Search Results (25)

A model for the flow and thermal explosion of a micropolar gas is investigated, assuming the equation of state for a real gas. This model describes the dynamics of a gas mixture (fuel and oxidant) undergoing a one-step irreversible chemical reaction. The real gas model is particularly suitable in this context because it more accurately reflects reality under extreme conditions, such as high temperatures and high pressures. Micropolarity introduces local rotational dynamic effects of particles dispersed within the gas mixture. In this paper, we first derive the initial-boundary value system of partial differential equations (PDEs) under the assumption of spherical symmetry and homogeneous boundary conditions. We explain the underlying physical relationships and then construct a corresponding approximate system of ordinary differential equations (ODEs) using the Faedo–Galerkin projection. The existence of solutions for the full PDE model is established by analyzing the limit of the solutions of the ODE system using a priori estimates and compactness theory. Additionally, we propose a numerical scheme for the problem based on the same approximate system. Finally, numerical simulations are performed and discussed in both physical and mathematical contexts. Full article

We draw connections between eight different theories used to describe microscopic (atomic) and macroscopic (seismological) scales. In particular, we show that all these different theories belong to a particular case of a single partial differential equation, allowing us to gain new physical insights and draw connection among them. With this general understanding, we apply the micropolar theory to the description of shear-wave dispersion in marine sediments, showing how we can reproduce observations by only using two micropolar parameters in contrast to the seventeen parameters required by modifications of Biot’s theory. We next establish direct connections between the micro (laboratory) and macro (seismological) scales, allowing us to predict (and confirm) the presence of post-perovskite in the lowermost mantle based on laboratory experiments and to predict the characteristic length $L_c$ at which shear deformation becomes significant at seismological scales in the lowermost mantle. Full article

This paper examines the static and dynamic responses of strain gradient planar trusses. Classical elasticity (CE) theory lacks a material microstructural length parameter in its governing equations, making it insufficient to capture size-dependent effects. To address this limitation, higher-order continuum theories—such as micropolar, couple-stress, and strain gradient elasticity (SGE) theories—are essential. In this study, gradient elasticity theory is extended to describe the behavior of planar trusses by incorporating explicit internal length scales as additional material parameters. A key finding of this research is that the inclusion of the microstructural parameter results in a stiffening effect in both static and dynamic analyses. Full article

Understanding shear flow behavior in compressible, viscous, micropolar real gases is essential for both theoretical advancements and practical engineering applications. This study develops a comprehensive model that integrates micropolar fluid theory with compressible flow dynamics to accurately describe the behavior of real gases under shear stress. We formulate the governing equations by incorporating viscosity and micropolar effects and transform the obtained system into the mass Lagrangian coordinates. Two numerical methods, Faedo–Galerkin approximation and finite-difference methods, are used to solve it. These methods are compared using several benchmark examples to assess their accuracy and computational efficiency. Both methods demonstrate good performance, achieving equally precise results in capturing essential flow characteristics. However, the finite-difference method offers advantages in speed, stability, and lower computational demands. This research bridges gaps in existing models and establishes a foundation for further investigations into complex flow phenomena in micropolar real gases. Full article

In the present study, an effort was made to determine the effects of a porous matrix with different viscosities on the dynamic and static behaviors of rough short journal bearings taking into account the action of a squeezing film under varying loads without journal rotation. The micropolar fluid was regarded as a lubricant that contained microstructure additives in both the porous region and the film region. By applying Darcy’s law for micropolar fluids through a porous matrix and stochastic theory related to uneven surfaces, a standardized Reynolds-type equation was extrapolated. Two scenarios with a stable and an alternating applied load were analyzed. The impacts of variations in viscosity, the porous medium, and roughness on a short journal bearing were examined. We inspected the dynamic and static behaviors of the journal bearing. We found that the velocity of the journal center with a micropolar fluid decreased when there was a cyclic load, and the impact of variations in the viscosity and porous matrix diminished the load capacity and pressure in the squeeze film and increased the velocity of the journal center. Full article

