Applications of Multiple Scaling in Mechanics PDF Download

Author: Philippe G. Ciarlet
Publisher: Elsevier Masson
ISBN:
Category : Continuum mechanics
Languages : en
Pages : 368

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Author: Moubin E. T. Al LIU
Publisher: World Scientific
ISBN: 9814571709
Category : Science
Languages : en
Pages : 400

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Book Description
Multi-scale and multi-physics modeling is useful and important for all areas in engineering and sciences. Particle Methods for Multi-Scale and Multi-Physics systematically addresses some major particle methods for modeling multi-scale and multi-physical problems in engineering and sciences. It contains different particle methods from atomistic scales to continuum scales, with emphasis on molecular dynamics (MD), dissipative particle dynamics (DPD) and smoothed particle hydrodynamics (SPH). This book covers the theoretical background, numerical techniques and many interesting applications of the particle methods discussed in this text, especially in: micro-fluidics and bio-fluidics (e.g., micro drop dynamics, movement and suspension of macro-molecules, cell deformation and migration); environmental and geophysical flows (e.g., saturated and unsaturated flows in porous media and fractures); and free surface flows with possible interacting solid objects (e.g., wave impact, liquid sloshing, water entry and exit, oil spill and boom movement). The presented methodologies, techniques and example applications will benefit students, researchers and professionals in computational engineering and sciences --

Author: J.K. Kevorkian
Publisher: Springer Science & Business Media
ISBN: 1461239680
Category : Mathematics
Languages : en
Pages : 642

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Book Description
This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer Verlag, 1981). We present the material at a level that assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate-level course on the subject. Perturbation methods, first used by astronomers to predict the effects of small disturbances on the nominal motions of celestial bodies, have now become widely used analytical tools in virtually all branches of science. A problem lends itself to perturbation analysis if it is "close" to a simpler problem that can be solved exactly. Typically, this closeness is measured by the occurrence of a small dimensionless parameter, E, in the governing system (consisting of differential equations and boundary conditions) so that for E = 0 the resulting system is exactly solvable. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of E. In a regular perturbation problem, a straightforward procedure leads to a system of differential equations and boundary conditions for each term in the asymptotic expansion. This system can be solved recursively, and the accuracy of the result improves as E gets smaller, for all values of the independent variables throughout the domain of interest. We discuss regular perturbation problems in the first chapter.

Author: Francois Nicot
Publisher: Elsevier
ISBN: 0081025963
Category : Technology & Engineering
Languages : en
Pages : 388

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Book Description
Advances in Multi-Physics and Multi-Scale Couplings in Geo-Environmental Mechanics reunites some of the most recent work from the French research group MeGe GDR (National Research Group on Multiscale and Multiphysics Couplings in Geo-Environmental Mechanics) on the theme of multi-scale and multi-physics modeling of geomaterials, with a special focus on micromechanical aspects. Its offers readers a glimpse into the current state of scientific knowledge in the field, together with the most up-to-date tools and methods of analysis available. Each chapter represents a study with a different viewpoint, alternating between phenomenological/micro-mechanically enriched and purely micromechanical approaches. Throughout the book, contributing authors will highlight advances in geomaterials modeling, while also pointing out practical implications for engineers. Topics discussed include multi-scale modeling of cohesive-less geomaterials, including multi-physical processes, but also the effects of particle breakage, large deformations on the response of the material at the specimen scale and concrete materials, together with clays as cohesive geomaterials. The book concludes by looking at some engineering problems involving larger scales. - Identifies contributions in the field of geomechanics - Focuses on multi-scale linkages at small scales - Presents numerical simulations by discrete elements and tools of homogenization or change of scale

Author: Wim Van Paepegem
Publisher: Woodhead Publishing
ISBN: 0128189851
Category : Technology & Engineering
Languages : en
Pages : 766

