Micropolar Model Research Articles

Topology optimization of link mechanisms for comprehensive synthesis of component arrangement and structure using micropolar elasticity model

This paper proposes a method for topology optimization of link mechanisms with multiple outputs, using a multi-material micropolar elasticity model. This approach allows for comprehensive optimization of both the arrangement and structure of the link mechanism components. By utilizing a continuum model that incorporates micropolar elasticity, we can specify bending stiffness independently from tensile stiffness, resulting in deformation characteristics that approximate a link mechanism. The optimization problem of designing link mechanisms for multiple outputs is reformulated as a boundary value problem within this model framework. The design goal is to synthesize a link mechanism that not only follows a desired path but also possesses the required degrees of freedom. To achieve this, the objective function is defined by the displacement error under external force and the strain energy in the links. The multi-material micropolar elasticity model is then optimized through a gradient-based optimization method, focusing on this objective function. The effectiveness and applicability of our methodology are demonstrated through several numerical case studies.

A micropolar phase-field model for size-dependent electro-mechanical fracture

This article proposes a micropolar phase-field model for size-dependent brittle fracture in solids under electro-mechanical loading conditions. Considering displacement, micro-rotation, electric potential, and phase-field variable as the kinematic descriptors and employing the virtual power principle, we derive a set of coupled governing partial differential equations (PDEs) for size-dependent solids. Invoking the first and second laws of thermodynamics, we determine the constitutive relations for the thermodynamic fluxes. Carrying out the finite element implementation of the derived governing PDEs using the open-source Gridap package in Julia, we demonstrate the efficacy of the proposed phase-field model through a few representative numerical examples. Especially the importance of the proposed model in incorporating the effect of relative rotation, i.e., the difference between macro- and micro-rotation, on the response of solids under electro-mechanical loading is shown that may not be possible with the existing non-local models such as strain-gradient or couple-stress approaches. To capture the experimentally observed size effects in solids under electro-mechanical loading, the proposed model does not demand higher-order continuity of finite element shape functions, unlike a typically used strain gradient model. To demonstrate the efficacy of the proposed model, we have compared our results against demanding experimental and numerical benchmark results available in the literature. We provide a parametric study to unravel the effect of different micropolar material parameters on the electro-mechanical response of a brittle solid. Interestingly, the proposed micropolar model is less sensitive to the phase-field length scale than the conventional non-polar phase-field models.

On progressive failure of sand considering fabric evolution with micropolar hypoplastic model

To study the progressive failure of sand considering the multi-scale and its fabric evolution, the fabric is used as the quantitative link from micro to macro, then the influence of fabric on the anisotropic critical state is adopted to establish a hypoplastic model, and the fabric evolution and micropolar theory are employed to describe the mesoscopic mechanism of local deformation, finally, the simulations of discrete element methods (DEM) and finite element methods (FEM) is coordinated to reproduce the progressive failure. In the DEM biaxial simulations, the distribution of the contact normal is quantitatively determined by the novel orthotropic fabric tensor, and the difference in particle shapes and sample position showed that the fabric evolution is obvious, especially inside and outside the shear band, and before or after the shear band penetration. The fabric evolution of DEM is implanted into the corresponding location of the FEM sample, the results indicate that the macro-meso incorporation hypoplastic model can effectively describe strain localization evolution and progressive failure. The internal length of micropolar theory and particle size are identified as the main factors influencing the shear band thickness. The anisotropic fabric influences the shear band patterns, with circular and elliptical particles tending to form an "X-shape" shear band, while square and triangular particles tend to form a "L-shape" shear band.

