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Finite thickness

About: Finite thickness is a(n) research topic. Over the lifetime, 1245 publication(s) have been published within this topic receiving 19481 citation(s).
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Journal ArticleDOI
Abstract: A mathematical analysis of a new approach to solidification problems is presented. A free boundary arising from a phase transition is assumed to have finite thickness. The physics leads to a system of nonlinear parabolic differential equations. Existence and regularity of solutions are proved. Invariant regions of the solution space lead to physical interpretations of the interface. A rigorous asymptotic analysis leads to the Gibbs-Thompson condition which relates the temperature at the interface to the surface tension and curvature.

699 citations

Journal ArticleDOI
18 Mar 2009-Physical Review E
TL;DR: Experimental, numerical, and theoretical investigations of a normal drop impact onto a liquid film of finite thickness are presented, finding a good agreement with the numerical predictions of the phenomena.
Abstract: In the present work experimental, numerical, and theoretical investigations of a normal drop impact onto a liquid film of finite thickness are presented. The dynamics of drop impact on liquid surfaces, the shape of the cavity, the formation and propagation of a capillary wave in the crater, and the residual film thickness on the rigid wall are determined and analyzed. The shape of the crater within the film and the uprising liquid sheet formed upon the impact are observed using a high-speed video system. The effects of various influencing parameters such as drop impact velocity, liquid film thickness and physical properties of the liquids, including viscosity and surface tension, on the time evolution of the crater formation are investigated. Complementary to experiments the direct numerical simulations of the phenomena are performed using an advanced free-surface capturing model based on a two-fluid formulation of the classical volume-of-fluid (VOF) model in the framework of the finite volume numerical method. In this model an additional convective term is introduced into the transport equation for phase fraction, contributing decisively to a sharper interface resolution. Furthermore, an analytical model for the penetration depth of the crater is developed accounting for the liquid inertia, viscosity, gravity, and surface tension. The model agrees well with the experiments at the early times of penetration far from the wall if the impact velocity is high. Finally, a scaling analysis of the residual film thickness on the wall is conducted demonstrating a good agreement with the numerical predictions.

478 citations

Journal ArticleDOI
Abstract: This paper in concerned with the extension of the shell theory and numerical analysis presented in Part I, II and III to include finite thickness stretch and initial variable thickness. These effects play a significant role in problems involving finite membrane strains, contact, concentrated surface loads and delamination (in composite shells). We show that a direct numerical implementation of the standard single extensible director shell model circumvents the need for rotational updates, but exhibits numerical ill-conditioning in the thin shell limit. A modified formulation obtained via a multiplicative split of the director field into an extensible and inextensible part is presented, which involves only a trivial modification of the weak form of the equilibrium equations considered in Part III, and leads to a perfectly well-conditioned formulation in the thin-shell limit. In sharp contrast with previous attempts in the context of the degenerated solid approach, the thickness stretch is an independent field, not a dependent variable updated iteratively via the plane stress condition. With regard to numerical implementation, an exact update procedure which automatically ensures that the thickness stretch remains positive is presented. For the present theory, standard displacement models would exhibit ‘locking’ in the incompressible limit as a result of the essentially three-dimensional character of the constitutive equations. A mixed formulation is described which circumvents this difficulty. Numerical examples are presented that illustrate the effects of the thickness stretch, the performance of the proposed mixed interpolation, and the well-conditioned response exhibited by the present approach in the thin-shell (inextensible director) limit.

434 citations

Journal ArticleDOI
Abstract: The homogenization theory for periodic media allows the global behaviour of masonry to be derived from the behaviour of the constitutive materials (brick and mortar). Such a procedure has been used by many authors but always in an approximate manner. In particular, the homogenization procedure has always been performed in several successive steps, head joints and bed joints being introduced successively. Moreover, masonry was considered either as a two-dimensional media under the plane stress assumption (very thin media), or as a three-dimensional bulk (very thick media), so that its finite thickness was never taken into account. The homogenization theory for periodic media is implemented here in a rigorous way, i.e. in one step and on the real geometry of masonry (finite thickness and actual bond pattern). Numerical applications are carried out and the results are compared with the predictions based on existing simplified approaches. All the above-mentioned approximations turn out to slightly affect the inplane elastic characteristics of masonry, but it is anticipated that, in the non-linear range (plasticity or damage), the same approximations might lead to erroneous results, quantitatively as well as qualitatively (value of the ultimate load and mode of failure).

394 citations

Journal ArticleDOI
Abstract: We establish the equations of motion of an isothermal viscous Cahn-Hilliard fluid and we investigate the dynamics of fluids having moving contact lines under this theory. The force singularity arising in the classical model of capillarity is no longer present. This removal is due to a mass transfer across the interface combined with a finite thickness of the interface. A numerical simulation of the flow in the immediate vicinity of the contact line shows the connection between the static contact angle, the dynamic angle and points out the influence of the velocity.

320 citations

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Topic's top 5 most impactful authors

Faruk Yigit

7 papers, 70 citations

Andrei Kotousov

7 papers, 196 citations

N. Rudraiah

5 papers, 75 citations

Dong-Sheng Jeng

4 papers, 338 citations

Luigi Verolino

3 papers, 9 citations