Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
4
4
2006
Applications of s-FEM to the Problems of Composite Materials with Initial Strain-Like Terms
411-428
Satoyuki
Tanaka
Department of Nano-structure and Advanced Materials, Graduate School of Science and Engineering, Kagoshima University, 1-21-40 Korimoto, Kagoshima 890-0065, Japan
Hiroshi
Okada
Department of Nano-structure and Advanced Materials, Graduate School of Science and Engineering, Kagoshima University, 1-21-40 Korimoto, Kagoshima 890-0065, Japan
Yoshimi
Watanabe
Department of Engineering Physics, Electronics and Mechanics, Graduate School of Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan
Teppei
Wakatsuki
Department of Engineering Physics, Electronics and Mechanics, Graduate School of Engineering, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan
In this paper, the applications of s-FEM that involve initial strain-like terms are presented. When s-FEM is applied to the analyses of composite materials, the overall structure or the region of unit cell is modeled by a global finite element model and each reinforcing particle/fiber and its immediate vicinity are modeled by a local finite element model. Many local finite element models are placed in the analysis region and they are allowed to overlap each other. When the particles/fibers are the same in their shapes, the same local finite element models can be placed repeatedly. Therefore, generating an analysis model that has many particles/fibers is a simple task. Modifying their distributions is even more trivial. The s-FEM formulation is extended so that it can incorporate with the initial strain-like terms first. The formulations for the analyses of residual stress and of elasto-viscoplastic problems are presented. Numerical procedures to form stiffness matrices and how to choose material and strain history data when finite elements overlap each other are then discussed. We solved the problems of wavy shape memory alloy fiber/plaster composite material and of particulate composite material whose matrix material experiences an elasto-viscoplastic deformation.
Multiscale Modeling for Planar Lattice Microstructures with Structural Elements
429-444
Isao
Saiki
Department of civil Engineering, Tohoku University, Sendai 980-8579, Japan
Ken
Ooue
Kawada Construction Co., Ltd, Tokyo 114-8505, Japan
Kenjiro
Terada
Department of civil Engineering, Tohoku University, Sendai 980-8579, Japan
Akinori
Nakajima
Department of Civil Engineering, Utsunomiya University, Utsunomiya 321-8585, Japan
Formulations of linear and nonlinear multiscale analyses for media with lattice periodic microstructures based on the homogenization theory are proposed. For continuum media, the conventional homogenization theory leads to boundary value problems of continuum for both micro- and macroscales. However, it is rational to discretize lattice microstructures, such as cellular solids, by frame elements since they consist of slender members. The main difficulty in utilizing structural elements, such as frame elements, for microscale problems is due to the inconsistency between the kinematics assumed for the frame elements and the periodic displacement field for the microscale problem. In order to overcome this difficulty, we propose a formulation that does not employ the periodic microscale displacement, but the total displacement, including the displacement due to uniform deformation as well as periodic deformation, as the independent variable of the microscale problem. Some numerical examples of cellular solids are provided to show both the feasibility and the computational efficiency of the proposed method.
Effects of Shape and Size of Crystal Grains on the Strengths of Polycrystalline Metals
445-460
Kenjiro
Terada
Department of civil Engineering, Tohoku University, Sendai 980-8579, Japan
Ikumu
Watanabe
Department of Civil Engineering, Tohoku University, Aza-Aoba 6-6-06, Aramaki, Aoba-ku, Sendai, Miyagi 980-8579, Japan
Masayoshi
Akiyama
Corporate R&D Laboratories, Sumitomo Metal Industries Ltd., Fuso-cho 1-8, Amagasaki, Hyogo 660-0891, Japan
We investigate the effects of shape and size of crystal grains on the yielding behavior of polycrystalline metals by applying the two-scale finite element method, which is based on the homogenization theory combined with the constitutive models in crystal plasticity. After introducing the formulation of crystal-plasticity-based two-scale modeling, we characterize the mechanical behavior of a single crystal grain. Then, we first examine the effect of grain shape on macroscopic strengths by carrying out numerical experiments on several patterns of grain shapes and inhomogeneities of grain size distribution. Next, we explore the dependency of the various macroscopic strengths on the grain size, which are evaluated as the average behavior of aggregate representative volume elements (RVEs) or microstructures. We are here concerned with the empirical Hall-Petch relationship and intend to assess its possible sources for it apart from intergranular deformations.
