Microrotation Fields Research Articles

A microstructural defect-orientation informed phase field model

Micro-cracks, micro-voids and other such defects, which typically coalesce to form macroscopic cracks, could be represented through incompatible, local rotations of material points, i.e. micro-regions. Specifically, based on a micropolar or Cosserat continuum-like hypothesis that requires attaching directors to material points, we track the evolving frame rotation and hence the microstructural orientation during quasi-brittle damage. We introduce a critical energy release rate incorporating the wryness tensor, which in turn is a function of the micro-rotation field and its gradient within the damaged region. The (pseudo) rotation field appears as additional degrees of freedom to describe a frame field, whose evolution is particularly significant within a diffused region of evolving damage as obtained through a phase-field formulation of brittle fracture. We emphasize that, unlike micropolar continua where it contributes to elastic energy, the wryness tensor appears only in the fracture energy in our approach. Thus, without damage, the solid conforms to the classical continuum. By making suitable modifications to the terms within the elastic energy and applying the principle of virtual work, we arrive at the governing partial differential equations (PDEs). For assessing the proposed framework, we choose a specific form of energy density and demonstrate, through numerical examples, the effect of the newly introduced parameters. The classical phase-field model is readily recovered by switching off the micro-rotation. Additionally, we explore a potential application of this model in representing and propagating initial defects.

Spin resolved topological bulk state in acoustics

Extremely rare topologically protected acoustic energy sink is presented in this article. Acoustic topological phenomena are generally described using quantum anomalous hall effects (QAHE), quantum valley hall effects (QVHE), and quantum spin hall effects (QSHE) where spin orbit coupling is predominant. Topological edge states are demonstrated by bulk-boundary distinction when the bulk is insulated. In this article topological acoustic conductor and its phenomena are theoretically demonstrated where the boundaries are insulated. This is exactly opposite to the behavior of a topological acoustic insulator. Phenomena presented in this article could not be explained by any of the trio Quantum Hall effects. To explain the phenomenon phononic crystals or PnCs were designed to obtain accidental triple degeneracies, resulting a Dirac-like cone at the Γ point (k→=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overrightarrow{k}=0$$\\end{document}). The phenomenon is microarchitecture and microrotation field independent. Here time reversal symmetry or the space inversion symmetry is not broken, and the degenerated ‘Deaf band’ dominates the local dispersion with a syncline top band. This scenario results in continuously changing ‘up spin’ and ‘down spin’ of the wave energy in the media and remain trapped without specific preferential direction of wave transport. The spin was found to generate the spin angular momentum, causing the switching in geometric phase from 0-2π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0-2\\pi$$\\end{document} in cyclic pattern, keeping the energy trapped inside the bulk media.

Global well-posedness and large-time behavior of solutions to the 3D inviscid magneto-micropolar equations with damping

We first establish the existence of global strong solutions to the 3D inviscid incompressible magneto-micropolar equations with a velocity damping in Sobolev spaces H K ( K ⩾ 3 ) , where the H 3 norm of initial data is small, but its higher order derivatives could be large. Combining the H ˙ − s norm ( 0 ≤ s < 3 2 ) or B ˙ 2 , ∞ − s norm ( 0 < s ≤ 3 2 ) of the initial magnetic field is finite with some tricky interpolation estimates, we show ‖ ∇ n B ( t ) ‖ L 2 ≤ C 0 ( 1 + t ) − n 2 − 3 2 p + 3 4 and two faster decay rates for the velocity and the micro-rotation field ‖ ∇ n ( U , w ) ( t ) ‖ L 2 ≤ C 0 ( 1 + t ) − n 2 − 3 2 p + 1 4 , which are shown to be the usual L p − L 2 ( 1 ≤ p ≤ 2 ) type of the optimal time decay rates for 3D inviscid incompressible magneto-micropolar equations with damping. We then conclude the damping term contributes to weaken the assumption of initial condition and enhance the decay rate of velocity compared to the classical incompressible viscous magneto-micropolar equations. Meanwhile, for the 3D inviscid compressible magneto-micropolar fluid, the damping term also has the same effect on the decay rate of the velocity.

