Principles Of Continuum Mechanics Research Articles

Review of "Principles of Continuum Mechanics. A Study of Conservation Principles with Applications"

Review of "Principles of Continuum Mechanics. A Study of Conservation Principles with Applications"

터보챠저 저어널 베어링에서 물과 윤활유가 혼합될 때 베어링 성능에 관한 연구

In this study, using the governing equations for thermohydrodyamic lubrication involving the homogeneous mixture of incompressible fluid derived by based on the principle of continuum mechanics, it is discussed the effects of water dispersed within engine oil on the performance of high speed journal bearing of a turbocharger. The governing equations are the general equations being able to be applied on the mixture of Newtonian fluid and non-Newtonian fluid. Here, the fluid viscosity index, n of power-law non-Newtonian fluid is supposed to be 1 for the application of the journal bearing on a turbocharger lubricated with the mixture of two Newtonian fluids, water dispersed within engine oil. The results related with the bearing performance are showed that the friction force and bearing load capacity decrease as increasing the volume percent of water.

Optimal boundary control of a diffusion–convection-reaction PDE model with time-dependent spatial domain: Czochralski crystal growth process

In this paper the optimal boundary control problem for diffusion–convection-reaction processes modeled by partial differential equations (PDEs) defined on time-dependent spatial domains is considered. The model of the transport system with time-varying domain arises in the context of high energy consuming Czochralski crystal growth process in which the crystal temperature regulation must successfully account for the change in the crystal spatial domain due to the crystal growth process realized by the pulling crystal out of melt. Starting from the first principles of continuum mechanics and transport theorem the time-varying parabolic PDE describing temperature evolution is derived and represented as a nonautonomous parabolic evolution system on an appropriately defined function space which is exactly transformed in the infinite-dimensional boundary control problem for which a boundary linear quadratic regulator is proposed. Properties of the solution of the time-varying parabolic PDEs given by the two-parameter evolutionary system are utilized in the synthesis of the optimal boundary regulator, and the control law is applied to the model given by a two-dimensional partial differential equation in the cylindrical coordinates representing the Czochralski crystal growth process with one-dimensional growth direction. Finally, numerical results demonstrate optimal stabilization of the two-dimensional temperature distribution in the crystal.

A Continuum model for pressure-flow relationship in human pulmonary circulation

A continuum model was introduced to analyze the pressure-flow relationship for steady flow in human pulmonary circulation. The continuum approach was based on the principles of continuum mechanics in conjunction with detailed measurement of vascular geometry, vascular elasticity and blood rheology. The pulmonary arteries and veins were considered as elastic tubes and the "fifth-power law" was used to describe the pressure-flow relationship. For pulmonary capillaries, the "sheet-flow" theory was employed and the pressure-flow relationship was represented by the "fourth-power law". In this paper, the pressure-flow relationship for the whole pulmonary circulation and the longitudinal pressure distribution along the streamlines were studied. Our computed data showed general agreement with the experimental data for the normal subjects and the patients with mitral stenosis and chronic bronchitis in the literature. In conclusion, our continuum model can be used to predict the changes of steady flow in human pulmonary circulation.

터빈오일과 물이 혼합될 때 증기터빈 선박엔진 저어널 베어링의 열유체윤활 해석

In this study, using the governing equation for thermohydrodyamic lubrication involving the homogeneous mixture of incompressible fluid derived by based on the principle of continuum mechanics, it is discussed the effects of water within turbine oil on the performance of high speed journal bearing of a steam turbine shipping engine. The governing equation is the general equation being able to be applied on the mixture of Newtonian fluid and non-Newtonian fluid. Here, the fluid viscosity index, n of power-law non-Newtonian fluid is supposed to be 1 for the application of the journal bearing in a steam turbine shipping engine lubricated with the mixture of two Newtonian fluid, for example, water within turbine oil. The results related with the bearing performance are showed.

