Begell House
International Journal for Multiscale Computational Engineering
International Journal for Multiscale Computational Engineering
1543-1649
2
3
2004
Multiscale Modeling of Fatigue for Ductile Materials
A multiscale model is developed for fatigue-life predictions of elastoplastic solids and structures. The fatigue problem is formulated using a variant of the mathematical homogenization theory developed to account for almost-periodic fields. Multiple temporal scales are employed to resolve the solution within a load cycle as well as to predict the useful life span of a structural component. The concept of "almost periodicity" is introduced to account for irreversible inelastic deformation, which gives rise to nonperiodic fields in the time domain. By this approach, the original initial boundary value problem is decomposed into coupled microchronological (fast timescale) and macrochronological (slow timescale) problems. The proposed life prediction methodology was implemented in ABAQUS and verified against the direct cycle-by-cycle simulation.
Caglar
Oskay
Department of Civil and Environmental Engineering, Vanderbilt University, Nashville,
Tennessee 37235, USA
Jacob
Fish
Civil Engineering and Engineering Mechanics, Columbia University, New York, New York
10027, USA
25
Space-time Multiscale Laminated Theory
Multiscale computational techniques in space and time are developed to study the impact response of thin, elastic, laminated composites. The displacement field is approximated using asymptotic expansion in space and time. Using the homogenization procedure in space and time, nonlocal membrane and bending equations of motion are derived. The nonlocal equations are stabilized to filter out the higher frequency content. The multiscale model is verified for membrane and bending problems.
Ryan
Lund
New York State Department of Transportation
Jacob
Fish
Civil Engineering and Engineering Mechanics, Columbia University, New York, New York
10027, USA
21
Determination of the Material Intrinsic Length Scale of Gradient Plasticity Theory
The enhanced gradient plasticity theories formulate a constitutive framework on the continuum level that is used to bridge the gap between the micromechanical plasticity and the classical continuum plasticity. The later cannot predict the size effects since it does not posses an intrinsic length scale. To assess the size effects, it is indispensable to incorporate an intrinsic material length parameter l into the constitutive equations. However, the full utility of gradient-type theories hinges on one's ability to determine the constitutive length-scale parameter l that scales the gradient effects. Thus, the definition and magnitude of the intrinsic length scale are keys to the development of the new theory of plasticity that incorporates size effects. The classical continuum plasticity is also unable to predict properly the evolution of the material flow stress since the local deformation gradients at a given material point are not accounted for. The gradient-based flow stress is commonly assumed to rely on a mixed type of dislocations: those that are initially randomly or statistically distributed, which are referred to as statistically stored dislocations (SSDs), and those formed to account for the additional strengthening mechanism associated with the deformation gradients, which are referred to as geometrically necessary dislocations (GNDs). In this work two micromechanical models to assess the coupling between SSDs and GNDs are discussed. One in which the SSDs and GNDs are simply summed (model-I) and one in which, implicitly, their accompanying strength are added (model-II). These two dislocation interaction models, which are based on Taylor's hardening law, are then used to identify the deformation-gradient-related intrinsic length-scale parameter l in terms of measurable microstructural physical parameters. The paper also presents a method for identifying the material intrinsic length parameter l from micro hardness results obtained by conical or pyramidal indenters.
Rashid K. Abu
Al-Rub
Department of Civil Engineering, Catholic University of America, Washington, DC 20064, USA
George
Voyiadjis
Louisiana State University
24
Composite Grid Atomistic Continuum Method: An Adaptive Approach to Bridge Continuum with Atomistic Analysis
The Composite Grid Atomistic Continuum Method, a method to couple continuum and atomistic models, is proposed in a three-dimensional setting. In this method, atomistic analysis is used only at places where it is needed in order to capture the intrinsically nonlinear/nonlocal behavior of the material at the atomic scale, while continuum analysis is used elsewhere for efficiency. The atomistic model is defined on a separate grid that overlaps the continuum in selected regions. The atomistic and the smallest scale continuum model are connected by appropriately defined operators. The continuum model provides boundary conditions to the discrete model while the atomistic model returns correcting eigenstrains. The adaptive selection of the spatial regions where the atomistic correction is needed is made based on error indicators developed to capture the nonlinearity and nonlocality modeling errors. The method is applied to represent dislocation nucleation from crack tips and nanoindentation in aluminum.
Mark S.
