Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
9
2
2011
A NOVEL PHYSICAL APPROACH FOR MODELING PLASTIC DEFORMATION IN THIN MICROWIRES
137-148
H.
Farahmand
Department of Mechanical Engineering, Islamic Azad University of Kerman Branch, Kerman, Iran
Ali Reza
Saidi
Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran
S.
Arabnejad
Young Researchers Club, Kerman branch, Islamic Azad University, Kerman, Iran
Several experimental results contribute to the effects of length scale parameters. Most models for these experimental data are developed based on strain gradient theory. Compared with the scale of dislocation movement and hardening mechanisms, which are used to model the physical-based strain gradient, plastic deformation in microstructures is sufficiently large, so that finite plasticity theory could be well justified. Therefore, the main objective of this work is to develop a strain gradient theory with the cooperation of dislocation theory and finite plastic as a new constitutive equation. This procedure is accomplished with the intrinsic length scale relation, which is dedicated to the phenomenological development of plasticity laws for microstructures in finite plasticity. It is a new process of expressing the plastic deformation result for microstructures. Finally, the result of this new theory is indicated for microwires.
A THEORETICAL AND NUMERICAL MULTISCALE FRAMEWORK FOR THE ANALYSIS OF PATTERN FORMATION IN PROTEIN CRYSTAL ENGINEERING
149-174
Marcello
Lappa
CTC, Naples, Italy
The relevance of self-organization, pattern formation, nonlinear phenomena, and nonequilibrium behavior in a wide range of problems related to macromolecular crystal engineering calls for a concerted approach using the tools of statistical physics, thermodynamics, fluid dynamics, nonlinear dynamics, mathematical modeling, and numerical simulation in synergy with experimentally oriented work. The reason behind such a need is that in many instances of relevance in this field one witnesses an interplay between molecular and macroscopic-level entities and processes. Along these lines, two models are defined here and discussed in detail, one dealing with issues of complex behavior at the microscopic level and the other referring to the strong nonlinear nature of macroscopic evolution. Such models share a common fundamental feature, a group of equations strictly related from a mathematical point of view to the kinetic conditions used to model mass transfer at the crystal surface. Model diversification then occurs on the basis of the desired scale length; i.e., according to the level of detail required by the analysis (local or global). If the local evolution of the crystal surface is the subject of the investigation (distribution of the local growth rate along the crystal face, shape instabilities, onset of surface depressions due to diffusive and/or convective effects, etc.; i.e., all those factors dealing with the local history of the shape) the model is conceived to provide microscopic and morphological details. For this specific case a kinetic-coefficient-based moving boundary numerical (computational fluid dynamics) strategy is carefully developed on the basis of the volume-of-fluid methods (also known as the volume tracking methods) and level-set techniques, which have become popular in the last years as numerical techniques capable of modeling complex multiphase problems as well as for their capability to undertake a fixed-grid solution without resorting to mathematical manipulations and transformations. On the contrary, if the size of the crystals is negligible with respect to the size of the reactor (i.e., if they are small and undergo only small dimensional changes with respect to the overall dimensions of the cell containing the feeding solution), the shape of the crystals is ignored and the proposed approach relies directly on an algebraic formulation of the nucleation events and on the application of an integral form of the mass balance kinetics for each protein crystal. The applicability and the suitability of the different submodels are discussed according to some worked examples of practical interest. Pattern formation in these processes is described here with respect to crystal shapes, nuclei spatial discrete arrangements, and the convective multicellular structures arising as a consequence of buoyancy forces, thus enriching the discussions with some interdisciplinary flavor.