Cilia-assisted flow of electrically conducting micropolar fluid in a heated curved channel under Soret and Dufour effects

Cilia flow plays a crucial role in biological systems such as the movement of mucus in the respiratory tract, circulation of cerebrospinal fluid in the brain, and propulsion of sperm cells. Understanding the cilia flow of viscous fluids is essential for elucidating the biomechanics of these processes and their implications for health and disease. Motivated by such numerous biomedical applications, this article aims to exhibit the influence of heat and mass transfer on the ciliary flow of electrical conducting micropolar fluid in a curved channel. The energy and concentration equations are modulated with viscous dissipation, Soret, and Dufour effects. The constitutive equations are simplified by the hypothesis of lubrication approximation theory and then solved numerically using the implicit finite difference method (FDM). Results for velocity, pumping phenomenon, concentration, thermal field, rate of heat transfer, streamlines, skin friction coefficient, Nusselt number, and Sherwood number are analyzed subject to pertinent parameters. The study reveals that velocity is enhanced via both the micropolar parameter and curvature parameter. Temperature enhances for larger values of Dufour and Brickman numbers. Furthermore, the radial magnetic field plays a resistive role in the trapped bolus. The findings presented in this study should prove beneficial for researchers in the domains of medicine, engineering, science, and fluid mechanics. Further, it is found that the micropolar fluid model is more suitable for biofluids like blood.

Nonlinear dynamics of micropolar two-phase fluids: Multiple exact solutions

Dual and triple solutions induced by a flexible planar surface for a micropolar two-phase fluid model are studied. The two-phase behavior in the micropolar fluid model occurs due to phase transitions between the fluid phases, influenced by interfacial stresses and heat transfer. The physical implications of these transitions are significant in understanding flow behavior under different mechanical and thermal conditions. This study examines the critical parameters and conditions that lead to these phase transitions, resulting in dual or triple solutions in the flow dynamics. The flow and thermal fields are exact solutions of the steady, two-dimensional two-phase micropolar fluid equations in the form of similarity solution. It is shown that dual and triple exact solutions exist for a highly nonlinear system. Triple solutions exist for the skin friction and temperature gradient identified by the critical numbers ac and μc. It is noted that for sufficiently small values of stretching strength parameter the dual branches for two of the triple solutions exist only in the regions μ≥μc3, and μ≤μc4, where μc3=−5.23 and μc4=−7.72. Numerical results are also provided, validating the model and offering insights into its accuracy and behavior of the model.

Turbulent Micropolar Open-Channel Flow

The present paper focuses on the investigation of the turbulent characteristics of an open-channel flow by employing the micropolar model. The underlying model has already been proven to correctly describe the secondary phase of turbulent wall-bounded flows. The open-channel case comprises an ideal candidate to further test the micropolar model as many environmental flows carry a secondary phase, the behavior of which is of great interest for applications such as sedimentation transport and debris flow. Direct Numerical Simulations (DNSs) have been carried out on an open channel for Reb = 11,200 based on mean crossectional velocity, channel height, and the fluid kinematic viscosity. The simulated results are compared against previous experimental as well as Langrangian DNS data of similar flows, with excellent agreement. The micropolar model is capable of describing the same problem but in an Eulerian frame, thus significantly simplifying the computational cost and complexity.

Overall constitutive properties of stratified lattices with alternating chirality.

The present research focuses on a continuum description of stratified metamaterials achieved through the superposition of layers with alternating chirality. Each layer is constructed as a periodic assembly of centre-symmetric periodic cells, formed by a recurring arrangement of rigid circular discs connected by elastic ligaments. The layers are interconnected through elastic pins passing through the centres of aligned discs, allowing for either restrained or free relative rotation. A micropolar continuum model is used to describe each individual layer. The overall response of the metamaterials to in-plane forces is derived using a multi-field non-local model, expressed in terms of the average and difference of displacement and rotational fields. The overall micropolar and standard (Cauchy) constitutive tensors have been determined in closed form. The validity of the equivalent generalized micropolar model has been confirmed through comparison with discrete Lagrangian solutions of representative examples. In addition, a detailed analysis of a pseudo-indentation test has been carried out. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'.