Shephard
Rensselaer Polytechnic Institute
Catalin
Picu
Rensselaer Polytechnic Institute
D. K.
Datta
Scientific Computation Research Center, RPI, Troy, NY 12180-3590
19
Multilevel Parallel Programming for Multiscale Modeling of Composite Materials
This paper presents work aimed at implementing an efficient multilevel parallel model for an adaptive multiscale finite element model. The FEM model combines a traditional displacement based finite element model with a microstructural Voronoi cell finite element method (VCFEM) for multiscale modeling of heterogeneous microstructures with nonuniform microstructural heterogeneities. Three levels of hierarchy are used in the model, including (a) level-0 of pure macroscopic analysis; (b) level-1 of macro-micro coupling, used for signaling the switch over from macroscopic analyses to pure microscopic analyses; and (c) level-2 regions of pure microscopic modeling. A distributed/shared memory (DSM) cluster system is used for code development and execution, where multiprocessor nodes offer shared memory on the node and distributed memory between the nodes. The approach uses multiple parallel models to efficiently distribute the level-1 and level-2 workloads across multiple workstations based on computational requirements. The Message Passing Interface (MPI) library is used for distributed memory decomposition between nodes, and multithreading using the OpenMP (OMP) library is used for shared memory decomposition on each node. An efficient iterative multigrid solver is also integrated. The details of these implementations are discussed and numerical results, which demonstrate the ability of the parallel model to solve problems in a fast and efficient manner, are provided.
Paul M.
Eder
Department of Mechanical Engineering, Ohio State University, Columbus, Ohio 43210
James E.
Giuliani
Science and Technology Support Group, The Ohio Supercomputer Center 1224 Kinnear Rd., Columbus, Ohio, 43210
Somnath
Ghosh
Department of Civil Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA
23
A Non Split Projection Strategy for Low Mach Number Flows
In the context of the direct numerical simulation of low Mach number reacting flows, the aim of this article is to propose a new approach based on the integration of the original differential-algebraic equation (DAE) system of governing equations, without further differentiation. In order to do so while preserving a possibility of easy parallelization, it is proposed to use a one-step index 2 DAE time integrator, the Half Explicit Method (HEM). In this context, we recall why the low Mach number approximation belongs to the class of index 2 DAEs and discuss why the pressure can be associated with the constraint. We then focus on a fourth-order HEM scheme and provide a formulation that makes its implementation more convenient. Practical details about the consistency of initial conditions are discussed prior to focusing on the implicit solve involved in the method. The method is then evaluated using the Modified Kaps Problem, since it has some of the features of the low Mach number approximation. Numerical results are presented, confirming the validity of the strategy. A brief summary of ongoing efforts is finally provided.
P.P.
Pebay
Sandia National Laboratories P.O. Box 969, M.S. 9051, Livermore, CA 94451
Habib N.
Najm
Sandia National Laboratories, Livermore, CA, 94551
J. G.
Pousin
National Institute for Applied Sciences, MAPLY U.M.R. CNRS 5585, Leonard de Vinci, 69621 Villeurbanne cedex, France
16
Multiscale Modeling for Micropolar Flow in a Structure with One Bundle of Tubes
The asymptotic analysis of a micropolar flow through a wavy tube structure is studied. We suppose that the domain depends on a small parameter that represents the width and the order of the periodicity of the domain. The Stokes and Navier-Stokes problems in the union of tubes (with a constant section) were earlier studied. The generalization of the Method of Asymptotic Partial Decomposition of Domain in a structure with some periodic tubes is described and justified in order to propose a simplified modeling for the bloodstream.
R.
Stavre
Institute of Mathematics "Simion Stoilow", Romanian Academy, P.O. Box 1-764 RO-70700 Bucharest, Romania
D.
Dupuy
Equipe d'Analyse Numerique, UPRES EA 3058, Universite de Saint-Etienne, 23, rue Paul Michelon, 42 023 Saint-Etienne Cedex 2, France
Gregory P.
Panasenko
ICJ UMR CNRS 5208, University of Lyon, 23, rue P. Michelon, 42023, Saint Etienne, France
15
Subsonic Lamb Waves in Anisotropic Plates
A six-dimensional complex formalism for analysis of Lamb waves propagating with subsonic speed in anisotropic plates is formulated. Conditions for nonexistence of certain Lamb waves in anisotropic plates are obtained. An example of transversely isotropic plate having "forbidden" speed at which no subsonic Lamb wave propagates is presented.
Sergey
Kuznetsov
Institute for Problems in Mechanics
10
Finite Element Modeling of a Coupled Thermo-Hydro-Mechanical Process in Porous Media
This article concerns finite element modeling of a coupled thermo-hydro-mechanical process in porous media. In the article, governing differential equations for such a coupled problem of multiphases are reviewed, and a fully coupled semi-discrete finite element formulation is derived in a three-dimensional setting. Based on the fully coupled formulation, sequential partitioned finite element analysis procedures are studied for situations when the coupling effects are relatively small and approximations can be made to decouple the phase interaction. Thereafter, material modeling of mechanical behavior is studied in the framework of viscoplasticity, and a heuristic approach to modeling the thermal effect in a viscoplastic solid is discussed in terms of pressure-sensitive (for instance, Ducker—Prager and Mohr—Coulomb) yield surfaces. The coupled finite modeling technique has currently been applied in two important areas: the geological disposal of nuclear wastes and highway engineering (or road mechanics), and in this article we demonstrate such an industrial application with a numerical example.
Lingfu
Zeng
AF Energy and Environment Ltd., SE-40515 Goteborg, Sweden
Nils-Erik
Wiberg
Department of Structural Mechanics, Chalmers University of Technology, S-41296 Goteborg, Sweden
18