A nonlinear multi-field coupled model for soils

A nonlinear multi-field coupled model for multi-constituent three-phase soils is derived by using the hybrid mixture theory. The balance equations with three levels (constituents, phases and the whole mixture soil) are set up under the assumption that soil is composed of multi-constituent elastic-plastic solid skeleton (which is different from the linearization method) and viscous liquid and ideal gas. With reasonable constitutive assumptions in such restrictive conditions as the principles of determinism, equipresence, material frame-indifference and the compatible principle in continuum mechanics, a theoretical framework of constitutive relations modeling three-phase soil in both non-equilibrium and equilibrium states is established, thus the closed field equations are formed. In the theoretical framework, the concept of effective generalized thermodynamic forces is introduced, and the nonlinear coupling constitutive relations between generalized dissipation forces and generalized flows within the system at nonequilibrium state are also presented. On such a basis, four special coupling relations, i.e., solid thermal elastic-plastic constitutive relation, liquid visco-elastic-plastic constitutive relation, the generalized Fourier’s law, and the generalized Darcy’s law are put forward. The generalized or nonlinear results mentioned above can degenerate into the linear coupling results given by Bennethum and Singh. Based on a specific dissipation function, the concrete form of generalized Darcy’s law is deduced, which may degenerate into the traditional form of Darcy’s law by neglecting the influence of skeleton deformation and temperature. Without considering temperature and other coupling effects, the nonlinear coupled model in this paper can degenerate into a soil elastic-plastic constitutive model.

Principles of continuum mechanics: a study of conservation principles with applications

As most modern technologies are no longer discipline-specific but involve multidisciplinary approaches, undergraduate engineering students should be introduced to the principles of mechanics so that they have a strong background in the basic principles common to all disciplines and are able to work at the interface of science and engineering disciplines. This textbook is designed for a first course on principles of mechanics and provides an introduction to the basic concepts of stress and strain and conservation principles. It prepares engineer-scientists for advanced courses in traditional as well as emerging fields such as biotechnology, nanotechnology, energy systems, and computational mechanics. This simple book presents the subjects of mechanics of materials, fluid mechanics, and heat transfer in a unified form using the conservation principles of mechanics.

Reddy, J.N.: Principles of Continuum Mechanics. A Study of Conservation Principles with Applications

Reddy, J.N.: Principles of Continuum Mechanics. A Study of Conservation Principles with Applications

How far cardiac cells can see each other mechanically

We ask the question whether cardiac cells, separated by a soft solid medium, can interact with one another mechanically, and if so, then how does the interaction depend on cell–cell separation, and the stiffness of the medium. First, we show that cardiac cells can be stimulated by a mechanical signal alone. We culture primary chicken embryonic cardiomyocytes on a 2D soft substrate. A mechanical probe is used to apply local cyclic stretch on the substrate near quiescent cells (cells not beating). Within 10 cycles of stretch, the cells begin to beat, and continue to do so for hours after the stimulation, while control non-beating cells remain quiescent. Next, we show that a beating cardiac cell (instead of the probe) can stimulate a neighbor. Our 2D culture of cardiomyocytes on a deformable soft substrate (0.5–1 kPa) shows that closer the cells are as a pair, higher is the probability of both of them beating over longer time. This probability is much higher than that of both cells beating as a pair when they are cultured on a harder substrate (47 kPa), or the probability of a single cell beating on the same soft substrate (0.5–1 kPa). The cell–cell interaction, namely, the stretch induced by one contractile cell onto another is modeled using the principles of continuum mechanics. The close correspondence between the predicted cell–cell interaction and the experimental observations suggests that cardiac cells are mechanically coupled through the deformable substrate, and that the coupling decreases with increasing distance between them and the substrate stiffness. The quantitative analysis and the experimental results provide a biophysical basis for the understanding of cell–cell interaction in cardiac tissue through the deformation field of the in vivo soft microenvironment.

Fatigue of Constructional Steel S460 under Complex Cyclic Stress and Strain Sequences

The constructional fine-grained steel S460 shows considerably high fatigue performance. In the last two decades this material has been investigated experimentally in great detail. These results served as basis for developing models and algorithms aiming at improvement of fatigue life assessments. The paper summarizes both the cyclic deformation and failure behaviour. The experimental results are compared with the results obtained by applying the models. Simple uniaxial loading is addressed also as a complex multiaxial, non-proportional elastic-plastic straining. The deformation behaviour is described by an enhanced plasticitymodel based on continuum mechanics principles. Cyclic softening and hardening, ratcheting and cyclic mean stress relaxation as well as non-proportional hardening are taken into account. The fatigue cracking behaviour is modelled based on a critical plane approach where the short crack growth calculations determine the critical plane of shortest fatigue life.

Application of the entropy generation minimization method to solid mechanics

This paper reports on a study that explored the application of the entropy generation minimization method to solid mechanics. After reviewing the definition of thermodynamic process and the principles of continuum mechanics, the constitutive equations of four categories of solid behaviors namely thermoelasticity, thermoviscoelasticity, thermoplasticity, and thermoviscoplasticity are discussed. Based on the computation of entropy generation due to mechanical harmonic loading in these four categories, a problem is presented. Several nondimensional parameters are defined using material, loading, and geometric parameters. The effects of nondimensional parameters on entropy generation due to heat conduction and internal dissipation are obtained and the solutions to minimize entropy generation are discussed.