Design of Nonlinear Autoregressive Neuro-Computing Structure for Bioconvective Micropolar Nanofluidic Model

In the present arena, the tools of artificial intelligence (AI) play a significant role in research across various fields by enabling advanced data analysis, pattern recognition and decision-making. This research work presents the numerical investigation of bioconvective micropolar nanofluidic model (BCMNFM) by employing the knacks of AI-based nonlinear autoregressive (NAR) approach with a combination of backpropagated Levenberg–Marquardt neural networks (BLMNNs) represented as NAR-BLMNNs. This research work investigates the flow design to highlight the attributes of mass and heat exchange. A dataset for BCMNFM is created by applying the Adam numerical procedure by variation of unsteadiness parameter ([Formula: see text], magnetic field parameter ([Formula: see text] thermophoresis parameter (Nt), Brownian motion parameter (Nb), bioconvection Peclet number (Pe) and spin gradient viscosity parameter ([Formula: see text] The skills of AI-based NAR-BLMNNs technique is then utilized on the dataset created for BCMNFM to investigate the approximate solutions. The achieved and impactful values of performance consistently range between [Formula: see text] and [Formula: see text] across all scenarios of BCMNFM. The precision and the validation of predicted approach NAR-BLMNNs is exceptionally established by the graphical demonstration for all scenarios of MSE, regression metrics, error histograms and time series graphs. The numerical calculations attained through AI-based NAR-BLMNNs technique further rationalize the precision of the proposed methodology for solving the BCMNFM effectively and efficiently.

A micropolar damage model for size-dependent concrete fracture problems and crack propagation simulated by PDDO method

Lots of experiments observe the size-dependent phenomena of concrete mechanical behaviors. In this paper, the micropolar theory is adopted to describe the size effects by introducing two size-related parameters into their constitutive equations, named coupling number N and characteristic length l. A micropolar damage model is built for size-dependent concrete fracture problems utilizing the bond-based peridynamic (PD) idea. That is, the material damage and fracture behaviors are determined by the local damage factors of the PD bonds. Then, the tensile strength of a concrete specimen is numerically estimated by the PD differential operator (PDDO) method. The influences of the size parameters N and l on the tensile strength are studied. By comparing with the transformed Bažant size-effect law and the fitting error analysis, the reasonable values of N and l are determined for a certain reinforced concrete composite. Finally, by using the determined micropolar damage model, the crack propagation paths in concrete members are numerically simulated.

Time-periodic electrokinetic analysis of a micropolar fluid flow through hydrophobic microannulus

The oscillating aspects of pressure-driven micropolar fluid flow through a hydrophobic cylindrical microannulus under the influence of electroosmotic flow are analytically studied. The study is based on a linearized Poisson–Boltzmann equation and the micropolar model of Eringen for microstructure fluids. An analytical solution is obtained for the distributions of electroosmotic flow velocity and microrotation as functions of radial distance, periodic time, and relevant parameters. The findings of the present study demonstrate that, unlike the decrease in flow rate resulting from the micropolarity of fluid particles, velocity slip and spin velocity slip, when contrasted with Newtonian fluids, act as a counteractive mechanism that tends to enhance the flow rate. Additionally, the findings indicate that a square plug-like profile in electroosmotic velocity amplitude is observed when the electric oscillating parameter is low and the electrokinetic width is large, for both Newtonian and micropolar fluids. Moreover, in cases where there is a wide gap between the cylindrical walls and a high-frequency parameter, the electroosmotic velocity and microrotation amplitudes tend to approach zero at the center of the microannulus across all ranges of micropolarity and zeta potential parameters. Furthermore, it has been observed that the amplitude of microrotation strength rises as slip and spin slip parameters increase. Across the entire spectrum of micropolarity, the zeta potential ratio influences both the dimension and direction of the electroosmotic velocity profiles within the electric double layer near the two cylindrical walls of the microannulus. The study emphasizes the physical quantities by presenting graphs for various values of the pertinent parameters juxtaposing them with existing data in the literature and comparing them with the Newtonian fluids.Graphic abstract