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Book Description
Multi-scale modelling of composites is a very relevant topic in composites science. This is illustrated by the numerous sessions in the recent European and International Conferences on Composite Materials, but also by the fast developments in multi-scale modelling software tools, developed by large industrial players such as Siemens (Virtual Material Characterization toolkit and MultiMechanics virtual testing software), MSC/e-Xstream (Digimat software), Simulia (micromechanics plug-in in Abaqus), HyperSizer (Multi-scale design of composites), Altair (Altair Multiscale Designer) This book is intended to be an ideal reference on the latest advances in multi-scale modelling of fibre-reinforced polymer composites, that is accessible for both (young) researchers and end users of modelling software. We target three main groups: This book aims at a complete introduction and overview of the state-of-the-art in multi-scale modelling of composites in three axes: • ranging from prediction of homogenized elastic properties to nonlinear material behaviour • ranging from geometrical models for random packing of unidirectional fibres over meso-scale geometries for textile composites to orientation tensors for short fibre composites • ranging from damage modelling of unidirectionally reinforced composites over textile composites to short fibre-reinforced composites The book covers the three most important scales in multi-scale modelling of composites: (i) micro-scale, (ii) meso-scale and (iii) macro-scale. The nano-scale and related atomistic and molecular modelling approaches are deliberately excluded, since the book wants to focus on continuum mechanics and there are already a lot of dedicated books about polymer nanocomposites. A strong focus is put on physics-based damage modelling, in the sense that the chapters devote attention to modelling the different damage mechanisms (matrix cracking, fibre/matrix debonding, delamination, fibre fracture,...) in such a way that the underlying physics of the initiation and growth of these damage modes is respected. The book also gives room to not only discuss the finite element based approaches for multi-scale modelling, but also much faster methods that are popular in industrial software, such as Mean Field Homogenization methods (based on Mori-Tanaka and Eshelby solutions) and variational methods (shear lag theory and more advanced theories). Since the book targets a wide audience, the focus is put on the most common numerical approaches that are used in multi-scale modelling. Very specialized numerical methods like peridynamics modelling, Material Point Method, eXtended Finite Element Method (XFEM), isogeometric analysis, SPH (Smoothed Particle Hydrodynamics),... are excluded. Outline of the book The book is divided in three large parts, well balanced with each a similar number of chapters:

Author: Changjun Hu
Publisher: Springer Nature
ISBN: 9813299878
Category : Computers
Languages : en
Pages : 254

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Book Description
This book constitutes the referred proceedings of two workshops held at the 32nd ACM International Conference on Supercomputing, ACM ICS 2018, in Beijing, China, in June 2018. This volume presents the papers that have been accepted for the following workshops: Second International Workshop on High Performance Computing for Advanced Modeling and Simulation in Nuclear Energy and Environmental Science, HPCMS 2018, and First International Workshop on HPC Supported Data Analytics for Edge Computing, HiDEC 2018. The 20 full papers presented during HPCMS 2018 and HiDEC 2018 were carefully reviewed and selected from numerous submissions. The papers reflect such topics as computing methodologies; parallel algorithms; simulation types and techniques; machine learning.

Author: K.J Bathe
Publisher: Elsevier
ISBN: 008052947X
Category : Technology & Engineering
Languages : en
Pages : 2485

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Book Description
Bringing together the world's leading researchers and practitioners of computational mechanics, these new volumes meet and build on the eight key challenges for research and development in computational mechanics.Researchers have recently identified eight critical research tasks facing the field of computational mechanics. These tasks have come about because it appears possible to reach a new level of mathematical modelling and numerical solution that will lead to a much deeper understanding of nature and to great improvements in engineering design.The eight tasks are: - The automatic solution of mathematical models - Effective numerical schemes for fluid flows - The development of an effective mesh-free numerical solution method - The development of numerical procedures for multiphysics problems - The development of numerical procedures for multiscale problems - The modelling of uncertainties - The analysis of complete life cycles of systems - Education - teaching sound engineering and scientific judgement Readers of Computational Fluid and Solid Mechanics 2003 will be able to apply the combined experience of many of the world's leading researchers to their own research needs. Those in academic environments will gain a better insight into the needs and constraints of the industries they are involved with; those in industry will gain a competitive advantage by gaining insight into the cutting edge research being carried out by colleagues in academia. Features - Bridges the gap between academic researchers and practitioners in industry - Outlines the eight main challenges facing Research and Design in Computational mechanics and offers new insights into the shifting the research agenda - Provides a vision of how strong, basic and exciting education at university can be harmonized with life-long learning to obtain maximum value from the new powerful tools of analysis

