Nonuniform State Research Articles

Effects of nonuniform initial stress state on apparent fracture toughness

We analyze the nonuniform stress state in the vicinity of the fracture tip and its impact on apparent fracture toughness. It is shown that prescribing the boundary conditions at the deformed fracture faces allows one to take into account the effect of nonuniform tectonic stresses acting in the plane of the fracture. We conclude that the fracture may take an ellipsoidal form (aspect ratio departs from unity) as a result of interactions with anisotropic distribution of initial stresses, which leads to nonuniform growth in longitudinal and vertical directions. An expression for the effective stress intensity coefficient (fracture toughness) is obtained as a function of the nonuniform initial stress state. A simplified asymptotic approximation to the solution for the effective apparent fracture toughness is given, which may be further implemented into the near-tip asymptotics used in the form of a tip element in the numerical implementation of a Planar3D approach to hydraulic fracture simulation.

Spatial pattern formation in reaction-diffusion models: a computational approach.

Reaction-diffusion equations have been widely used to describe biological pattern formation. Nonuniform steady states of reaction-diffusion models correspond to stationary spatial patterns supported by these models. Frequently these steady states are not unique and correspond to various spatial patterns observed in biology. Traditionally, time-marching methods or steady state solvers based on Newton's method were used to compute such solutions. However, the solutions that these methods converge to highly depend on the initial conditions or guesses. In this paper, we present a systematic method to compute multiple nonuniform steady states for reaction-diffusion models and determine their dependence on model parameters. The method is based on homotopy continuation techniques and involves mesh refinement, which significantly reduces computational cost. The method generates one-parameter steady state bifurcation diagrams that may contain multiple unconnected components, as well as two-parameter solution maps that divide the parameter space into different regions according to the number of steady states. We applied the method to two classic reaction-diffusion models and compared our results with available theoretical analysis in the literature. The first is the Schnakenberg model which has been used to describe biological pattern formation due to diffusion-driven instability. The second is the Gray-Scott model which was proposed in the 1980s to describe autocatalytic glycolysis reactions. In each case, the method uncovers many, if not all, nonuniform steady states and their stabilities.

Особенности процессов деформирования монокристаллического никелида титана при действии импульса всестороннего сжатия

Using the example of single-crystal titanium nickelide, the importance of taking into account the volume compressibility anisotropy when calculating the processes of elastoplastic deformation in materials with cubic symmetry of elastic properties is shown. It is shown that the process of uniform volumetric deformation corresponds to the process of non-uniform stress state for materials with cubic symmetry of properties for some orientations of the calculated coordinate system relative to the directions of the main crystallographic axes. The index surface of volume compressibility (or the reciprocal of it - the compression modulus) has a non-spherical shape and is a function of Euler angles. This is shown for the first time by solving a model problem - determining the stress and strain states of a spherical body made of single-crystal titanium nickelide under the action of a comprehensive compression pulse. In the general case of orienting the calculated coordinate system relative to the directions of the main crystallographic axes, an initially spherical body of single-crystal titanium nickelide is deformed into a biaxial ellipsoid under the influence of a comprehensive compression pulse.

Artificial Dense Lattices of Magnetic Skyrmions.

Multilayer Co/Pt films with perpendicular magnetic anisotropy are irradiated by focused a He+ ion beam to locally reduce the anisotropy value. The irradiated spots with the diameters of 100 and 200 nm are arranged in square lattices with the periods of 200 and 300 nm. The formation of nonuniform magnetic states within the spots was observed by magnetic force microscopy methods. We use the concentric distribution of the irradiation fluence within the spot to obtain the radial modulation of the anisotropy constant. This allows us to induce magnetic skyrmions during magnetization reversal of the system. The skyrmions remained stable at zero external magnetic field at room temperature. Magnetization hysteresis loops of the samples were investigated by magnetooptical methods and the results are in good agreement with micromagnetic simulations.

Implementation of Incremental Yield Condition for Continual Problems with Singularity

The limit elastic state of an infinitely large half-plane under the action of concentrated vertical and horizontal forces has been considered. The gradient yield condition specifying the elasto-plastic material yielding initial moment at non-uniform stress state is used as the limit state criterion. The analytical expressions allowing to interpret the result in the singular point have been derived.

