can be obtained by adjusting appropriately the thickness of inserted AlN layer and Al component.

Full polar optical phonon states and dispersive spectra of a wurtzite GaN/AlN rectangular quantum wire

Within the framework of the dielectric continuum model and Loudon's uniaxial crystal model, the full polar optical phonon modes including the quasi-confined (QC) modes, the propagating (PR) modes, the half-space (HS) modes, and the interface optical (IO) modes in a quasi-one-dimensional (Q1D) wurtzite rectangular quantum wire (QWR) structure are deduced and analyzed. The analytical phonon states, their dispersion equations and polar polarization eigenvectors are derived. Numerical calculation of dispersive spectra for these modes is performed on a wurtzite GaN/AlN rectangular QWR. The behavior of the QC mode reducing to the IO mode is observed clearly in the dispersive curves of these modes, which reveals that the present theories of phonon modes are self-consistency and correct for the description of phonon modes in wurtzite Q1D rectangular NW. These observations and results reveal that the confined dimensionality and cross-section shape influence greatly the dispersive properties of phonon modes in wurtzite quantum confined systems.

Elastic Viscoplastic Sub-impacts of Free-free Beam Struck by Rigid Mass

By employing the overstress model,the effect of strain rate on local elastic viscoplastic contact deformation and free-free beam dynamics is considered.A local elastic viscoplastic uniaxial compression deformation model is presented to take into account the multiple impact-contact deformations.By the use of the finite difference method and the impact and separation conditions,the sub-impact phenomenon of a free-free beam horizontally stuck by a rigid mass is investigated.It is found that the horizontal impact is indeed a complicated process including elastic viscoplastic sub-impacts.The effect of strain rate of the beam has a significant role in local contact deformation and beam dynamics.It results in the obvious variations of impact force,elastic deformation and viscoplastic deformation of the beam.The present numerical simulations are compared with those solved by the three-dimensional dynamic finite element method.The comparisons illustrate that the present method is reasonable.

Stabilisation yields strong convergence of macroscopic magnetisation vectors for micromagnetics without exchange energy

The convexified Landau–Lifshitz minimisation problem in micromagnetics leads to a degenerate variational problem. Therefore strong convergence of finite element approximations cannot be expected in general. This paper introduces a stabilized finite element discretization which allows for surprising the strong convergence of the discrete magnetisation fields with reduced convergence order for a uniaxial model problem. This yields a convergent method for the approximation of the Young measure which characterises the enforced microstructure for the generalized solution of the non-relaxed Landau–Lifshitz problem.

Nonlinear Seismic Analysis of Circular Concrete-Filled Steel Tube Members and Frames

Accurate nonlinear formulations are necessary for the assessment of structures under seismic and other extreme loading. In this work, a three-dimensional distributed plasticity beam element formulation for circular concrete-filled steel tubes has been developed for nonlinear static and dynamic analyses of composite seismic force resisting systems. A mixed basis for the element formulation was adopted to allow for accurate modeling of both material and geometric nonlinearities. The formulation utilizes uniaxial cyclic constitutive models for the concrete core and steel tube that account for the salient features of each material, as well as the interaction between the two, including concrete confinement and local buckling of the steel tube. The accuracy of the formulation was verified against a wide variety of experimental results. The verification confirms the capability of the formulation to accurately produce realistic simulations of element and frame behavior.

On the simulation of nonlinear hardening in metallic materials using the concept of representative directions

AbstractWe generalize a uniaxial model of finite strain viscoplasticity using the concept of representative directions. As a result, a new phenomenological material model is obtained, which can describe the mechanical behavior under arbitrary loading conditions. The original uniaxial model takes the nonlinear isotropic and kinematic hardening into account, but it does not cover the distortional hardening. We show that the isotropic and kinematic hardening is completely retained during the process of generalization. Moreover, the distortional hardening effects are naturally induced by the concept. The resulting material model is validated by a comparison with real experimental data. (© 2011 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

A new beam-column model for seismic analysis of RC frames – Part I: Model derivation

In this study, a reliable and computationally efficient beam-column model is proposed for seismic analysis of Reinforced Concrete (RC) frames. The model is a simplified version of the Flexibility-Based Fiber Models (FBFMs), which rely on dividing the element length into small segments and dividing the cross section of each segment into concrete and steel fibers. In the proposed model, only the two end sections are subdivided into fibers and uniaxial material models that consider the various behavioral characteristics of steel and concrete under cyclic loading conditions are assigned for the cross section fibers.The proposed model is simpler than the FBFMs as it does not require monitoring the responses of many segments along the element length, which results in a significant reduction in computations. The inelastic lengths at the ends of the proposed model are divided into two inelastic zones; cracking and yielding. The inelastic lengths vary according to the loading history and are calculated in every load increment. The overall response of the RC member is estimated using preset flexibility distribution functions along the element length. A flexibility factor η is utilized to facilitate selecting the proper flexibility distribution shape. The proposed model is implemented into the computer program DRAIN-2DX.

The Secondary Development of Nonlinear Viscoelastic Constitutive Model Based on ABAQUS

Based on the subroutine VUMAT, user-defined material model in the nonlinear finite element software ABAQUS/EXPLICIT, a nonlinear viscoelastic constitutive model is developed. The validify of the subroutine has been proven through the standard uniaxial tensile model. The shortage of finite element softwares which only have linear viscoelastic constitutive model is remedied. This paper presents the process of developing a material constitutive model and some useful technology. It can be referred for extending the material constitutive model in finite element softwares.