Simulação transiente de um reator de leito fluidizado em 3D

Reatores de leito fluidizado atingiram o ápice de aplicação a partir dos anos 80 e 90. Desde então, esses equipamentos têm se tornado importantes na geração termelétrica, pois abrem as opções dos combustíveis utilizados, os quais podem apresentar qualidade inferior àqueles usados em processos industriais com alto grau de conversão. Essa técnica não está muito difundida no Brasil, onde as opções para o uso de tecnologias de geração elétrica estão em aberto. A geração térmica é uma opção que pode usar leito fluidizado para a combustão de materiais como carvão e biomassas. Os modelos matemáticos, por sua vez, têm se mostrado eficientes para investigar condições operacionais de processos industriais virtualmente. O modelo desenvolvido utiliza o conceito de multifases, multicomponente simulando o escoamento transiente em 3D. As equações de transporte de massa, momento e energia são resolvidas pelo método de volumes finitos. As fases são modeladas usando os princípios da mecânica do contínuo, onde uma coleção de partículas idênticas é considerada. Os resultados obtidos através da simulação de reator de leito fluidizado borbulhante se mostram de acordo com dados experimentais.

Band-like Stress Fiber Propagation in a Continuum and Implications for Myosin Contractile Stresses

Stress fibers are band-like features that form with sarcomere-like actin and myosin arrangement between cell regions, resisting myosin contractility. We consider three aspects of stress fiber formation: (1) they form by cytoskeletal actin–myosin interaction when myosin contractile forces are resisted, (2) they propagate in a band-like manner, and (3) they maintain a level of stress and material continuity with the cytoskeleton. This suggests that any description of myosin force should capture the band-like propagation of stress fibers within the constraints of a continuum model. Recent studies describe myosin force as increasing proportional to the cytoskeletal resistance in that direction, but do not capture the band-like propagation of myosin stresses in a continuum. While the spreading of myosin stresses in continuum models is commonly attributed to the elliptic nature of continuum equations, we show that it comes from an incomplete description of the myosin force. Qualitative observations of cytoskeletal actin–myosin interaction indicate the interaction to be ‘zipper-like’; myosin contractile forces get transmitted by bending actin filaments in directions away from that of the cytoskeletal resistance. A simple coarse-grained implementation of the lateral myosin forces that arise from the zippering action reproduces band-like stress propagation within a continuum model for the first time. This model also shows actin packing into the stress channel and its propagation along the edge for square and triangular constrained cells; features not captured earlier. Physically, the lateral contractile forces prevent stress spreading by balancing perpendicular shear forces that arise when stress channels through a continuum. Mathematically, these forces render the continuum stress equation hyperbolic. This paper presents a theoretical argument, based on continuum mechanics principles, that it is the zippering actin–myosin action that allows for band-like stress fiber propagation within a coarse-grained cytoskeletal continuum, and that any visualization of the cytoskeletal stress field should account for lateral contractile forces accompanying the much-acknowledged contractile force along a stress fiber.

Generalized variational principle in dissipative hydrodynamics and continuum mechanics

В работе представлена формулировка обобщенного вариационного принципа для диссипативных гидродинамических и механических систем в виде суммы вариационных принципов Гамильтона и Онзагера в терминах смещений механического и температурного полей. В этом случае система уравнений диссипативной гидродинамики соответствует уравнениям движения механического и температурного полей, получаемых из условия стационарности действия, построенного на лагранжиане в виде разности кинетической и свободной энергий, а также интеграла по времени от диссипативной функции с квадратичными формами всех слагаемых.

Full 3D finite element Cosserat formulation with application in layered structures

In this paper, a full three-dimensional (3D) finite element Cosserat formulation is developed within the principles of continuum mechanics in the small deformation framework. The developed finite element formulation is general; however, the proposed constitutive laws incorporate the effect of the internal length parameter of 3D layered continua. The extension of the existing two-dimensional (2D) Cosserat formulation to the 3D framework is novel and is consistent with plate theory which can be considered as the 3D version of beam theory. The results demonstrate a high level of consistency with the analytical solutions predicted by plate theory as well as predictions by alternative numerical techniques such as the discrete element method.