Computational micropolar model of hybrid nanofluid flow across a wedge

Non-Newtonian flow from wedges is a vital problem in coatings, polymer processing etc. Hence the main aim is to investigate the convective boundary layer flow of micropolar hybrid nanofluid (MHN)from a wedge. It is assumed that the wedge surface is isothermal. The Eringen model is employed to define micropolar fluid. Nanoscale Tiwari–Das formulations are used to study the specific effects of nanoparticles and volume fractions. The dimensionless boundary value problem arises by suitable coordinate transformations as a system of nonlinearly coupled ordinary differential equations. The so-called Falkner Skan flow case is resolved. Dimensionless, transformed, coupled momentum, microrotation, boundary layer equations are resolved using the numerical scheme MATLAB bvp4c. The parameteric investigations are performed on hybrid nanofluids using water as the basis liquid and varying volume fractions from 0 to 8%. Affirmation with previous work is done. The consequence of Eringen micropolar parameter, Hartree pressure gradient parameter, nanoparticle volume fraction, Eckert number, heat absorption (sink) parameter, on the flow and physical characteristics are visualized graphically and in tables. With rising material factor and volume fraction of nanoparticle, temperature is markedly enhanced. Increases in volume fraction dampen angular velocity close to the wedge surface, while farther from the wall, the opposite effect is seen. Temperature and thermal boundary layer thickness are both greatly enhanced by increasing Eckert number. With an increase in the volume proportion of nanoparticles, velocity decreases. Heat generation raises temperatures while a heat sink lowers them. The pressure gradient parameter increases skin friction while decreasing Nusselt number. Nusselt number for hybrid nanofluid is higher than for nanofluid.

Impacts of activation energy and electroosmosis on peristaltic motion of micropolar Newtonian nanofluid inside a microchannel

This study investigates the impact of electroosmosis on the peristaltic flow of unsteady micropolar nanofluid with heat transfer. The findings could enhance the design of peristaltic pumps, potentially improving drug delivery systems, simulations of blood flow in medical devices, and cancer treatments. The fluid under investigation adheres to a micropolar model and flows through a microchannel that exhibits peristalsis along its walls. Moreover, the system is subjected to various external effects, including a uniform magnetic field, the electroosmotic phenomenon, heat absorption, and a chemical reaction with activation energy. Consequently, the problem is mathematically modulated by a system of nonlinear partial differential equations governing the velocity, temperature, and nanoparticle concentration. By employing wave transformation, these governing equations are reduced to ordinary differential equations (ODEs). The reduced equations were solved both analytically, using the homotopy perturbation method, and numerically, using the Runge–Kutta–Merson method. A comparison was made between the solutions, which were found to be closely aligned. Furthermore, a series of figures were employed to provide visual representation and discussion of the implications of the physical properties. The calculations reveal that the electroosmotic flow (EOF) enhances the axial flow of the micropolar fluid along the direction of the applied electric field. It is also observed that the increase in the activation energy (which indicates a low reaction rate) increases the concentration profile whereas the increase in the reaction rate parameter reduces the concentration profile. Additionally, the spin velocity of the particles is diminished by either an increase in the magnetic parameter or the coupling parameter.

Oscillations of coaxial hydrophobic spherical colloidal particles in a micropolar fluid

The microstructured flow field of a micropolar model around a straight chain of multiple hydrophobic spherical particles oscillating rectilinearly along their line of centers is studied under the conditions of low Reynolds numbers. In general, the particles can exhibit variations in both radius and amplitude of oscillations, and they are allowed to be unevenly spaced. The amplitudes are required to be small in comparison with a characteristic length, which can be considered as the radius of the larger particle. The concepts of slip length and spin slip length are introduced to characterize the partial slip and spin slip boundary conditions at the hydrophobic surfaces of the colloidal particles. The differential equations that govern the system are solved through a semi-analytical approach in combination with boundary collocation techniques. The interaction effects between the particles are assessed through the in-phase and out-of-phase drag force coefficients acting on each particle for various values of geometrical and physical parameters. The numerical schemes are carried for the case of two oscillating spherical particles. The results of this investigation indicate that the drag coefficients are notably influenced by the presence of the second particle, micropolarity, frequency, and slip parameters. The current study reveals that the impact of the micropolarity parameter is not significant on the in-phase force coefficient for slippage parameter values less than one. However, it becomes significant for slippage parameter values exceeding one. Typically, when particles oscillate in opposing modes, in-phase coefficient values surpass 1, whereas they fall below 1 when oscillating in the same mode. The present study is driven by the necessity to gain a deeper comprehension of the fluid tapping mode employed in atomic force microscope devices, especially when this mode pertains to microstructures in the vicinity of a curved surface.