Author: Irina Kalashnikova
Publisher: Stanford University
ISBN:
Category :
Languages : en
Pages : 178

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Book Description
A discontinuous enrichment method (DEM) for the efficient finite element solution of advection-dominated transport problems in fluid mechanics whose solutions are known to possess multi-scale features is developed. Attention is focused specifically on the two-dimensional (2D) advection-diffusion equation, the usual scalar model for the Navier-Stokes equations. Following the basic DEM methodology [1], the usual Galerkin polynomial approximation is locally enriched by the free-space solutions to the governing homogeneous partial differential equation (PDE). For the constant-coefficient advection-diffusion equation, several families of free-space solutions are derived. These include a family of exponential functions that exhibit a steep gradient in some flow direction, and a family of discontinuous polynomials. A parametrization of the former class of functions with respect to an angle parameter is developed, so as to enable the systematic design and implementation of DEM elements of arbitrary orders. It is shown that the original constant-coefficient methodology has a natural extension to variable-coefficient advection-diffusion problems. For variable-coefficient transport problems, the approximation properties of DEM can be improved by augmenting locally the enrichment space with a "higher-order" enrichment function that solves the governing PDE with the advection field a(x) linearized to second order. A space of Lagrange multipliers, introduced at the element interfaces to enforce a weak continuity of the solution and related to the normal derivatives of the enrichment functions, is developed. The construction of several low and higher-order DEM elements fitting this paradigm is discussed in detail. Numerical results for several constant as well as variable-coefficient advection-diffusion benchmark problems reveal that these DEM elements outperform their standard Galerkin and stabilized Galerkin counterparts of comparable computational complexity by a large margin, especially when the flow is advection-dominated.

Author: Xingjie Peng
Publisher: Frontiers Media SA
ISBN: 2832545378
Category : Technology & Engineering
Languages : en
Pages : 105

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Book Description
A nuclear reactor operates in an environment where complex multi-physics and multi-scale phenomena exist, and it requires consideration of coupling among neutronics, thermal hydraulics, fuel performance, chemical dynamics, and coupling between the reactor core and first circuit. Safe, reliable, and economical operation can be achieved by leveraging high-fidelity numerical simulation, and proper considerations for coupling among different physics and required to provide powerful numerical simulation tools. In the past simplistic models for some of the physics phenomena are used, with the recent development of advanced numerical methods, software design, and high-performance computing power, the appeal of multi-physics and multi-scale modeling and simulation has been broadened.

Author: Mohamed Jebahi
Publisher: John Wiley & Sons
ISBN: 1848217714
Category : Technology & Engineering
Languages : en
Pages : 216

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Book Description
Complex behavior models (plasticity, crack, visco-elascticity) are facing several theoretical difficulties in determining the behavior law at the continuous (macroscopic) scale. When homogenization fails to give the right behavior law, a solution is to simulate the material at a mesoscale using the discrete element model (DEM) in order to directly simulate a set of discrete properties that are responsible for the macroscopic behavior. Originally, the discrete element model was developed for granular material. This book, the second in the Discrete Element Model and Simulation of Continuous Materials Behavior set of books, shows how to choose the adequate coupling parameters to avoid spurious wave reflection and to allow the passage of all the dynamic information both from the fine to the coarse model and vice versa. The authors demonstrate the coupling method to simulate a highly nonlinear dynamical problem: the laser shock processing of silica glass.