A stochastic constitutive model for disordered cellular materials: Finite-strain uni-axial compression

AbstractA stochastic constitutive model is developed for describing the continuum-scale mechanical response of disordered cellular materials. In the present work, attention is restricted to finite-strain uni-axial compression under quasi-static loading conditions. The development begins with an established cellular-scale mechanical model, but departs from traditional modeling approaches by generalizing the cellular-scale model to accommodate finite strain. The continuum-scale model is obtained by averaging the cellular-scale mechanical response over an ensemble of foam cells. Various stochastic material representations are considered through the use of probability density functions for the relevant material parameters, and the effects of the various representations on the continuum-scale response are investigated. Combining cellular-scale mechanics with a stochastic material representation to derive a continuum-scale constitutive model offers a promising new approach for simulating the finite-strain response of cellular materials. Results demonstrate that increasing a material’s degree of polydispersity can produce the same stiffening effects as increasing the initial solid-volume fraction. Additionally, particular stochastic material representations are shown to provide upper and lower bounds on the mechanical response of the cellular materials under investigation, while suitable choices for the stochastic representation are shown to accurately reproduce experimental stress–strain data through the large deformations associated with densification

Efficient Algorithm on a Non-staggered Mesh for Simulating Rayleigh-Benard Convection in a Box

An efficient semi-implicit second-order-accurate finite-difference method is described for studying incompressible Rayleigh-Benard convection in a box, with sidewalls that are periodic, thermally insulated, or thermally conducting. Operator-splitting and a projection method reduce the algorithm at each time step to the solution of four Helmholtz equations and one Poisson equation, and these are are solved by fast direct methods. The method is numerically stable even though all field values are placed on a single non-staggered mesh commensurate with the boundaries. The efficiency and accuracy of the method are characterized for several representative convection problems.Comment: REVTeX, 30 pages, 5 figure

Turbulence Modeling Using Fractional Derivatives

We propose a new turbulence model in this work. The main idea of the model is that the shear stresses are considered to be random variables and we assume that their differences with respect to time are Lévy-type distributions. This is a generalization of the classical Newton’s law of viscosity. We tested the model on the classical backward facing step benchmark problem. The simulation results are in a good accordance with real measurements

Amplitude measurements of Faraday waves

A light reflection technique is used to measure quantitatively the surface elevation of Faraday waves. The performed measurements cover a wide parameter range of driving frequencies and sample viscosities. In the capillary wave regime the bifurcation diagrams exhibit a frequency independent scaling proportional to the wavelength. We also provide numerical simulations of the full Navier-Stokes equations, which are in quantitative agreement up to supercritical drive amplitudes of 20%. The validity of an existing perturbation analysis is found to be limited to 2.5% overcriticaly.Comment: 7 figure