Application of micropolar fluid model to blood flow through catheterized artery with stenosis and thrombosis

This paper presents a model of nonisothermal blood flow through a diseased arterial segment due to the presence of stenosis and thrombosis. The rheological properties of the blood in the annulus are captured by utilizing micropolar fluid model. The equation describing the blood flow and heat transfer is developed under the assumption that stenosis growth into the lumen of the artery is small as compared to the average radius of the artery. Biological processes like intimal proliferation of cells or changes in artery caliber may be activated by small growths that cause moderate stenotic blockages. Closed-form solutions for temperature, velocity, resistance impedance and wall shear stress are obtained and then utilized to estimate the impact of various physical parameters on micropolar blood flow. Graphs are plotted to illustrate variations in temperature, velocity, shear stress at the wall and resistance impedance against different controlling parameters. The results are also validated via the bvp4c approach.

Exploring microrotational effects and temperature variations in electroosmotic peristalsis in tapered microchannel

AbstractThe current study is based on the effects of microrotational dynamics, microinertial effects, and temperature changes on electroosmotic peristalsis in a tapered microchannel. This has been addressed by an analytical study of heat transfer in the setting of electroosmotic peristaltic flow involving a micropolar fluid, specifically considering a symmetrically tapered channel. The Navier–Stokes equation, the Poisson–Boltzmann equation, the energy equation, and the micropolar fluid model are all included in the mathematical model. On the flow and temperature fields, a thorough parametric analysis is carried out, investigating the impacts of numerous variables, including the micropolar parameter, Prandtl number, Brinkman number, Grashof number, thermal conductivity ratio, and channel aspect ratio. The findings show that peristalsis and electroosmosis both contribute to higher heat transfer rates. Notably, the electroosmotic parameter and Brinkman number have a substantial impact on the distribution of temperature. The micropolar parameter and Brinkman number have a significant effect on the flow and temperature fields. Furthermore, electrokinetic phenomena are crucial in controlling the axial and spin velocities of the micropolar fluid. These findings have significant ramifications for the design and optimization of microfluidic devices in engineering and biomedical applications that employ the electroosmotic peristaltic flow of micropolar fluids.

Equivalent micropolar model for porous guided bone regeneration mesh: Optimum design for desired mechanical properties

In the present work, a micropolar continuum model is adopted to homogenise a heterogeneous porous model of Guided Bone Regeneration (GBR) meshes. GBR meshes are used in dentistry as mechanical barriers to isolate and protect the area of bone loss from the surrounding tissue while allowing new bone growth. The mechanical constants of the continuum are derived based on the strain energy equivalence of a periodic porous plate with its equivalent ortho-tetragonal micropolar model under prescribed boundary conditions. The effects of various architectural features such as pore shapes, patterns and sizes on the material parameters are investigated. The results show that the micropolar theory provides a better prediction of the response of the 2D porous geometries considered for the GBR mesh, compared to the classical Cauchy theory. The collected equivalent material parameters are further used for GBR mesh design, considering both mechanical and biomedical requirements. As an example, different materials and arrangements are analysed to find micropolar constitutive parameters that are comparable to bone parameters reported in the literature. This allows the GBR mesh to possess the mechanical performance that matches the adjacent bones.

Numerical study of hydromagnetic bioconvection flow of micropolar nanofluid past an inclined stretching sheet in a porous medium with gyrotactic microorganism

The present article centers on the examination of novel bioconvection phenomena involving gyrotactic microorganisms and a micropolar nanofluid model with hydro-magnetic flow. The flow traversed a stretchable inclined plate within the permeable medium. Heat absorption and thermal radiation are considered. The objective of this study is to assess the rate of heat transfer exhibited by nanofluid when unicellular microorganisms are present. Mathematical complex flow model is converted to nonlinear dimensional less system of differential equation through adopting the appropriate similarity variables. For the non-linear nanofluid problem, the (FDM) finite difference method (Lobatto IIIA) is applied with a range of collocation sites and an accuracy of order 4–5. (Lobatto IIIA) excels in solving coupled differential equations, even those with high nonlinearities. Nanofluid containing gyrotactic microbes is highly applicable in bioscience, geoscience and eco science. The effects of dimensional less parameters on flow field, energy distribution, nanofluid concentration and density of microorganism concentration profiles analyzed through the graphical and tabulation representation. This basic research will aid scientists and engineers in controlling fluid flow and improving complex systems that make use of it.