Melting heat transfer of micropolar nanofluid flow through porous medium

The study of melting heat transfer in micropolar nanofluid flow through porous media can provide insights into optimizing various industrial and engineering processes, as well as improve our understanding of fluid transport through porous media in environmental and biomedical applications. This study focuses on the impact of Brownian motion, thermophoresis, internal heat generation/absorption, chemical reaction and melting effects on two-dimensional micropolar nanofluid flow across a permeable stretchy surface with a stagnation point. Appropriate similarity transformations are chosen in order to convert the system of the nonlinear ordinary differential equation. The results for various parameters are examined by applying the shooting method with BVP5C technique. Furthermore, graphs and tables are used to explore the impact of significant factors that affected the velocity, microrotation, thermal behavior, and concentration of nanofluids. Results reveals that the increase in values of Brownian motion and thermophoresis parameters caused a growth in the Sherwood number and drop in the Nusselt number. The upshot of the stretching parameter (SP) on velocity, temperature, concentration and microrotation is studied. Results reveal that the velocity and microrotation fields remain constant while thermal activity increases for SP[Formula: see text][Formula: see text][Formula: see text]1. The higher value of the SP increases the concentration.

Finite element based direct and iterative approach to investigate a magneto-micropolar flow through a rectangular channel

This article aims to numerically compute the magnetic induced flow in the framework of higher order continuum through its implementation using FreeFem++. The flow through a rectangular channel is assumed laminar, incompressible and under constant applied pressure. External magnetic field is applied through the boundary of the channel. To compute the physical response theory of micropolar continuum is taken into consideration and governing dynamics is described in the form of coupled partial differential equations in velocity, induction and microrotation field variables along with associated boundary conditions. Sparse linear system is thus obtained with the application of finite element method. The resulting system is then solved by sparse solver available in unsymmetric multifrontal package (UMFPACK) through FreeFem++. The variational form of the model is presented and implemented in FreeFem++. Pertinent to physical significance different parameters i.e., magnetic Reynolds number, Hartmann number, micropolar coupling constant, micropolar parameter are studied and results are shown through simulations and graphs.It is observed that with an increase in micropolar coupling parameter the magnetic induction as well as the microrotational velocity of particles decreases in the medium. The maximum magnitude of microrotational velocities is observed near walls of the channel. The microrotational spin in the channel flow slows down due to an increase in induced magnetic field. Moreover, it is found that direct solver for the asymmetric sparse linear system arise in this case does not lead to stable solution. This instability in the solution arises when the Hartmann number in simulations increases than a value of 1.5. Therefore, iterative solver based on generalized minimal residual method (GMRES) should be adopted to weed out the instabilities due to fine scale oscillations of translational as well as microrotational motions of the fluid particles in case of large Hartmann number.

Effect of imperfect interface on the effective properties of elastic micropolar multilaminated nanostructures

AbstractIn this paper, the problem of a heterogeneous elastic micropolar nanostructure with a periodic structure subject to imperfect contact conditions is analyzed through the two‐scale asymptotic homogenization method (AHM). The imperfect interface is modeled as a generalization of the well‐known spring model; that is, the homogeneous imperfect interface is described by the following conditions: tractions and coupled stress are continuous, but displacements and microrotations are discontinuous across the imperfect interface. The jumps in displacements and microrotations are proportional to the interface traction and coupled stress components, respectively. In particular, micropolar multilaminated nanocomposites with centro‐symmetric isotropic constituents and imperfect contact conditions are studied. From AHM, the solutions for the displacement and microrotation fields are found by means of two‐scale series expansions depending on a local (microscopic) variable and a global (macroscopic) variable. The local problem statements and the corresponding effective properties are explicitly described. The formulation depends on the constituent physical properties, the imperfection parameters, the cell length in the y3‐direction, and the phase's volume fractions. Numerical results are illustrated and discussed. We concluded that the effective moduli are affected by the imperfections and the cell length in the y3‐direction.

