Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
9
4
2011
PrefaceSPECIAL ISSUEMULTISCALE MODELING AND UNCERTAINTY QUANTIFICATION OF HETEROGENEOUS MATERIALS
vii-viii
10.1615/IntJMultCompEng.v9.i4.10
George
Stefanou
Aristotle University of Thessaloniki
The papers for this special issue are included in Volume 9, Issues 3 and 4, 2011 of International Journal for Multiscale Computational Engineering and will focus on multiscale modeling and uncertainty quantification of heterogeneous materials. Particular emphasis is given to advanced computational methods which can greatly assist in tackling complex problems of multiscale stochastic material modeling. The papers can be grouped into several thematic topics that include homogenization and computation of effective elastic properties of random composites, development of computational models for large-scale heterogeneous microstructures, stochastic analysis and design of heterogeneous materials, and multiscale models for the simulation of fracture mechanisms in polycrystalline materials.
The first part which is published in Volume 9, Issue 3 includes the following articles.
Homogenization of Fiber-Reinforced Composites with Random Properties Using the Least-Squares Response Function Approach, M. Kaminski
Large-Scale Computations of Effective Elastic Properties of Rubber with Carbon Black, Fillers, A. Jean, F. Willot, S. Cantournet, S. Forest, and D. Jeulin
Elastic and Electrical Behavior of Some Random Multiscale Highly-Contrasted Composites, F. Willot and D. Jeulin
Overall Elastic Properties of Polysilicon Films: A Statistical Investigation of the Effects of Polycrystal Morphology, S. Mariani, R. Martini, A. Ghisi, A. Corigliano, and M. Beghi
Variational Formulation on Effective Elastic Moduli of Randomly Cracked Solids, X. F. Xu and G. Stefanou
The second part of the special issue consists of eight papers dealing with the development of computational models for large-scale heterogeneous microstructures, the stochastic analysis and design of heterogeneous materials, and multiscale models for the simulation of fracture mechanisms in poly-crystalline materials.
HYBRID COMPUTING MODELS FOR LARGE-SCALE HETEROGENEOUS 3D MICROSTRUCTURES
365-377
10.1615/IntJMultCompEng.v9.i4.20
Kai
Schrader
Bauhaus-Universität Weimar, Institute of Structural Mechanics, D-99423 Weimar, Germany
Carsten
Konke
Bauhaus-Universität Weimar, Institute of Structural Mechanics, Germany
microscale continuum modeling
heterogeneous 3D elasticity problems
domaindecomposition
preconditioning
distributed computing
In recent years design and assessment of engineering structures are done in numerical simulation environments, applying state-of-the-art models from CAD, computational mechanics and visual analytics. Over the last two decades there has been a strong trend toward integration of theoretical and numerical models from material science on different scales up to the atomic lattice into simulation models for engineering applications, by applying multiscale models in combination with homogenization techniques or concurrent multiscale models. Especially for investigating new and heterogeneous materials, multiscale models can be applied to study material physics, such as damage initiation and propagation, on appropriate scales and integrate this information into large-scale engineering models. A major drawback of multiscale models in materials science is their enormous demand for computing power with respect to computing time and main memory. This paper suggests a method to split a heterogeneous material model, consisting of a matrix material and embedded inclusions with interfacial transition zones, into zones of elastic and inelastic behavior and to customize the discretization methods for these two zones in an appropriate way. We propose the application of structured and unstructured meshes in a hybrid fashion and to solve the resulting equation systems with several million degrees of freedom by iterative solver techniques. In order to consider the damage evolution behavior, a regularized anisotropic damage model is used and the incremental-iterative solution for this problem is based on sequential linear analysis, following the sawtooth concept of Rots et al. (2006).
STOCHASTIC ANALYSIS OF ONE-DIMENSIONAL HETEROGENEOUS SOLIDS WITH LONG-RANGE INTERACTIONS
379-394
10.1615/IntJMultCompEng.v9.i4.30
Alba
Sofi
Dipartimento Patrimonio Architettonico ed Urbanistico, University Mediterranea di Reggio Calabria, Italy
Mario
Di Paola
Dipartimento di Ingegneria Strutturale, Aerospaziale e Geotecnica, Università degli Studi di Palermo, Viale delle Scienze, I-90128, Palermo, Italy
Massimiliano
Zingales
Dipartimento di Ingegneria Strutturale, Aerospaziale e Geotecnica, Università degli Studi di Palermo, Italy
nonlocal elasticity
long-range interactions
random mass density field
response statistics
Random mass distribution in one-dimensional (1D) elastic solids in the presence of long-range interactions is studied in this paper. Besides the local Cauchy contact forces among adjacent elements, long-range forces depending on the product of interacting masses, as well as on their relative displacements, are considered. In this context, the random fluctuations of the mass distribution involve a stochastic model of the nonlocal interactions, and the random displacement field of the body is provided as the solution of a stochastic integro-differential equation. The presence of the random field of mass distribution is reflected in the random kernel of the solving integro-differential equation with deterministic static and kinematic boundary conditions, since the long-range interactions have no effects at the borders. Numerical applications are reported to highlight the effects of fluctuations of the mass field along the body on the long-range forces and the mechanical response of the 1D elastic body considered.