Localized magnetic non-uniformities in an antiferromagnet with a system of dislocations

In the crystal lattice of an antiferromagnet, dislocations are the origin of specific lines in the field of antiferromagnetic vector I, resembling disclinations in the field of the vector-director for nematic liquid crystals. A single atomic dislocation creates a delocalized non-uniform state – a spin disclination. A “compensated” system of dislocations, a closed dislocation loop in a three-dimensional antiferromagnet or a pair of point dislocations in a two-dimensional antiferromagnet, are shown to form a localized spin non-uniformity, similar to a soliton. For an isotropic or easy-plane antiferromagnet the shape of these solitons is ellipsoidal or circular in three- or two-dimensional cases, respectively. The geometry of a lattice defect differs from that of a soliton; for example, a planar lattice defect, a dislocation loop, produces a nearly spherical three-dimensional spin non-uniformity. In the presence of in-plane anisotropy, a domain wall forms in the easy-plane and ends on the dislocation line (points).

An Expanding Cavity Model for Indentation Analysis of Shape Memory Alloys

Abstract The mechanical and functional responses of shape memory alloys (SMAs), which are often used in small volume applications, can be evaluated using instrumented indentation tests. However, deciphering the indentation test results in SMAs can be complicated due to the combined effects of the non-uniform state of stress underneath the indenter and stress-induced phase transformation. To address this issue, an expanding cavity model (ECM) applicable to spherical indentation of SMAs is developed in this work based on an analytical solution for an internally pressurized hollow sphere. Analytical expressions for key indentation parameters such as the mean contact pressure and size of the transforming zone are obtained, whose validity is evaluated by recourse to finite element simulations and published experimental data for a Ni–Ti alloy. It is shown that the ECM predicts the above parameters reasonably well for indentation strains varying from 0.01 to 0.04. Also, a method is proposed to determine the critical stress required to initiate phase transformation under uniaxial compression based on the application of the ECM to interpret the indentation stress–strain response.

Localized strain fields in honeycomb materials with convex and concaved cells

Characterizing the local deformations and strain fields in ligaments of periodic honeycomb materials is instrumental to applications such as cores of sandwich structure as well as honeycomb shaped tunable phononic crystals, compliant metamaterials, and 4D printed shape memory materials. Such applications employ honeycomb shaped materials whose nonlinear behavior is controlled by localized deformations in their ligaments. These local deformations can exhibit values and complex non-uniform states that far exceed the overall macroscopic deformations and strains sustained by the honeycomb material in value and complexity. Each of the aforementioned applications can be better designed with an improved understanding of the evolution of local strain fields in honeycombs' ligaments during their deformation. This work aims to characterize the local strains and deformations developing in honeycomb ligaments near honeycombs’ macroscopic onset of yielding. Finite element computations and the full field strain measurement technique digital image correlation (DIC) are used to measure and characterize the local deformations in the ligaments of concaved and convex honeycombs. Results show nonlinear strain gradients and significant localization in deformed ligaments. Moreover, complex state of stress comprising biaxial normal stresses and shear stresses exists near plastic zones.

Experimental determination of the shear strength of peat from standard undrained triaxial tests: correcting for the effects of end restraint

Conventional triaxial tests on peats are strongly criticised due to the very high shear strength parameters obtained from standard data elaboration, leading to unrealistic factors of safety when used in geotechnical design and assessment. Various operational approaches have been proposed in the literature to overcome this difficulty; however, they seem to lack consistent mechanical background. Some of the issues related to the shear strength evaluation of peats from triaxial tests come from the non-uniform stress and strain states developing in the samples well before failure is attained, due to end restraint effects. Undrained triaxial compression tests were performed on reconstituted peat to examine the influence of end restraint on the deviatoric stress, excess pore pressure and deviatoric strain response. Samples were tested with standard rough end platens and with modified platens to reduce the friction between the sample and bottom and top caps. Four different initial height-to-diameter ratios were examined, to reduce the consequences of rough end platens on the sample response. The results indicate that end restraint contributes dramatically to overestimating the shear strength of peat, due to the increase in both the calculated deviatoric stress and the measured excess pore pressure at the bottom of the sample. Suggestions are given to quantify the influence of end restraint in the interpretation of standard data, in an attempt to suggest viable procedures to determine more reliable effective and undrained shear strength parameters from standard triaxial tests.