Fused deposition modelling (FDM) is an additive manufacturing technique widely used for rapid prototyping. This method facilitates the creation of parts with intricate geometries, making it suitable for advanced applications in fields such as tissue engineering, aerospace, and electronics. Despite its advantages, FDM often results in the formation of voids between the deposited filaments, which can compromise mechanical properties. However, in some cases, such as the design of scaffolds for bone regeneration, increased porosity can be advantageous as it allows for better permeability. On the other hand, the introduction of nano-additives into the FDM material enhances design flexibility and can significantly improve the mechanical properties. Therefore, modelling FDM-produced components involves complexities at two different scales: nanoscales and microscales. Material deformation is primarily influenced by atomic-scale phenomena, especially with nanoscopic constituents, whereas the distribution of nano-reinforcements and FDM-induced heterogeneities lies at the microscale. This work presents multiscale modelling that bridges the nano and microscales to predict the mechanical properties of FDM-manufactured components. At the nanoscale, molecular dynamic simulations unravel the atomistic intricacies that dictate the behaviour of the base material containing nanoscopic reinforcements. Simulations are conducted on polylactic acid (PLA) and PLA reinforced with silver nanoparticles, with the properties derived from MD simulations transferred to the microscale model. At the microscale, non-classical micropolar theory is utilised, which can account for materials’ heterogeneity through internal scale parameters while avoiding direct discretization. The developed mechanical model offers a comprehensive framework for designing 3D-printed PLA nanocomposites with tailored mechanical properties. Full article

To tackle suspensions of particles of any shape, the thermodynamics of a Cosserat continuum are developed by the method suggested by Landau and Khalatnikov for the mathematical description of the super-fluidity of liquid 2He. Such an approach allows us to take into account the rotation of particles and their form. The flows of suspensions of neutrally buoyant rod-like particles are considered in detail. These suspensions include linear polymer solutions, FD-virus and worm-like micelles. The anisotropy of the suspensions is determined through the inclusion of the micro-inertia tensor in the rheological constitutive equations. The theory predicts gradient banding, temporal volatility of apparent viscosity and hysteresis of the flux-pressure curve. The transition from the isotropic phase to the nematic phase is also captured. Our mathematical model predicts the formation of flock-like inhomogeneities of concentration jointly with the hindrance effect. Full article

A reinforced concrete shear wall is an important building structure. Once damage occurs, it not only causes great losses to various properties but also seriously endangers people’s lives. It is difficult to achieve an accurate description of the damage process using the traditional numerical calculation method, which is based on the continuous medium theory. Its bottleneck lies in the crack-induced discontinuity, whereas the adopted numerical analysis method has the continuity requirement. The peridynamic theory can solve discontinuity problems and analyze material damage processes during crack expansion. In this paper, the quasi-static failure and impact failure of shear walls are simulated by improved micropolar peridynamics, which provides the whole process of microdefect growth, damage accumulation, crack initiation, and propagation. The peridynamic predictions are in good match with the current experiment observations, filling the gap of shear wall failure behavior in existing research. Full article

The main goal of this research is to provide a novel model that describes an optically heated layer of an excited non-local microelongated semiconductor material. In a rotating field, the model is examined as the photo-excitation processes occur. The model presents the microelongation scalar function, which describes the microelement processes according to the micropolar-thermoelasticity theory. The model analyses the interaction situation between optical-thermomechanical waves under the impact of rotation parameters when the microelongation parameters are taken into consideration according to the photo-thermoelasticity theory. During the electronic and thermoelastic deformation, the fundamental governing equations were obtained in dimensionless form, and they were investigated using the harmonic wave methodology. Two-dimensional general solutions for the fundamental fields of an isotropic, homogeneous, and linear non-local microelongated semiconductor medium are derived (2D). The free surface of the medium is subjected to several conditions to produce complete solutions due to the laser pulse. The physical properties of silicon (Si) material are used to show numerical modeling of the main fields. Some comparisons are made and graphically shown under the impact of various relaxation time and rotational parameters. Full article

This work focuses on presenting a novel model describing a layer of an excited microelongated semiconductor material. During the photo-excitation processes, the model is investigated in a rotational field. The model introduced the microelongation scalar function, which describes the microelement processes according to the micropolar-thermoelasticity theory. The model studies the interaction case between optical-thermo-mechanical waves under the effect of rotation parameters when the microelongation parameters are taken into consideration according to the photo-thermoelasticity theory. The main governing equations have been taken in a dimensionless form during the electronic and thermoelastic deformation and they have been studied under the harmonic wave technique. The general solutions of the basic fields of isotropic, homogeneous, and linear microelongated semiconductor medium are obtained in two dimensions (2D). Many conditions are taken at the free surface of the medium to obtain the complete solutions. The physical parameters of silicon (Si) are used to illustrate the numerical simulation of the main fields. Several comparisons were performed and illustrated graphically under the influence of different parameters of relaxation time and rotation. Full article