Combined impact of Lorentz force, micro-rotation, and thermo-migration of particles: Dynamics of micropolar fluids experiencing nonlinear thermal radiation and activation energy

The functional qualities of magneto-micropolar fluid with tiny particles allow for increased lubricating oil usage, increased industrial output, and the development of nanotechnology. However, in such a situation, little or nothing is known about the significance of Lorentz force associated with the behaviour of conducting fluids in magnetic fields, micro-rotation, and thermo-migration of particles as applicable to the control of liquid metals or plasmas. This study focuses on the combined impact of Lorentz force, micro-rotation, and thermo-migration of particles on the dynamics of micropolar fluids experiencing nonlinear thermal radiation and Arrhenius chemical reaction associated with the activation energy. The reactive non-Newtonian, magneto-micropolar nanoparticle fluid flows over a configured two-dimensional stretchy vertical plate. The flow is influenced by activation energy, Brownian movement of tiny particles, thermo-migration of particles and nonlinear thermal radiation. By means of suitable similarity quantities, the partial differential equations governing the flow equations are reduced to ordinary differential equations, and solved numerically using Fehlberg integrating Runge–Kutta scheme. It is worth concluding that the Lorentz force, micro-rotation, and thermo-migration of particles strongly affects the dynamics of micropolar fluids near the wall. A tiny number of particle spins produced by collisions with the boundary dominate the micro-rotation field.

Evaluating the solid solution, local chemical ordering, and precipitation strengthening contributions in multi-principal-element alloys

Numerous theoretical and experimental studies suggest that the chemical ordering microstructure plays an important role for the strength and plastic deformation in the multi-principal-element alloy (MPEA). Despite the importance of this fact has been well confirmed, little is known about the influence of chemical ordering degree from the atomic scale to nano scale for the nanocrystal MPEA over a wide grain size range. In the present work, considering the abnormal local stacking fault energy originated from the heterogeneous chemical element concentration, the modified Hall-Petch relationship is elaborately established in MPEA, quite different from the traditional alloys. Additionally, the effects of the solid solution, local chemical ordering, and precipitation on the strengthening contribution and strain partition are evaluated. The increase of the chemical ordering degree improves the stacking fault energy and deformation gradient, as well as microrotation field. This trend leads to the yield strength owing to the formation of the slender shear bands. The geometry of the ordered structure is deformed and twisted to a certain extent, for the compatible plastic deformation. This work gives the atomic understanding of chemical-ordering-degree dominated strengthening mechanisms, to develop the strong and ductile MPEAs with desired properties. Data availability statementThe data that support the findings of this study are available from the corresponding author upon reasonable request.

Automated Analysis of Continuum Fields from Atomistic Simulations Using Statistical Machine Learning

Atomistic simulations of the molecular dynamics/statics kind are regularly used to study small‐scale plasticity. Contemporary simulations are performed with tens to hundreds of millions of atoms, with snapshots of these configurations written out at regular intervals for further analysis. Continuum scale constitutive models for material behavior can benefit from information on the atomic scale, in particular in terms of the deformation mechanisms, the accommodation of the total strain, and partitioning of stress and strain fields in individual grains. Herein, a methodology is developed using statistical data mining and machine learning algorithms to automate the analysis of continuum field variables in atomistic simulations. Three important field variables are focused on: total strain, elastic strain, and microrotation. The results show that the elastic strain in individual grains exhibits a unimodal lognormal distribution, while the total strain and microrotation fields evidence a multimodal distribution. The peaks in the distribution of total strain are identified with a Gaussian mixture model and methods to circumvent overfitting problems are presented. Subsequently, the identified peaks are evaluated in terms of deformation mechanisms in a grain, which, e.g., helps to quantify the strain for which individual deformation mechanisms are responsible. The overall statistics of the distributions over all grains are an important input for higher scale models, which ultimately also helps to be able to quantitatively discuss the implications for information transfer to phenomenological models.

