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Continuum mechanics

About: Continuum mechanics is a research topic. Over the lifetime, 5042 publications have been published within this topic receiving 181027 citations.


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09 Oct 2009
TL;DR: In this article, a thermal lattice Boltzmann equation (LBE) multiphase model is proposed to simulate the thermal two-phase flow model, which is based on microscopic models and mesoscopic kinetic equations.
Abstract: This dissertation presents a systematic development of a new thermal lattice Boltzmann multiphase model. Unlike conventional CFD methods, the lattice Boltzmann equation (LBE) method is based on microscopic models and mesoscopic kinetic equations in which the collective behavior of the particles in a system is used to simulate the continuum mechanics of the system. Due to this kinetic nature, the LBE method has been found to be particularly useful in applications involving interfacial dynamics and complex boundaries, e.g. multiphase or multicomponent flows. First, the methodology and general concepts of the LBE method are introduced. Following this introduction, an accurate mass conserving wall boundary condition for the LBE method is proposed together with benchmark test results. Next, the widely used Shan and Chen (SC) single component two-phase flow model is presented, as well as improvements to that model. In this model, by incorporating fluid-fluid interaction, phase separation and interfacial dynamics can be properly captured. Sharp interfaces between phases can be easily obtained without any additional numerical treatment. In order to achieve flexibility for the surface tension term, an additional force term which represents the contribution of surface tension is incorporated into the fluid-fluid interaction force term. The validity of this treatment is verified by our simulation results. Different equations of state are also incorporated into this model to compare their behavior. Finally, based on the SC model, a new and generalized lattice Boltzmann model for simulating thermal two-phase flow is described. In this model, the SC model is used to simulate the fluid dynamics. The temperature field is simulated using the passive-scalar approach, i.e. through modeling the density field of an extra component, which evolves according to the advection-diffusion equation. By coupling the fluid dynamics and temperature field through a suitably defined body force term, the thermal two-phase lattice Boltzmann model is obtained. Our simulation results show that different equations of state, variable wettability, gravity and buoyancy effects, and relatively high Rayleigh numbers can be readily simulated by this new model. Lastly, the accomplishments of this study are summarized and future perspectives are provided.

44 citations

Journal ArticleDOI
TL;DR: In this paper, a new mathematical framework is proposed to model the process of thermal oxidation in silicon, derived from the fundamental conservation equations of mechanics, and a thermodynamically consistent constitutive equation for silicon dioxide is suggested to represent recent experimental data.
Abstract: This work focuses on a new mathematical framework to model the process of thermal oxidation in silicon. The mathematical model is derived from the fundamental conservation equations of mechanics. The mass balance law provides the description of the oxidant transport and the Si–SiO2 interface motion, and momentum balance provides the framework to model the displacements and stresses in the bulk and the oxide. The displacements define the geometry of the final oxide structure. The large expansion is treated within a mathematically exact formulation following a split of the deformation gradient. A thermodynamically consistent constitutive equation for silicon dioxide is suggested to represent recent experimental data. Copyright © 2000 John Wiley & Sons, Ltd.

44 citations

Book ChapterDOI
01 Jan 2016
TL;DR: In this article, the authors present a phenomenological theory of constitutive relations, which is based on the Cauchy stress tensor and the kinematical quantities of a material.
Abstract: The chapter starts with overview of the derivation of the balance equations for mass, momentum, angular momentum, and total energy, which is followed by a detailed discussion of the concept of entropy and entropy production. While the balance laws are universal for any continuous medium, the particular behavior of the material of interest must be described by an extra set of material-specific equations. These equations relating, for example, the Cauchy stress tensor and the kinematical quantities are called the constitutive relations. The core part of the chapter is devoted to the presentation of a modern thermodynamically based phenomenological theory of constitutive relations. The key feature of the theory is that the constitutive relations stem from the choice of two scalar quantities, the internal energy and the entropy production. This is tantamount to the proposition that the material behavior is fully characterized by the way it stores the energy and produces the entropy. The general theory is documented by several examples of increasing complexity. It is shown how to derive the constitutive relations for compressible and incompressible viscous heat-conducting fluids (Navier–Stokes–Fourier fluid), Korteweg fluids, and compressible and incompressible heat-conducting viscoelastic fluids (Oldroyd-B and Maxwell fluid).

44 citations

Journal ArticleDOI
TL;DR: In this paper, the authors analyzed the impact of adhesion force on nano-manipulation analysis for both spherical and conical tip shape. And they compared different nano-contact mechanics models, such as Hertz, Derjaguin-Muller-Toporov (DMT), Johnson-Kendall-Roberts-Sperling (JKRS), Burnham-Colton-Pollock (BCP), Maugis-Dugdale (MD), Carpick-Ogletree-Salmeron (COS), Pietre
Abstract: Atomic force microscopy is applied to measure intermolecular forces and mechanical properties of materials, nano-particle manipulation, surface scanning and imaging with atomic accuracy in the nano-world. During nano-manipulation process, contact forces cause indentation in contact area between nano-particle and tip/substrate which is considerable at nano-scale and affects the nano-manipulation process. Several nano-contact mechanics models such as Hertz, Derjaguin–Muller–Toporov (DMT), Johnson–Kendall–Roberts–Sperling (JKRS), Burnham–Colton–Pollock (BCP), Maugis–Dugdale (MD), Carpick–Ogletree–Salmeron (COS), Pietrement–Troyon (PT), and Sun et al. have been applied as the continuum mechanics approaches at nano-scale. In this article, indentation depth and contact radius between tip and substrate with nano-particle for both spherical and conical tip shape during nano-manipulation process are analyzed and compared by applying theoretical, semiempirical, and empirical nano-contact mechanics models. The effects of adhesion force, as the main contrast point in different nano-contact mechanics models, on nano-manipulation analysis is investigated for different contact radius, and the critical point is discussed for mentioned models.

44 citations

Journal ArticleDOI
TL;DR: It is found that the mechanical properties of spring networks are strongly dependent on the mesh configuration, and it is hard to express the area incompressibility observed in biological membranes using a simple spring network model.
Abstract: A capsule is a liquid drop enclosed by a solid, deformable membrane. To analyze the deformation of a capsule accurately, both the fluid mechanics of the internal and external fluids and the solid mechanics of the membrane must be solved precisely. Recently, many researchers have used discrete spring network models to express the membrane mechanics of capsules and biological cells. However, it is unclear whether such modeling is sufficiently accurate to solve for capsule deformation. This study examines the correlations between the mechanical properties of the discrete spring network model and continuum constitutive laws. We first compare uniaxial and isotropic deformations of a two-dimensional (2D) sheet, both analytically and numerically. The 2D sheet is discretized with four kinds of mesh to analyze the effect of the spring network configuration. We derive the relationships between the spring constant and continuum properties, such as the Young modulus, Poisson ratio, area dilation modulus, and shear modulus. It is found that the mechanical properties of spring networks are strongly dependent on the mesh configuration. We then calculate the deformation of a capsule under inflation and in a simple shear flow in the Stokes flow regime, using various membrane models. To achieve high accuracy in the flow calculation, a boundary-element method is used. Comparing the results between the different membrane models, we find that it is hard to express the area incompressibility observed in biological membranes using a simple spring network model.

44 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202363
2022136
2021150
2020176
2019181
2018185