Objectivity tests for Navier–Stokes simulations: The revealing of non-physical solutions produced by Laplace formulations

Laplace formulations are weak formulations of the Navier–Stokes equations commonly used in computational fluid dynamics. In these schemes, the viscous terms are given as a function of the Laplace diffusion operator only. Despite their popularity, recently, it has been proven that they violate a fundamental principle of continuum mechanics, the principle of objectivity. It is remarkable that such flaw has not being noticed before, neither detected in numerical experiments. In this work, a series of objectivity tests have been designed with the purpose of revealing such problem in real numerical experiments. Through the tests it is shown how, for slip boundaries or free-surfaces, Laplace formulations generate non-physical solutions which widely depart from the real fluid dynamics. These tests can be easily reproduced, not requiring complex simulation tools. Furthermore, they can be used as benchmarks to check consistency of developed or commercial software. The article is closed with a discussion of the mathematical aspects involved, including the issues of boundary conditions and objectivity.

An Evolution Equation which describes Random Deformation of a Surface derived by a Variational Principle of Continuum Mechanics

An Evolution Equation which describes Random Deformation of a Surface derived by a Variational Principle of Continuum Mechanics

ROLLING PROCESS SIMULATION USING A DEVELOPED EULERIAN FORMULATION

ABSTRACTIn this paper, an Eulerian formulation is developed from the more general ArbitraryLagrangian Eulerian (ALE) formulation and is used in rolling process simulation.Starting from the basic principles of continuum mechanics, a consistent ALEformulation is derived. An Eulerian formulation is then obtained by fixing the finiteelement mesh in space. A finite element program based on the Eulerian formulationhas been developed. The program is used to simulate a steady state rolling process.The roll pressure distribution is compared with published experimental results.Comparisons reveal the effectiveness of the developed formulation.

Characterization and Modeling of the Effect of Environmental Degradation on Interlaminar Shear Strength of Carbon/Epoxy Composites

Accelerated ageing experiments have been conducted to address durability issues of carbon/epoxy composites to be used for emerging facilities and infrastructure, such as, bridges and buildings, in different climatic zones. The degradation of carbon/epoxy composites under UV, hygrothermal exposure, and applied tensile stress has been investigated. The tests were designed to capture the synergistic effects of field exposure and extreme temperatures, viz., hot/dry, hot/wet, cold/dry, and cold/wet conditions. Short beam shear tests (SBST) were performed for the determination of interlaminar shear strength (ILSS) of conditioned composite specimens. The hot/dry samples showed increased strength, while the hot/wet ones showed a decrease in strength. It is conjectured that conditioning at 90 °C possibly contributed to an increase in the ILSS from post curing. For the hot/wet samples (90 °C, immersed in water) the results indicate that strength degradation due to moisture-induced hydrolysis overshadowed the post-curing effect. The samples subjected to shear stress under hot conditions (90 °C) showed a higher ILSS, possibly due to improved crosslink density arising from post-cure. There is insignificant variation in the ILSS of UV treated and the UV untreated control samples. All the SBST test data reported in this work are from tests performed at room temperature and ambient humidity after environmental ageing. A two-dimensional cohesive layer constitutive model with a prescribed traction-separation law constructed from the basic principles of continuum mechanics, taking into account hygrothermal mechanisms that are likely to occur within a cohesive bi-material interface, such as between adjacent plies in a laminate, was applied to simulate interlaminar failure in the SBST specimens, using Finite Element Analysis (FEA). A phenomenological predictive model was developed using the finite element results.

Two numerical models for landslide dynamic analysis

Two microcomputer-based numerical models (Dynamic ANalysis (DAN) and three-dimensional model DAN (DAN3D)) have been developed and extensively used for analysis of landslide runout, specifically for the purposes of practical landslide hazard and risk assessment. The theoretical basis of both models is a system of depth-averaged governing equations derived from the principles of continuum mechanics. Original features developed specifically during this work include: an open rheological kernel; explicit use of tangential strain to determine the tangential stress state within the flowing sheet, which is both more realistic and beneficial to the stability of the model; orientation of principal tangential stresses parallel with the direction of motion; inclusion of the centripetal forces corresponding to the true curvature of the path in the motion direction and; the use of very simple and highly efficient free surface interpolation methods. Both models yield similar results when applied to the same sets of input data. Both algorithms are designed to work within the semi-empirical framework of the “equivalent fluid” approach. This approach requires selection of material rheology and calibration of input parameters through back-analysis of real events. Although approximate, it facilitates simple and efficient operation while accounting for the most important characteristics of extremely rapid landslides. The two models have been verified against several controlled laboratory experiments with known physical basis. A large number of back-analyses of real landslides of various types have also been carried out. One example is presented. Calibration patterns are emerging, which give a promise of predictive capability.