PERTURBATION-BASED STOCHASTIC MICROSCOPIC STRESS ANALYSIS OF A PARTICLE-REINFORCED COMPOSITE MATERIAL VIA STOCHASTIC HOMOGENIZATION ANALYSIS CONSIDERING UNCERTAINTY IN MATERIAL PROPERTIES
395-408
10.1615/IntJMultCompEng.v9.i4.40
Sei-ichiro
Sakata
Department of Electronic and Control Systems Engineering, Interdisciplinary Faculty of Science and Engineering, Shimane University, Japan
F.
Ashida
Department of Electronic and Control Systems Engineering, Interdisciplinary Faculty of Science and Engineering, Shimane University, Japan
K.
Enya
Graduate School of Shimane University, Japan
stochastic microscopic stress analysis
stochastic homogenization
perturbation
multiscaleanalysis
particle-reinforced composites
This paper discusses stochastic multiscale stress analysis of a particle-reinforced composite material via the stochastic homogenization analysis. A microscopic random variation causes a random variation of a homogenized property and microscopic stress. For this stochastic stress analysis, a first-order perturbation-based approach is employed. The perturbation-based approach consists of stochastic homogenization, stochastic macroscopic, and microscopic stress analysis procedures. As an example, stochastic microscopic stress analysis for a microscopic random variation of a glass particle-reinforced composite material using the perturbation-based technique is performed. The obtained results are compared with the results of the Monte Carlo simulation; validity and application limit of the first-order perturbation-based approach is investigated.
INVERSE STOCHASTIC HOMOGENIZATION ANALYSIS FOR A PARTICLE-REINFORCED COMPOSITE MATERIAL WITH THE MONTE CARLO SIMULATION
409-423
10.1615/IntJMultCompEng.v9.i4.50
Sei-ichiro
Sakata
Department of Electronic and Control Systems Engineering, Interdisciplinary Faculty of Science and Engineering, Shimane University, Japan
F.
Ashida
Department of Electronic and Control Systems Engineering, Interdisciplinary Faculty of Science and Engineering, Shimane University, Japan
Y.
Shimizu
Graduate School of Shimane University, Japan
inverse stochastic homogenization
stochastic homogenization
homogenization problem
optimization
composite material
This paper proposes a numerical method for identifying microscopic randomness in an elastic property of a component material of a particle-reinforced composite material. Some reports on the stochastic homogenization analysis considering a microscopic random variation can be found in the literature. A microscopic stress field is influenced by the microscopic variation, and stochastic microscopic stress analysis is also important. In the previous reports it is assumed that the microscopic random variation is known. However, it is sometimes difficult to identify a microscopic random variation in a composite material, especially after the manufacturing process. Therefore, an identification process for microscopic randomness by solving an inverse problem is needed for the stochastic microscopic stress analysis. This kind of problem is called "inverse stochastic homogenization." In this paper solving an inverse stochastic homogenization problem is attempted with inverse homogenization analysis and Monte Carlo simulation is used for the stochastic homogenization analysis. The inverse homogenization analysis is performed with the homogenization method and an optimization technique. Some techniques for the inverse stochastic homogenization analysis with the Monte Carlo simulation are developed. With numerical results, validity and accuracy of the methods are discussed.
STOCHASTIC DESIGN AND CONTROL IN RANDOM HETEROGENEOUS MATERIALS
425-443
10.1615/IntJMultCompEng.v9.i4.60
Raphael
Sternfels
School of Civil and Environmental Engineering, 372 Hollister Hall, Cornell University, Ithaca, New York 14853, USA
Phaedon-Stelios
Koutsourelakis
Continuum Mechanics Group, Technical University of Munich, Boltzmannstrasse 15, 85748
Garching, Germany
uncertainty quantification
sequential Monte Carlo
random heterogenous materials
topology optimization
This paper discusses a sampling framework that enables optimization of complex systems characterized by high-dimensional uncertainties and design variables. We are especially concerned with problems relating to random heterogeneous materials where uncertainties arise from the stochastic variability of their properties. In particular, we reformulate topology optimization problems to account for the design of truly random composites. In addition, we address the optimal prescription of input loads/excitations in order to achieve a target response by the random material system. The methodological advances proposed in this paper consist of an adaptive sequential Monte Carlo scheme that economizes the number of runs of the forward solver and allows the analyst to identify several local maxima that provide important information with regard to the robustness of the design. We further propose a principled manner of introducing information from approximate models that can ultimately lead to further reductions in computational cost.