Size-dependent spatial magnetization profile of manganese-zinc ferrite Mn0.2Zn0.2Fe2.6O4 nanoparticles

We report the results of an unpolarized small-angle neutron scattering (SANS) study on Mn-Zn ferrite (MZFO) magnetic nanoparticles with the aim to elucidate the interplay between their particle size and the magnetization configuration. We study different samples of single-crystalline MZFO nanoparticles with average diameters ranging between 8 to 80 nm, and demonstrate that the smallest particles are homogeneously magnetized. However, with increasing nanoparticle size, we observe the transition from a uniform to a nonuniform magnetization state. Field-dependent results for the correlation function confirm that the internal spin disorder is suppressed with increasing field strength. The experimental SANS data are supported by the results of micromagnetic simulations, which confirm an increasing inhomogeneity of the magnetization profile of the nanoparticle with increasing size. The results presented demonstrate the unique ability of SANS to detect even very small deviations of the magnetization state from the homogeneous one.

Smart Materials Based on a High and Low Temperatures SME-Alloys

The analysis of the nature of low plasticity of composites with strengthening of hard phases are shown that plastic shear constraint in thin interlayer of the binding phase does not provide the small scale of the structural level of deformation. As a result, a material undergoes a brittle fracture. Therefore, one should find another mechanism for relaxation of internal stress concentrations in composites during loading.The aim of a present paper is to illustrate the concept of how use a shape memory alloys with phase transformation for metal matrix composites. It has been studied shape memory based alloys and deformation and fracture of MMC with phase transformations in matrix.It have been shown that if plastic deformation is considered as local structural transformation and instability in the material is provided from the very beginning, this will result in a general increase of plasticity due to a decrease in the scale of the structural level of plastic deformation.Deformation tests of composites near the phase transition temperature show that there are different transformations induced by a highly non-uniform stress state of the binding phase. Under loading the “quasi-amorphous state” is formed in the binding phase after formation of a microcrystalline, highly misoriented structure with the characteristic size of crystallites less than 10 nm. This structure has high plasticity and strong hardening. It governs an efficient transfer of external load to solid particles, inducing dislocation glide even in typically brittle titanium carbide particles during non-uniform loading.

Corrections to the Landau kinetic equation for a weakly dissipative randomly driven system and the fluctuation-dissipation theorem

This paper is devoted to the derivation of a kinetic equation for many-body one-component dissipative systems in an external random field. The system under consideration was discussed in the recent paper by Sliusarenko et al. [J. Math. Phys. 56, 043302 (2015)], where a generalization of the Vlasov kinetic equation was obtained. The potential interaction is assumed to be small (the corresponding small parameter λ), the dissipation interactions and the correlation functions of the external random field are considered as small quantities estimated by one small parameter μ for the simplicity. The kinetic equation is obtained up to the terms of the orders λ2μ0, λ1μ1, λ0μ2 inclusive. In weakly spatially nonuniform states of the system, this gives corrections to the Landau–Vlasov kinetic equation caused by the dissipation and external random field. In the case λ ≫ μ after the mean free time, the system reaches a state approximately described by the Maxwell distribution. The dissipation and random field will lead to the evolution of the system temperature. A time evolution equation for the temperature in spatially uniform states is derived on the basis of the obtained kinetic equation by a generalized Chapman–Enskog method which takes into account that the kinetic equation is an approximate one. This temperature time evolution equation is investigated up to the terms of the order μ3 inclusive. It is shown that under some conditions the final stage of the system evolution is a steady state. A fluctuation-dissipation theorem for this state is discussed. In this steady state, the system is described by a distribution function that contains corrections to the Maxwell distribution.