Unraveling hot deformation behavior and microstructure evolution of nanolamellar TiAl/Ti3Al composites

An in-depth understanding of the deformation behavior of a nanolamellar TiAl/Ti3Al composite is prerequisite to control the mechanical properties of this material. Nevertheless, to obtain the excellent performance, the role of microstructure evolution on the deformation mechanism maps at a wide temperature range is still required. To this end, the effect of temperature on the compressive response and deformation mechanism of a nanolamellar TiAl/Ti3Al composite is investigated using molecular dynamics simulations. The deformation-induced α2→γ phase transformation results in the softening, and the deformation twinning causes the strain hardening. The high temperature reduces the local shear strain along the interface, to enhance the deformation capacity of the γ phase. At a low strain, the dislocation slip on the single slip system is the dominant deformation mode; at a medium strain, the phase transformation controls the plastic deformation; at a high strain, the deformation twinning associated with the activation of the multi-slip systems is responsible for the late plastic stage. The phase interface bents towards the γ phase, and then the α2 phase grows up, resulting in the evolution of the dynamic complex microstructures. The origin of the nanoscale plasticity event depends upon the atomic-scale deformation gradient field and the atomic-scale microrotation field. The current temperature-dependent deformation mechanism maps provide an insight into the design and fabrication of the advanced nanolamellar TiAl/Ti3Al composites with outstanding strength and ductility.

Numerical modeling of MHD micropolar fluid flow and melting heat transfer under thermal radiation and Joule heating

The purpose of this paper is to discuss the melting heat transfer and flow of a micropolar fluid due to an exponentially stretching sheet, analogous to ordinary fluid. The impacts of slip parameter, viscous dissipation, Joule heating, heat source, and thermal radiation are anticipated. The transport of heat, momentum, and angular momentum is expressed mathematically using a set of partial differential equations (PDEs). The PDEs are turned into a set of dimensionless ordinary differential equations by employing similarity variables adequately and interpreted numerically utilizing a well-known computer language in-built software bvp4c solver in MATLAB. It is noticed that the impacts of several parameters (Prandtl number, Eckert number, magnetic, heat generation parameters, etc.) on physical quantities and flow fields (velocity, temperature, and microrotation profiles) are remarkable and which are exhibited graphically and discussed in details. It is detected that, by enhancing the melting parameter, the microrotation profile appears to be dwindling near the wall; however, it is eventually lifted. Increasing the slip parameter depletes the velocity and microrotation fields, whereas it has reverse effect on the thermal field. Moreover, the thermal field is positively affected by viscous dissipation and heat generation, but slightly more enhancement has been seen for ordinary fluid compared to micropolar fluid.

Interior $$\epsilon$$-regularity theory for the solutions of the magneto-micropolar equations with a perturbation term

We develop here a particular version of the partial regularity theory for the magneto-micropolar equations (MMP) where a perturbation term is added. These equations are used in some special cases, such as in the study of the evolution of liquid crystals or polymers, where the classical Navier–Stokes equations are not an accurate enough model. The incompressible magneto-micropolar system is composed of three coupled equations: the first one is based in the Navier–Stokes system, the second one considers mainly the magnetic field while the last equation introduces the microrotation field representing the angular velocity of the rotation of the fluid particles. External forces are considered and a specific perturbation term is added as it is quite useful in some applications.