IDENTIFICATION AND PROBABILISTIC MODELING OF MESOCRACK INITIATIONS IN 304L STAINLESS STEEL
445-458
10.1615/IntJMultCompEng.v9.i4.70
J.
Rupil
CEA Saclay, DEN-DANS/DMN/SRMA/LC2M; and LMT Cachan, ENS Cachan/CNRS/UPMC/PRES UniverSud Paris, France
L.
Vincent
CEA Saclay, DEN-DANS/DMN/SRMA/LC2M, F-91191 Gif sur Yvette Cedex, France
F.
Hild
LMT Cachan, ENS Cachan/CNRS/UPMC/PRES UniverSud Paris, France
Stephane
Roux
LMT Cachan, ENS Cachan/CNRS/UPMC/PRES UniverSud Paris; and Laboratoire d'Etudes Aérodynamique (LEA), Université de Poitiers, ENSMA, CNRS, France
crack initiation
digital image correlation
identification
mechanical fatigue
poisson pointprocess
A probabilistic model is proposed to simulate the growth of fatigue damage in an austenitic stainless steel at a mesoscopic scale. Several fatigue mechanical tests were performed to detect and quantify mesocrack initiations for different loadings by using digital image correlation. The number of initiated mesocracks is experimentally determined. The process is then described by a Poisson point process. The intensity of the process is evaluated by using a multiscale approach based on a probabilistic crack initiation law in a typical grain.
STOCHASTIC PROCESSES OF {1012} DEFORMATION TWINNING IN HEXAGONAL CLOSE-PACKED POLYCRYSTALLINE ZIRCONIUM AND MAGNESIUM
459-480
10.1615/IntJMultCompEng.v9.i4.80
Irene J.
Beyerlein
Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico, 87545, USA
R. J.
McCabe
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
C. N.
Tome
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
hcp
statistics
probability
twinning
magnesium
zirconium
EBSD
Deformation twinning is an important mechanism for metals with hexagonal close-packed (hcp) crystal structures such as titanium, magnesium, beryllium, and zirconium, as well as metals with other low-symmetry crystal structures. This article presents a multiscale constitutive model for the plastic deformation of hcp polycrystalline metals that is built upon the viscoplastic self-consistent (VPSC) polycrystal scheme. This framework includes a novel probabilistic model for predicting when, where, and which variants nucleate, a dislocation density model for crystallographic slip, and a micromechanical model for twin lamella thickening and twin reorientation. Length scales of an individual slip or twinning system and the polycrystalline aggregate are interactively connected. Here, this constitutive model is applied to high-purity magnesium (Mg) and zirconium (Zr) deformed under loading conditions where twinning is intense. Correlations are made between the formation of deformation twins, bulk stress-strain behavior and texture development, and individual grain properties such as size and crystallographic orientation.
COUPLED COHESIVE ZONE REPRESENTATIONS FROM 3D QUASICONTINUUM SIMULATION ON BRITTLE GRAIN BOUNDARIES
481-501
10.1615/IntJMultCompEng.v9.i4.90
Torsten
Luther
Institute of Structural Mechanics, Bauhaus University Weimar , Germany
Carsten
Konke
Bauhaus-Universität Weimar, Institute of Structural Mechanics, Germany
hierarchical multiscale concept
intergranular fracture
traction separation law
nonlocalquasicontinuum method
This paper contributes to a hierarchical multiscale concept for the simulation of brittle intergranular fracture in polycrystalline materials, for example, aluminum. Intended is the numerical investigation of physical fracture phenomena on an atomistic microscale and the integration of resulting parameters into damage models on the engineering continuum scale. A procedure for computational intergranular fracture analysis on the atomistic scale is presented, and the transition to coupled cohesive zone representations of continuum models is explained. The brittle intergranular fracture process on the atomistic scale is investigated in three dimensions, applying a parallelized nonlocal quasicontinuum method, which was implemented for the robust and efficient analysis of grain boundary fracture in polycrystalline metals with arbitrary misorientation. The nonlocal quasicontinuum method fully describes the material behavior by atomistic potential functions but reduces the number of atomic degrees of freedom by introducing kinematic couplings in regions of a smooth deformation field. Interface separation laws are obtained from tensile and shear simulations on the atomistic scale, and extracted cohesive parameters are used for parameterization of traction separation laws, which are part of coupled cohesive zone models, to simulate the brittle interface decohesion in heterogeneous polycrystal structures.