Ferroelectric Tunnel Junctions Enhanced by a Polar Oxide Barrier Layer

Ferroelectric tunnel junctions (FTJs) have recently aroused significant interest due to the interesting physics controlling their properties and potential application in nonvolatile memory devices. In this work, we propose a new concept to design high-performance FTJs based on ferroelectric/polar-oxide composite barriers. Using density functional theory calculations, we model electronic and transport properties of LaNiO3/PbTiO3/LaAlO3/LaNiO3 tunnel junctions and demonstrate that an ultrathin polar LaAlO3(001) layer strongly enhances their performance. We predict a tunneling electroresistance (TER) effect in these FTJs with an OFF/ON resistance ratio exceeding a factor of 104 and ON state resistance as low as about 1 kΩμm2. Such an enhanced performance is driven by the ionic charge at the PbTiO3/LaAlO3 interface, which significantly increases transmission across the FTJ when the ferroelectric polarization of PbTiO3 is pointing against the intrinsic electric field produced by this ionic charge. This is due to the formation of a two-dimensional (2D) electron or hole gas, depending on the LaAlO3 termination being (LaO)+ or (AlO2)-, respectively, which is formed to screen the polarization charge of the nonuniform polarization state. This 2D electron (hole) gas can be switched ON and OFF by the reversal of ferroelectric polarization, resulting in the giant TER effect. The proposed design suggests a new direction for creating FTJs with a stable and reversible ferroelectric polarization, a sizable TER effect, and a low-resistance-area product, as required for memory applications.

Chimera States in Networks of Locally and Non-locally Coupled SQUIDs

Planar and linear arrays of SQUIDs (superconducting quantum interference devices) operate as nonlinear magnetic metamaterials in microwaves. Such {\em SQUID metamaterials} are paradigmatic systems that serve as a test-bed for simulating several nonlinear dynamics phenomena. SQUIDs are highly nonlinear oscillators which are coupled together through magnetic dipole-dipole forces due to their mutual inductance; that coupling falls-off approximately as the inverse cube of their distance, i.~e., it is non-local. However, it can be approximated by a local (nearest-neighbour) coupling which in many cases suffices for capturing the essentials of the dynamics of SQUID metamaterials. For either type of coupling, it is numerically demonstrated that chimera states as well as other spatially non-uniform states can be generated in SQUID metamaterials under time-dependent applied magnetic flux for appropriately chosen initial conditions. The mechanism for the emergence of these states is discussed in terms of the multistability property of the individual SQUIDs around their resonance frequency and the attractor crowding effect in systems of coupled nonlinear oscillators. Interestingly, controlled generation of chimera states in SQUID metamaterials can be achieved in the presence of a constant (dc) flux gradient with the SQUID metamaterial initially at rest.

Double Q-PID algorithm for mobile robot control

Many expert systems have been developed for self-adaptive PID controllers of mobile robots. However, the high computational requirements of the expert systems layers, developed for the tuning of the PID controllers, still require previous expert knowledge and high efficiency in algorithmic and software execution for real-time applications. To address these problems, in this paper we propose an expert agent-based system, based on a reinforcement learning agent, for self-adapting multiple low-level PID controllers in mobile robots. For the formulation of the artificial expert agent, we develop an incremental model-free algorithm version of the double Q-Learning algorithm for fast on-line adaptation of multiple low-level PID controllers. Fast learning and high on-line adaptability of the artificial expert agent is achieved by means of a proposed incremental active-learning exploration-exploitation procedure, for a non-uniform state space exploration, along with an experience replay mechanism for multiple value functions updates in the double Q-learning algorithm. A comprehensive comparative simulation study and experiments in a real mobile robot demonstrate the high performance of the proposed algorithm for a real-time simultaneous tuning of multiple adaptive low-level PID controllers of mobile robots in real world conditions.

Wall Temperature Modulates Transversal Spatiotemporal Pattern Selection in Shallow, Nonadiabatic Packed-Bed Reactors

Transversal temperature pattern formation has been observed in laboratory and industrial catalytic packed-bed reactors (PBRs) used for conducting exothermic reactions. These patterns or nonuniform states can strongly affect reactor performance and pose severe safety issues. Recent studies show that symmetry-breaking bifurcations may cause transversal pattern formation in a reactor operated under nonadiabatic conditions. In this study, we show that wall temperature, which dictates the instantaneous and overall heat exchange rate, strongly influences the selection and dynamics of various target and rotating patterns exhibited in a shallow nonadiabatic PBR. We demonstrate this by linear stability analysis-guided extensive numerical simulations of a shallow reactor model assuming periodic blocking-reactivation kinetics for the catalytic reaction. Transversal spatiotemporal patterns predicted in lab-scale (∼6 cm diameter) and/or bench-scale (∼60 cm) reactors, include rotating patterns, inward/outward/multi-rin...