MULTISCALE ANALYSIS OF STOCHASTIC FLUCTUATIONS OF DYNAMIC YIELD OF MAGNETORHEOLOGICAL FLUIDS
175-191
Yong-Bo
Peng
State Key Laboratory of Disaster Reduction in Civil Engineering, and Shanghai Institute of Disaster Prevention and Relief, Tongji University, Shanghai 200092, China
Jie
Li
State Key Laboratory of Disaster Reduction in Civil Engineering, and School of Civil Engineering, Tongji University, Shanghai 200092, China
The classical visco-plastic models of magnetorheological fluids are essentially phenomenological macroscale descriptions of fluids, incapable of revealing the interaction between suspensions and carrier fluids that results in a stochastic fluctuation of dynamic yield, and incapable of reflecting the impact of external magnetic fields on this fluctuation as well. In the present paper, the dynamical yield behavior of magnetorheological fluids is investigated by upscaling the information of the microscale interaction between particles, employing a large-scale molecular dynamical simulation technique, to the macroscale bulk behavior. We thus conduct a multiscale model of dynamic yield of magnetorheological fluids based on the conservation principle of system energy at different scales, so as to provide seamless information passing. The investigation reveals that the dynamic yield exhibits nonlinear and stochastic fluctuations due to the heterogeneity of sequence and number of cluster-sheet reconstructions with shear fields loading, and the Brownian motion of suspensions with initial random conditions. Besides, we investigate the thermal fluctuation of microscale particle motion, the variation of the relationship between stress and strain, and the variation of the constitutive relationship of shear rate. It is noted that the microscale thermal fluctuation is far more than the macroscale variation since that the upscaling from the microscale to the macroscale results in the degradation of fluctuations. The macroscale variation, meanwhile, is still significant, which is supposed to be considered in the design and optimization of magnetorheological fluids.
STATIC DEFLECTION ANALYSIS OF FLEXURAL SIMPLY SUPPORTED SECTORIAL MICRO-PLATE USING P-VERSION FINITE-ELEMENT METHOD
193-200
A. R.
Ahmadi
International Center for Science and High Technology and Environmental Sciences, Kerman, Iran
H.
Farahmand
Department of Mechanical Engineering, Islamic Azad University of Kerman Branch, Kerman, Iran
S.
Arabnejad
Young Researchers Club, Kerman branch, Islamic Azad University, Kerman, Iran
In this paper, flexural Kirchhoff plate theory is utilized for static analysis of isotropic sectorial micro-plates based on
a modified couple stress theory containing one material length scale parameter. The Levy method is implemented and
the resulting sixth-order differential equation is solved for the unknown deflection using the p-version finite-element
method. The Galerkin form of this differential equation is first reduced to its weak form and then solved using hierarchical
p-version finite elements with second-order global smoothness. The computed deflection distribution of the micro-plate
is compared with that of the classical theory, in which micro-effects are not present. A series of studies have revealed
that when the length scale parameters are considered, deflection of a sectorial plate decreases as the length scale effect is
increased; in other words, the micro-plate exhibits more rigidity.
SEECN: SIMULATING COMPLEX SYSTEMS USING DYNAMIC COMPLEX NETWORKS
201-214
Rick
Quax
Computational Science, University of Amsterdam, Netherlands
David A.
Bader
College of Computing, Georgia Institute of Technology, USA
Peter M. A.
Sloot
Computational Science, University of Amsterdam, Netherlands
Multiscale, multiphysics systems are too complex for traditional mathematical modeling and require numerical simulation, yet such systems arise everywhere from modeling the immune system and protein interaction to epidemic spread in a human population. Unfortunately, at present researchers create their own ad hoc programs for their particular study. To address this problem we present the simulator for efficient evolution on complex networks (SEECN), an expressive simulator of complex systems that optimizes for both single-core and parallel performance. In SEECN, a complex network represents the system where the nodes and edges have specified properties that dictate the dynamics of the network over time. Our application is a detailed model of HIV spread among men who have sex with men and serves to show the simulator's expressiveness and to evaluate its performance.