The solution of any engineering problem starts with a modelling process aimed at formulating a mathematical model, which must describe the problem under consideration with sufficient precision. Because of heterogeneity of modern engineering applications, mathematical modelling scatters nowadays from incredibly precise micro- and even nano-modelling of materials to macro-modelling, which is more appropriate for practical engineering computations. In the field of masonry structures, a macro-model of the material can be constructed based on various elasticity theories, such as classical elasticity, micropolar elasticity and Cosserat elasticity. Evidently, a different macro-behaviour is expected depending on the specific theory used in the background. Although there have been several theoretical studies of different elasticity theories in recent years, there is still a lack of understanding of how modelling assumptions of different elasticity theories influence the modelling results of masonry structures. Therefore, a rigorous approach to comparison of different three-dimensional elasticity models based on quaternionic operator calculus is proposed in this paper. In this way, three elasticity models are described and spatial boundary value problems for these models are discussed. In particular, explicit representation formulae for their solutions are constructed. After that, by using these representation formulae, explicit estimates for the solutions obtained by different elasticity theories are obtained. Finally, several numerical examples are presented, which indicate a practical difference in the solutions. Full article

The study of the effect of the microstructure is important and is most evident in elastic vibrations of high frequency and short-wave duration. In addition to deformation caused by temperature and acting forces, the theory of micropolar thermoelasticity is applied to investigate the microstructure of materials when the vibration of their atoms or molecules is increased. This paper addresses a two-dimensional problem involving a thermoelastic micro-polar half-space with a traction-free surface and a known conductive temperature at the medium surface. The problem is treated in the framework of the concept of two-temperature thermoelasticity with a higher-order time derivative and phase delays, which takes into consideration the impact of microscopic structures in non-simple materials. The normal mode technique was applied to find the analytical formulas for thermal stresses, displacements, micro-rotation, temperature changes, and coupled stress. The numerical results are graphed, and the effect of the discrepancy indicator and higher-order temporal derivatives is examined. There are also some exceptional cases that are covered. Full article

In this study, the limits of the Euler–Bernoulli theory in micromechanics are explored. Raman spectroscopy, which is extremely accurate and reliable, is employed to study the bending of a microbeam of a length of 191 μm. It is found that at the micro-scale, the Euler–Bernoulli theory remains an exact and consistent tool, and, possibly, other elasticity theories (such as micropolar theory, gradient elasticity theory, and couple stress theory) are not always required to study this phenomenon. More specifically, good correlation was achieved between the theoretical and experimental results, the former acquired via the theoretical equations and the latter obtained with the use of atomic force microscopy and Raman spectroscopy. The exact predicted strain of an atomic force microscope microbeam under bending, by Euler–Bernoulli equations is confirmed by Raman spectroscopy. Full article

The instabilities of soil specimens in laboratory or soil made geotechnical structures in field are always numerically simulated by the classical continuum mechanics-based constitutive models with finite element method. However, finite element mesh dependency problems are inevitably encountered when the strain localized failure occurs especially in the post-bifurcation regime. In this paper, an attempt is made to summarize several main numerical regularization techniques used in alleviating the mesh dependency problems, i.e., viscosity theory, nonlocal theory, high-order gradient and micropolar theory. Their fundamentals as well as the advantages and limitations are presented, based on which the combinations of two or more regularization techniques are also suggested. For all the regularization techniques, at least one implicit or explicit parameter with length scale is necessary to preserve the ellipticity of the partial differential governing equations. It is worth noting that, however, the physical meanings and their relations between the length parameters in different regularization techniques are still an open question, and need to be further studied. Therefore, the micropolar theory or its combinations with other numerical methods are promising in the future. Full article

It has been demonstrated that materials with microstructure, such as particle composites, show a peculiar mechanical behavior when discontinuities and heterogeneities are present. The use of non-local theories to solve this challenge, while preserving memory of the microstructure, particularly of internal length, is a challenging option. In the present work, composite materials made of rectangular rigid blocks and elastic interfaces are studied using a Cosserat formulation. Such materials are subjected to dynamic shear loads. For anisotropic media, the relative rotation between the local rigid rotation and the microrotation, which corresponds to the skewsymmetric part of strain, is crucial. The benefits of micropolar modeling are demonstrated, particularly for two orthotropic textures of different sizes. Full article