Nonuniform Quantum-Confined States and Visualization of Hidden Defects in Pb(111) Films

The spatial distribution of the differential conductance for ultrathin Pb films grown on Si(111)7x7 substrate is studied by means of low-temperature scanning tunneling microscopy and spectroscopy. The formation of the quantum--confined states for conduction electrons and, correspondingly, the appearance of local maxima of the differential tunneling conductance are typical for Pb films; the energy of such states is determined mainly by the local thickness of Pb film. We demonstrate that the magnitude of the tunneling conductivity within atomically flat terraces can be spatially nonuniform and the period of the small-scale modulation coincides with the period of Si(111)7x7 reconstruction. For relatively thick Pb films we observe large-scale inhomogeneities of the tunneling conductance, which reveal itself as a gradual shift of the quantized levels at a value of the order of 50 meV at distances of the order of 100 nm. We believe that such large-scale variations of the tunneling conductance and, respectively, local density of states in Pb films can be related to presence of internal defects of crystalline structure, for instance, local electrical potentials and stresses.

Investigations of MgO on Sintering Performance and Metallurgical Property of High-Chromium Vanadium-Titanium Magnetite

High-chromium vanadium-titanium magnetite (HCVTM) in the Hongge region has been used as an essential mineral resource in ironmaking. The effects of MgO on sintering performance and metallurgical properties were investigated by sintering pot tests, X-ray diffraction (XRD), and scanning electron microscopy-energy dispersive spectroscopy (SEM-EDS). HCVTM sinters with varying MgO contents (2.7–3.5%), which was achieved by adding dolomite, were tested for yield, strength, reduction degradation index (RDI), reduction index (RI), and softening-melting properties. The productivity and the comprehensive index were evaluated. The results show that yield and productivity increased, while the vertical sintering speed and the tumbler index (TI) initially increased then decreased with the increase of MgO content. The mineral structure of HCVTM sinter changed from a non-uniform state to a uniform state with increased MgO content. Most of the Mg2+ entered the magnetite lattice, while a small amount entered the perovskite and the calcium silicate. The increase of MgO content improved RDI and softening-melting properties while reducing RI. The best recommended amount of MgO was 3.3% from the comprehensive index.

Two Parameters Confinement Model for Clay Brick Masonry

Modeling of masonry confinement has been usually derived from concrete confinement, which was deeply tested in the last decades. However concrete and masonry have some crucial differences, e.g., ordinary concrete performance can be usually fully defined by the cylindrical compressive strength, while masonry does not. In the present work, a failure criterion is considered on a solid mechanics base. Such criteria are useful not only to introduce non-uniform stress states, as those developed in non-axisymmetric confined elements, but also to be implemented in FEM. The validity of the adopted failure criterion has been checked against actively confined clay brick masonry and a database of passive confinement tests available in the scientific literature.

A pore network model of porous electrodes in electrochemical devices

• A PNM is computationally efficient for analysing flow and transport processes in electrodes. • The concentration profile of electrolyte is non-uniform across the 3D electrode. • Pore size distribution and connectivity influence the intrusion of electrolyte in the electrode. • Current density across the electrode is non-uniform and related to the concentration profiles. A computationally efficient pore network model (PNM) has been developed to incorporate the transport and electrochemical phenomena occurring within porous electrodes. This PNM is validated on a synthetic cubic structure and subsequently run on a network obtained from X-ray computed tomography (X-CT) images of a sample of commercial porous carbon paper commonly used in electrochemical devices. The carbon paper's physical characteristics (pore-size distribution, permeability, porosity and electroactive surface area) are discussed. The concentration distribution of active species is examined considering solely the transient convective and diffusive transport processes initially, and subsequently is compared to the concentration of active species when migration and reactive transport factors are included. The results show non-uniformity in the concentration and pressure distributions in the electrode when considering the pure convective/diffusive transport processes. The migration and reactive processes are subsequently considered and are shown to be influenced by the rate in which the convective/diffusive flow permeates the electrode. A uniform steady decline in volume-averaged state of charge is shown, followed by a pore-scale non-uniform current density and state of charge distribution upon discharge. These results were obtained on a standard single core workstation highlighting the benefits of using a computationally inexpensive model.