CONVERGENCE AND STABILITY IN UPSCALING OF FLOW WITH INERTIA FROM THE PORESCALE TO MESOSCALE
215-229
Anna
Trykozko
University ofWarsaw, Interdisciplinary Center for Mathematical and Computational Modelling, 02-106 Warsaw, Poland
Malgorzata
Peszynska
Department of Mathematics, Oregon State University, USA
We propose an algorithm for computational upscaling of flow with inertia from porescale (microscale) to Darcy scale (laboratory scale, mesoscale). In particular, we solve the Navier-Stokes equations in complex pore geometries and average their solutions to derive properties of flow relevant at the laboratory scale in the non-Darcy model of flow. Convergence and stability of the algorithm are discussed. The project is a prototype of a computational laboratory for porous media that delivers the data for the non-Darcy model with inertia at the mesoscale.
MECHANO-CHEMICAL SIMULATION OF SOLID TUMOR DYNAMICS FOR THERAPY OUTCOME PREDICTIONS
231-241
Sven
Hirsch
Department of Electrical Engineering, ETH, CH-8092 Zürich, Switzerland
Dominik
Szczerba
Computer Vision Laboratory, ETH; IT'IS Foundation, Switzerland
Bryn
Lloyd
Department of Electrical Engineering, ETH, CH-8092 Zürich, Switzerland
Michael
Bajka
Division of Gynecology, University Hospital of Zürich, Switzerland
Niels
Kuster
IT'IS Foundation, CH-8004 Zürich, Switzerland
Gabor
Szekely
Department of Electrical Engineering, ETH, CH-8092 Zürich, Switzerland
Experimental investigations of tumors often result in data reflecting very complex underlying mechanisms. Computer models of such phenomena enable their analysis and may lead to novel and more efficient therapy strategies. We present a generalized finite-element mechano-chemical model of a solid tumor and assess its suitability for predicting therapy outcome. The model includes hosting tissue, tumor cells (vital and necrotic), nutrient (oxygen), blood vessels, and a growth inhibitor. At a certain time instant of the tumor development virtual therapies are performed and their outcomes are presented. The model parameters are obtained either directly from the available literature or estimated using multi-scale modeling. First results indicate the usefulness of multi-physics tumor models for predicting therapy response. In the proposed model a regression of a manifest tumor after therapy may be observed.
A MULTILEVEL MULTISCALE MIMETIC (M3) METHOD FOR AN ANISOTROPIC INFILTRATION PROBLEM
243-256
David
Moulton
Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
Daniil
Svyatskiy
Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
Konstantin
Lipnikov
Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
Modeling of multiphase flow in highly heterogeneous porous media must capture a broad range of spatial and temporal
scales that are strongly influenced by the complex structure of the subsurface environment. However, the most popular
discretization methods are based on a two-point flux approximation that is only accurate for simple geometries, such
as orthogonal meshes with mesh-aligned diagonal tensor permeabilities. In more realistic situations, such as sloping
layers with anisotropic permeabilities, these methods may provide qualitatively plausible results, but with O(1) errors.
The family of mimetic finite-difference discretizations uses a mimetic approximation of the flux to provide a robust
and accurate discretization in these more complex geometries. In addition, the increasing use of large-scale models
with high-resolution realizations of parameter fields is driving the need for efficient multiscale methods. Typically, these
methods are based on two-level concepts that do not effectively capture the coupling of local and global information
critical to anisotropic features. To address these problems we have recently developed a new hierarchical approach, dubbed
the multilevel multiscale mimetic (M 3) method, which builds on the mimetic methodology. The M 3 method is locally
mass conserving at all levels in its hierarchy, it supports unstructured polygonal grids and full tensor permeabilities,
and it can achieve large coarsening factors. To highlight the advantages of the mimetic flux approximation, as well as
the flexibility and efficiency of the M 3 method, we consider water infiltration into a two-dimensional layered anisotropic
medium. The mesh is aligned with the sloping layers, not the coordinate axes. First, we present a comparison of the
water infiltration resulting from the two-point and mimetic flux approximations. Then, we demonstrate that with an
efficient temporal updating strategy for the coarsening parameters, fine-scale accuracy of prominent features in the flow
is maintained by the M 3 method.