Time-dependent squeezing bio-thermal MHD convection flow of a micropolar nanofluid between two parallel disks with multiple slip effects

We performed numerical analysis on fluid model for incompressible, time dependent electrically conducting squeezing flow of micropolar fluid. The non-Newtonian fluid is confined across two disks in which lower disk is fixed while upper disk moves upward and downward. A uniform suction is made at the lower fixed disk. The Buorngiorno nanofluid theory is implemented to discuss the thermal performance by thermopherosis and Brownian motion phenomenon. Microorganism theory is applied to sustain the suspended nanoparticles by bioconvection induced through combined influence of magnetic field and buoyancy forces. The nonlinear system is reduced to a set of ordinary differential equation by similarity variables. The dimensionless quantities are discussed in pictorial way on velocity, temperature, concentration and microorganism fields. It is perceived that micropolar and magnetic parameters have opposite trend on micro-rotation field. Brownian motion and Thermopheresis parameters have similar kind of influence on temperature profiles and the thermal fields is reduced by suction parameter. Radial velocity curves declined by the squeezing Reynolds number. Numerically values of the physical parameters are also calculated and described through tabular format. It is calculated that slip parameters are reduced the Nusselt and Sherwood numbers values at the both disks respectively. At the center of the plane between two disks, the radial velocity curves are declined, whereas such profiles are enhanced at the lower and upper disks against the magnetic parameter. The increased suction parameter reduces the radial field of f′η. Moreover the radial profiles are of parabolic nature.Microrotation and magnetic parameters tend to rotate the microrotation field in opposite way. In the left region of the central plane, the profiles are enhanced, while in the right half plane the micorotation profiles are reduced. Furthermore, the microrotation curves are intersecting at η = 0.5, where the profiles turn into opposite way.

Cylindrical indentation in micropolar elasticity

Experiments existing in the literature present a scale dependence of the mechanical properties of certain materials. Such scale dependence is observable also in indentation experiments where the attained contact area and average pressure among other experimental outputs show a strong dependence upon the microstructure of the indented material. In this work we will examine the indentation of a rigid cylinder on an elastic half-plane within the context of the micropolar elasticity (also known as Cosserat elasticity). The micropolar theory of elasticity incorporates in addition to the displacement field, an independent kinematical microrotation field. Our results show the dependence of the shape of the pressure distribution, the average pressure and the width of the contact site below the indenter upon the microstructure of the material described through the material length as introduced through the micropolar theory. A comparison of the results with those obtained by the classical theory and the couple stress theory as well as a full field solutions regarding equivalent stresses are presented.

Soret-Dufour magneto-thermal radiative convective heat and mass transfer of chemically and thermally stratified micropolar fluid over a vertical stretching/shrinking surface in a porous medium

The present article deals with Soret Dufour free convective heat and mass transfer of a micropolar fluid over vertical stretching and shrinking sheets embedded in a Darcian porous medium with thermal radiation and magnetic field. We have obtained numerical solutions for the velocity, temperature, microrotation, and solute concentration fields for various values of the thermal radiation and microrotation material parameters, Prandtl number, chemical reaction, magnetic parameter, and Soret-Dufour number. Present results are obtained by using Runge-Kutta Fehlberg method with shooting technique and they are presented graphically and in tabular form for performing a critical analysis of various parametric values. It is explored that the velocity and temperature distribution decrease with enhancement in the Prandtl number and having reverse effects on the concentration distribution. Further, it is noticed that by increasing the values of the thermal radiation parameter, there is a rise in the velocity and temperature distributions. This work would find applications in the field of chemical engineering systems and magnetic materials processing.

Mathematical modeling of micropolar fluid flows through a thin porous medium

We study the flow of a micropolar fluid in a thin domain with microstructure, i.e., a thin domain with thickness \(\varepsilon \) which is perforated by periodically distributed solid cylinders of size \(a_\varepsilon \). A main feature of this study is the dependence of the characteristic length of the micropolar fluid on the small parameters describing the geometry of the thin porous medium under consideration. Depending on the ratio of \(a_\varepsilon \) with respect to \(\varepsilon \), we derive three different generalized Darcy equations where the interaction between the velocity and the microrotation fields is preserved.