Block preconditioning strategies for generalized continuum models with micropolar and nonlocal damage formulations

AbstractIn this work, preconditioning strategies are developed in the context of generalized continuum formulations used to regularize multifield models for simulating localized failure of quasi‐brittle materials. Specifically, a micropolar continuum extended by a nonlocal damage formulation is considered for regularizing both, shear dominated failure and tensile cracking. For such models, additional microrotation and nonlocal damage fields, and their interactions, increase the complexity and size of the arising linear systems. This increases the demand for specialized preconditioning strategies when iterative solvers are adopted. Herein, a block preconditioning strategy, employing algebraic multigrid methods (AMG) for approximating the application of sub‐block inverses, is developed and tested in three steps. First, a block preconditioner is introduced for linear systems resulting from micropolar models. For this case, a simple sparse Schur complement approximation, which is practical to compute, is proposed and analyzed. It is tested for three different discretizations. Second, the developed preconditioner is extended to reflect the additional nonlocal damage field. This extended three‐field preconditioner is tested on the simulation of a compression test on a sandstone sample. All numerical tests show an improved performance of the block preconditioning approach in comparison to a black‐box monolithic AMG approach. Finally, a problem‐adapted preconditioner setup strategy is proposed, which involves a reuse of the multigrid hierarchy during nonlinear iterations, and additionally accounts for the different stages occurring in the simulation of localized failure. The problem‐adapted preconditioning strategy has the potential to further reduce the total computation time.

Electrophoresis analysis of a hydrophobic spherical particle in a micropolar electrolyte solution

AbstractThe general expression for the time‐independent electrophoretic velocity of a spherical colloidal particle with a slippage surface in a microstructure electrolyte solution is derived. The two extreme cases of nonconducting and perfect conducting particles are investigated. The derived expression is valid for arbitrary Debye length and low particle zeta potentials. The concept of velocity spin slip is incorporated with the usual velocity slip at the particle's surface. The effect of the microstructure of fluid particles on the electrophoresis phenomena is discussed based on a micropolar fluid model. The influences of velocity slip and velocity spin slip are shown through various plots of electrophoretic velocity. The limiting case of electrolyte viscous solution is recovered. The principal findings of this research can be summarized as follows: As the micropolarity parameter increases, the normalized electrophoretic velocity decreases and reaches its peak in the case of Newtonian fluids. Additionally, the velocity slip acts as a counteracting factor that promotes an increase in the electrophoretic velocity. In the context of nonconducting particles, the normalized electrophoretic velocity rises as the spin slip parameter and Debye length decrease. Conversely, for perfectly conducting particles, it increases as the spin slip parameter and Debye length increase.

Regularity for a geometrically nonlinear flat Cosserat micropolar membrane shell with curvature

We consider the rigorously derived thin shell membrane \Gamma -limit of a three-dimensional isotropic geometrically nonlinear Cosserat micropolar model and deduce full interior regularity of both the midsurface deformation m\colon \omega\subset \mathbb{R}^{2}\to \mathbb{R}^{3} and the orthogonal microrotation tensor field R\colon \omega\subset \mathbb{R}^{2}\to \operatorname{SO}(3) . The only further structural assumption is that the curvature energy depends solely on the uni-constant isotropic Dirichlet-type energy term |\mathrm{D}R|^{2} . We use Rivière’s regularity techniques of harmonic-map-type systems for our system which couples harmonic maps to \operatorname{SO}(3) with a linear equation for m . The additional coupling term in the harmonic map equation is of critical integrability and can only be handled because of its special structure.