A model for soap film dynamics with evolving thickness

Previous research on animations of soap bubbles, films, and foams largely focuses on the motion and geometric shape of the bubble surface. These works neglect the evolution of the bubble’s thickness, which is normally responsible for visual phenomena like surface vortices, Newton’s interference patterns, capillary waves, and deformation-dependent rupturing of films in a foam. In this paper, we model these natural phenomena by introducing the film thickness as a reduced degree of freedom in the Navier-Stokes equations and deriving their equations of motion. We discretize the equations on a nonmanifold triangle mesh surface and couple it to an existing bubble solver. In doing so, we also introduce an incompressible fluid solver for 2.5D films and a novel advection algorithm for convecting fields across non-manifold surface junctions. Our simulations enhance state-of-the-art bubble solvers with additional effects caused by convection, rippling, draining, and evaporation of the thin film

Macroscopic Properties of Open-Cell Foams Based on Micromechanical Modelling

This paper presents a micromechanical analysis for the assessment of macroscopic behaviour of threedimensional open-cell solid foams. The analysis is based on material properties of a solid phase and topological arrangement of cell structure. A foam structure consists of idealized tetrahedral unit cells, which are built of four identical half-struts forming a diamond-like structure and identified as Plateau borders. Such a unit cell represents the essential microstructural features of foam. An analytical formulation of force-displacement relations for struts can be found by considering the affinity of node displacements in tensile, bending, and shear deformation. The elements of the stiffness matrix for a single cell are expressed as functions of the compliance coefficients for stretching and bending of struts. The effective elastic constants for metallic foam considered as isotropic material are determined as functions of foam relative density and compared with available results. In this paper we define an energy-based limit condition of linear elasticity for open-cell foams and calculate the critical energy density pertinent to a particular orthogonal energy state accounting for elementary interactions in a microstructure. The study based on the assumption of linear elasticity leads to simple analytical formulas. Nevertheless, it should be stressed that the proposed theoretical basis of micromechanical modelling could be also applied for the analysis of nonlinear elastic behaviour, plasticity, and failure of foams. Such problems require, however, a more complex numerical approach

A lattice Boltzmann model for heat transfer in porous media

Porous media are commonly found not only in the nature but also in industries. Furthermore, porous media is an important research prototype for a diversity of disciplines. So far a REV (representative elementary volume) scale lattice Boltzmann (LB) model has been proposed and popularly used for investigation on heat transfer in porous media. Unfortunately, such model suffers from a serious drawback that it cannot address an investigated domain where the heat capacitance (the product of density and specific heat capacity) of porous media varies spatially obviously. Such deficit restricts dramatically its applicable range. The purpose of the present work is to remedy such serious shortcoming in a simple way. Numerical validation demonstrates the capability and reliability of the present model. In order to clearly show the advantage of the present model, here a single-relaxation-time LB model is taken as an example to illustrate how to remedy the shortcoming of previous models. Its multiple-relaxation-time counterpart can be established straightforwardly in the same way

eXtended Variational Quasicontinuum Methodology for Lattice Networks with Damage and Crack Propagation

Lattice networks with dissipative interactions are often employed to analyze materials with discrete micro- or meso-structures, or for a description of heterogeneous materials which can be modelled discretely. They are, however, computationally prohibitive for engineering-scale applications. The (variational) QuasiContinuum (QC) method is a concurrent multiscale approach that reduces their computational cost by fully resolving the (dissipative) lattice network in small regions of interest while coarsening elsewhere. When applied to damageable lattices, moving crack tips can be captured by adaptive mesh refinement schemes, whereas fully-resolved trails in crack wakes can be removed by mesh coarsening. In order to address crack propagation efficiently and accurately, we develop in this contribution the necessary generalizations of the variational QC methodology. First, a suitable definition of crack paths in discrete systems is introduced, which allows for their geometrical representation in terms of the signed distance function. Second, special function enrichments based on the partition of unity concept are adopted, in order to capture kinematics in the wakes of crack tips. Third, a summation rule that reflects the adopted enrichment functions with sufficient degree of accuracy is developed. Finally, as our standpoint is variational, we discuss implications of the mesh refinement and coarsening from an energy-consistency point of view. All theoretical considerations are demonstrated using two numerical examples for which the resulting reaction forces, energy evolutions, and crack paths are compared to those of the direct numerical simulations.Comment: 36 pages, 23 figures, 1 table, 2 algorithms; small changes after review, paper title change

Dynamic problems for metamaterials: Review of existing models and ideas for further research

Metamaterials are materials especially engineered to have a peculiar physical behaviour, to be exploited for some well-specified technological application. In this context we focus on the conception of general micro-structured continua, with particular attention to piezoelectromechanical structures, having a strong coupling between macroscopic motion and some internal degrees of freedom, which may be electric or, more generally, related to some micro-motion. An interesting class of problems in this context regards the design of wave-guides aimed to control wave propagation. The description of the state of the art is followed by some hints addressed to describe some possible research developments and in particular to design optimal design techniques for bone reconstruction or systems which may block wave propagation in some frequency ranges, in both linear and non-linear fields. (C) 2014 Elsevier Ltd. All rights reserved