A generalized hysteresis model for biaxial response of pile foundations in sands

We present the development and calibration of a macroelement model that captures the response of piles in cohesionless soils subjected to biaxial lateral loading. The model is founded on actual physical mechanism of soil resistance and provides the framework for extending a uniaxial model to biaxial case by means of a single cross-stiffness parameter. Both upper and lower bounds for the cross-stiffness parameter are also presented. The model is calibrated and verified using three-dimensional finite element (FE) simulations of soil-pile interaction for uniformly prescribed displacement along the pile length. Comparison of predictions from uniaxial and biaxial models with the FE results for transient loading indicates that the response assuming no coupling between the two horizontal directions for biaxial loading can differ significantly from the ‘true’ response for some cases. Accounting for coupling in the lateral direction, the proposed model captures the transverse pile response with very good accuracy while retaining the simplicity and computational efficiency of macroelement formulations compared to 3D FE analyses.

Analysis of Uniaxial Dynamic Performance of Concrete-Filled Square Steel Tube Composite Column

Considering the strain rate then puts forward the modified uniaxial dynamic constitutive model related to strain rate in concrete-filled square steel tube and the modified calculation results match well with the experimental results. Based on the above conclusion, uniaxial compression performance finite element analysis with different strain rate among 10-5/s–10-3/s is completed, the results showed that strain rate can obviously change the dynamic performance of the concrete-filled square steel tube. Through the analysis of the influencing factors of the core concrete compressive strength, it is showed that with the increasing of the strain rate and the improving of concrete strength, the ultimate bearing capacity of concrete-filled square steel tube is higher and the ductility is reduced. With the increasing of stirrup ratio, ultimate bearing capacity is greater and the ductility is enhanced. With the sectional dimensions increasing, the ultimate bearing capacity is greater and the ductility is enhanced.

Small radius solitons in magnets with a strong planar anisotropy

The stable topological solitons with a small radius exist for ferromagnets with not small anisotropy. Even in the case of rather strong planar anisotropy, the spatial anisotropy of the soliton solution turns out to be so small that a soliton in dynamical experiments behaves similar to that for the case of a purely uniaxial model.

Micro-mechanical prediction of UD laminates behavior under combined compression up to failure: influence of matrix degradation

This article aims to model the behavior of carbon fiber-reinforced polymer laminates up to failure and predict the corresponding energy absorption, under mixed loadings involving compression. In Guimard JM, Allix O, Pechnik N and Thévenet P. [Statistical energy and failure analysis of CFRP compression behavior using a uniaxial microbuckling model. J Compos Mater 2007; 41: 2807–2828], a simplified 2D micro-model has been used in order to assess the influence of the fiber misalignment parameters on the micro-structural compression behavior, both in terms of critical stresses and dissipated energies. This article goes further by introducing the influence of a shear pre-stress and by considering an inelastic and damageable constitutive behavior for the matrix and not only an inelastic one as it is done in the literature. Together with fiber waviness, these three parameters are proven to be critical for the simulation of the kinking phenomenon. Particularly, the main effect of the damageable behavior of the matrix is to avoid unrealistically high hardening of the epoxy. This affects the results significantly and allows a better correlation of the model with experimental data. It is shown, by a statistical analysis, that failure stresses are sensitive to both shear pre-stresses and fiber waviness. Dissipated energies and kink-band size are found to be affected by a shear pre-stress as well but rather less sensitive to fiber waviness.

Ternary mixed crystal effect on electron mobility in a strained wurtzite AlN/GaN/AlN quantum well with an InxGa1−xN nanogroove

Based on the dielectric continuum phonon model, uniaxial model and force balance equation, the influence of an InxGa1−xN nanogroove inserted in a strained wurtzite AlN/GaN/AlN quantum well on electron mobility is studied. The results show that the optical phonon modes will be changed by the introduction of InGaN/GaN interfaces and the In component. It can be also found that the electron wave function will shift to the InGaN layer as long as the conductor band energy at GaN/InGaN interface gets lower than that at the AlN/GaN interface. Electron mobility first increases and then decreases as x increases, whereas the mobility is always greater than the case without an InGaN nanogroove when electrons mainly distribute in the GaN layer. Once most of the electrons transfers to the InGaN nanogroove, electron mobility drops sharply and then increases with the increase of x.

Polar optical phonon states and dispersive spectra of wurtzite ZnO nanocrystals embedded in zinc-blende MgO matrix

Based on the macroscopic dielectric continuum model and Loudon’s uniaxial crystal model, the polar optical phonon modes of a quasi-0-dimensional (Q0D) wurtzite spherical nanocrystal embedded in zinc-blende dielectric matrix are derived and studied. It is found that there are two types of polar phonon modes, i.e. interface optical (IO) phonon modes and the quasi-confined (QC) phonon modes coexisting in Q0D wurtzite ZnO nanocrystal embedded in zinc-blende MgO matrix. Via solving Laplace equations under spheroidal and spherical coordinates, the unified and analytical phonon states and dispersive equations of IO and QC modes are derived. Numerical calculations on a wurtzite/zinc-blende ZnO/MgO nanocrystal are performed. The frequency ranges of the IO and QC phonon modes of the ZnO/MgO nanocrystals are analyzed and discussed. It is found that the IO modes only exist in one frequency range, while QC modes may appear in three frequency ranges. The dispersive frequencies of IO and QC modes are the discrete functions of orbital quantum numbers l and azimuthal quantum numbers m. Moreover, a pair of given l and m corresponds to one IO mode, but to more than one branches of QC. The analytical phonon states and dispersive equations obtained here are quite useful for further investigating Raman spectra of phonons and other relative properties of wurtzite/zinc-blende Q0D nanocrystal structures.