Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
11
2
2013
AN OPTIMAL PREDICTION METHOD FOR UNDERRESOLVED TIME-MARCHING AND TIME-SPECTRAL
93-116
Allen
LaBryer
Department of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, Oklahoma
Peter J.
Attar
Department of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, Oklahoma
Prakash
Vedula
Department of Aerospace and Mechanical Engineering, University of Oklahoma, Norman, Oklahoma
The prevalence of multiscale phenomena in nonlinear dynamical systems often necessitates the use of reduced-order models. Similar in concept to the traditional view of spatial reduced-order models, under-resolved time-discretization schemes may be used to decrease the computational burden while sacrificing some level of accuracy. We present a framework based on the optimal prediction formalism that can be used to minimize the errors intrinsic to any timediscretization scheme. Models will be developed for the unresolved subgrid-scale dynamics and added to the governing equations. These subgrid-scale models will interact with the resolved timescales as the system evolves, rendering the optimal solution with respect to the chosen resolution. To demonstrate the technique, we study the van der Pol oscillator using a well-known time-marching scheme and a novel time-spectral method.
VARIATIONALLY CONSISTENT HOMOGENIZATION OF STOKES FLOWIN POROUS MEDIA
117-138
Carl
Sandstrom
Department of Applied Mechanics, Chalmers University of Technology, S-412 96 Gothenburg
Fredrik
Larsson
Department of Applied Mechanics, Chalmers University of Technology, S-412 96 Gothenburg
Seepage through a strongly heterogeneous material, consisting of open saturated pores, is modeled as a Stokes flow contained in a rigid matrix. Through homogenization of the problem, a two-scale formulation is derived. The subscale problem is that of a Stokes flow whereas the macroscale problem pertains to a Darcy flow. The prolongation of the macroscale Darcy flow fulfills the variational consistent macrohomogeniety condition and is valid for both linear and nonlinear subscale flows. The subscale problem is solved using the finite element method. Numerical results concerning both linear and nonlinear flow are presented.
FROM MICRO- TO MACROMODELS FOR IN-PLANE LOADED MASONRYWALLS: PROPOSITION OF A MULTISCALE APPROACH
139-159
Antonella
Cecchi
Department of Architecture Construction Conservation (DACC), University IUAV of Venice, Dorsoduro 2206, Venice, 30123, Italy
Alessia
Vanin
University IUAV di Venezia, ex Convento delle Terese, Dorsoduro 2206; 30123 − Venice, Italy
A multiscale model for the structural analysis of the in-plane response of masonry panels, characterized by periodic arrangement of blocks and mortar, is here presented. The model is based on two-scale use: at the microscopic level a classical Cauchy continuous is used, while at the macroscopic level a discrete macroelement model is adopted. Extensive literature exists on micro and macro approaches for masonry, but theories investigating a relationship between the two scales of analysis are still to be developed. With this aim, the authors propose a possible strategy to overcome the critical gap between two approaches. In particular, at the microlevel a homogenization procedure is used to calibrate a strut and tie model at the macrolevel. The purpose is refined modeling of a pier trough micro and macro relationship to analyze, in the perspective, complex masonry structures like historical buildings. Identification between continuous homogenized masonry panels and discrete systems of trusses is based on the equivalence of power spent in the two systems under the same boundary conditions. Hence a strut and tie macromodel in which truss inclination and truss stiffness calibration is obtained from homogenization microanalysis is proposed. In this way it is possible to take into account the sensitivity of some constitutive factors and geometric parameters of masonry, i.e., the arrangement of blocks. To verify the reliability of the procedure, some meaningful cases are analyzed.
MICROMORPHIC TWO-SCALE MODELLING OF PERIODIC GRID STRUCTURES
161-176
Ralf
Janicke
Ruhr-Universitat Bochum, Institut fur Mechanik-Kontinuumsmechanik, IA 3/28, Universitatsstr. 150, D−44780 Bochum, Germany
Hans-Georg
Sehlhorst
Numerical Structural Analysis with Application in Ship Technology, Technische Universität Hamburg, Hamburg, Germany
Alexander
Duster
Numerical Structural Analysis with Application in Ship Technology, Technische Universität Hamburg, Hamburg, Germany
Stefan
Diebels
Universitat des Saarlandes, Lehrstuhl fuer Technische Mechanik, Postfach 1511 50, D−66041 Saarbrucken, Germany
The present contribution focuses on the numerical homogenization of periodic grid structures. In order to investigate the micro-to-macroscale transition, a consistent numerical homogenization scheme will be presented, replacing a heterogeneous Cauchy microcontinuum by a homogeneous micromorphic substitute continuum on the macroscale. The extended degrees of freedom, namely, the microdeformation and its gradient, are to be interpreted in terms of geometrical deformation modes and the related loading conditions of the underlying unit cells. Assuming strain energy equivalence of the macro- and the microscale, the effective constitutive properties of a square and a honeycomb grid structure are identified and quantitatively validated in comparison to reference calculations with microscopic resolution.
MULTI-SCALE MODELLING OF SNOW MICROSTRUCTURE
177-184
Anna
Carbone
Applied Science and Technology Department, Politecnico di Torino,Torino, Italy; ETH Zurich, Switzerland
B. M.
Chiaia
Department of Structural and Geotechnical Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
B.
Frigo
Department of Structural and Geotechnical Engineering, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
C.
Turk
Applied Science and Technology Department, Politecnico di Torino, Corso Duca degli Abruzzi 24, I-10129 Torino, Italy
A three-dimensional multiscale spatial model of snow with evolving microstructure is presented. Many engineering and environmental problems require a comprehensive understanding of snow behavior which arises as a consequence of phenomena spanning a wide spectrum of spatial length scales. Snow is classically described as a granular heterogeneous medium consisting of air and three water phases: ice, vapor, and liquid. The ice phase consists of grains arranged on a matrix according to a random load-bearing skeleton. The challenge is to achieve a detailed description of the mechanical and morphological characteristics of different snow microstructures that may have the same global density. Snow density can be determined by in situ measurements with quite good accuracy, and by means of the box-counting method, the fractal dimension of snow samples characterized by grains with different diameters could be determined. It was suggested that the fractal dimension can be adopted as a relevant parameter for quantifying snow morphology, in terms of the distribution of voids, and density over a wide range of spatial scales. In this work this concept is further developed. Snow density is simulated by means of a lacunar fractal, namely, a generalized Menger sponge. Then, a fully threedimensional invasive stochastic fractal model is adopted. This model performs a three-dimensional mapping of the snow density to a three-dimensional fractional Brownian field. In particular, snow samples with evolving microstructure are quantified as a continuous function of the fractal dimension.