Chemically reactive MHD micropolar nanofluid flow with velocity slips and variable heat source/sink

The two-dimensional electrically conducting magnetohydrodynamic flow of micropolar nanofluid over an extending surface with chemical reaction and secondary slips conditions is deliberated in this article. The flow of nanofluid is treated with heat source/sink and nonlinear thermal radiation impacts. The system of equations is solved analytically and numerically. Both analytical and numerical approaches are compared with the help of figures and tables. In order to improve the validity of the solutions and the method convergence, a descriptive demonstration of residual errors for various factors is presented. Also the convergence of an analytical approach is shown. The impacts of relevance parameters on velocity, micro-rotation, thermal, and concentration fields for first- and second-order velocity slips are accessible through figures. The velocity field heightens with the rise in micropolar, micro-rotation, and primary order velocity parameters, while other parameters have reducing impact on the velocity field. The micro-rotation field reduces with micro-rotation, secondary order velocity slip, and micropolar parameters but escalates with the primary order velocity slip parameter. The thermal field heightens with escalating non-uniform heat sink/source, Biot number, temperature ratio factor, and thermal radiation factor. The concentration field escalates with the increasing Biot number, while reduces with heightening chemical reaction and Schmidt number. The assessment of skin factor, thermal transfer, and mass transfer are calculated through tables.

Micropolar fluid flow in a thick domain with multiscale oscillating roughness and friction boundary conditions

We consider an unsteady micropolar fluid flow in a two-dimensional domain Ωε. The velocity field is assumed to satisfy a fluid-solid friction interface condition on a part of the boundary while the micro-rotation field satisfies non-homogeneous Dirichlet boundary conditions. The problem is thus described by a non-linear coupled variational parabolic system for the fluid velocity vϵ, the pressure pϵ and the angular micro-rotation field Zϵ. The thickness and the roughness of the fluid domain are described by multiple separated scales of periodic oscillations, i.e. Ωε={(z1,z2):0<z1<L,0<z2<εmhε(z1)} with hε(z1)=h(z1,z1ε,z1ε2,⋯,z1εm), 0<ε<<1, and m≥2. Existence, uniqueness and uniform estimates of the solution (vϵ,pϵ,Zϵ) are stated. Then we study the asymptotic behaviour of the flow as ε tends to zero by using the multiple scale convergence method for reiterated homogenization. The assumption m≥2 raises several technical difficulties in the limit process and leads to non-standard divergence free conditions for the limit velocity. We derive the limit problem which is totally decoupled for the limit velocity and pressure (v0,p0) on the one hand and the limit micro-rotation field Z0 on the other hand. More precisely (v0,p0) is solution of a variational elliptic inequality and Z0 solves an elliptic partial differential equation, where the time variable appears as a parameter. Moreover we prove that v0,p0 and Z0 are uniquely determined by auxiliary well-posed problems.

Simultaneous impact of hybrid nano and dust particles on enhancement of heat transfer in fluid with micro-rotation and thermal memory effects

Simultaneous influence of thermal memory, micro-rotation, nanoparticles and dust particles are modeled using two-phase-conservation laws. The governing set of models is made dimensionless and expressions for skin friction, couple stress and heat flux are derived. Finite element method (FEM) is implemented for simulations purpose. Particles rotation has significantly impacted translational motion. Vortex effects are responsible in enhancing micro-rotations. However, this enhancement in micro-rotation field associated with mono-nano dusty fluid has received more impact rather than hybrid nanofluid. Thermal relaxation parameter characterizes memory effects in fluid due to which fluid restores its thermal equilibrium state. The fluid having viscoelastic rheology has this characteristics and such fluid offers resistance to momentum and thermal changes and tries to continue momentum and thermal equilibrium state.

Thermal performance of micro-polymers containing nano-solid structures during transport phenomenon

The inclusion of solid nano-structures in the liquid changes its rheology and hence its thermal performance. This article considers the impact of nano-solid structure on the ability of the polymer to transport heat. Mathematical models for nano-solid structures and conservation laws are finite element method. The impact of nano-solid structures on transportation of heat is studied via computed solutions. The micro-rotation field increases with an increase in vortex viscosity. The wall shear stress and wall couple stress are increased for vortex viscosity. However, the rate of heat transfer has shown decreasing behavior as a function vortex viscosity.