Three-Dimensional Finite Element Modeling for Concrete Materials Using Digital Image and Embedded Discontinuous Element
461-474
Gakuji
Nagai
Gifu University
Takahiro
Yamada
Graduate School of Environment and Information Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
A three-dimensional finite element modeling is proposed to simulate mechanical behaviors of concrete materials subjected to macroscopic loadings. Concrete materials are modeled as two-phase composites consisting of coarse aggregates, mortar, and their interfaces in order to consider tensile failures. Digital image processing techniques are employed for finite element modeling, and a mixed formulation based on the assumed enhanced strain method is employed to model the interfacial discontinuities in a voxel finite element. Numerical comparisons between a real concrete model and two imitative models are made.
Iterative Algorithms for Computing the Averaged Response of Nonlinear Composites under Stress-Controlled Loadings
475-486
Takahiro
Yamada
Graduate School of Environment and Information Sciences, Yokohama National University, 79-7 Tokiwadai, Hodogaya-ku, Yokohama 240-8501, Japan
Formulations of linear and nonlinear multiscale analyses for media with lattice periodic microstructures based on the homogenization theory are proposed. For continuum media, the conventional homogenization theory leads to boundary value problems of continuum for both micro- and macroscales. However, it is rational to discretize lattice microstructures, such as cellular solids, by frame elements since they consist of slender members. The main difficulty in utilizing structural elements, such as frame elements, for microscale problems is due to the inconsistency between the kinematics assumed for the frame elements and the periodic displacement field for the microscale problem. In order to overcome this difficulty, we propose a formulation that does not employ the periodic microscale displacement, but the total displacement, including the displacement due to uniform deformation as well as periodic deformation, as the independent variable of the micro scale problem. Some numerical examples of cellular solids are provided to show both the feasibility and the computational efficiency of the proposed method.
A Fast Multipole Boundary Integral Equation Method for Periodic Boundary Value Problems in Three-Dimensional Elastostatics and its Application to Homogenization
487-500
Y.
Otani
Department of Applied Analysis and Complex Dynamical Systems, School of Informatics, Kyoto University, Japan
N.
Nishimura
Department of Applied Analysis and Complex Dynamical Systems, School of Informatics, Kyoto University, Japan
This paper presents a fast multipole method (FMM) for periodic elastostatic problems in three dimensions. The proposed method periodizes the solution by using replica cells, but none of the lattice sums involved are divergent and, hence, there is no mathematical ambiguity in the formulation. We estimate macroscopic elastic constants of composites with rigid inclusions using the periodic FMM and the homogenization theory, which requires solutions of periodic boundary value problems for the microstructure. Good agreement is achieved between the macroscopic elastic constants obtained with the proposed method and those obtained with micromechanics.
A Stochastic Nonlocal Model for Materials with Multiscale Behavior
501-520
Jianxu
Shi
ABAQUS, Inc., Rising Sun Mills, 166 Valley Street, Providence, RI02909-2499
Roger
Ghanem
Department of Aerospace and Mechanical Engineering, University of Southern California, 210 KAP Hall, Los Angeles, California 90089, USA
Integral-type nonlocal mechanics is employed to model the macroscale behavior of multiscale materials, with the associated nonlocal kernel representing the interactions between mesoscale features. The nonlocal model is enhanced by explicitly considering the spatial variability of subscale features as stochastic contributions resulting in a stochastic characterization of the kernel. By appropriately representing the boundary conditions, the nonlocal boundary value problem (BVP) of the macroscale behavior is transformed into a system of equations consisting of a classical BVP together with two Fredholm integral equations. The associated integration kernels can be calibrated using either experimental measurements or micromechanical analysis. An efficient and computationally expedient representation of a resulting stochastic kernel is achieved through its polynomial chaos decomposition. The coefficients in this decomposition are evaluated from statistical samples of the disturbance field associated with a random distribution of microcracks. The new model is shown to be capable of predicting nonlocal features, such as the size effect and boundary effect, of the behavior of materials with random microstructures.
Study of Various Estimates of the Macroscopic Tangent Operator in the Incremental Homogenization of Elastoplastic Composites
521-543
Olivier
Pierard
Université Catholique de Louvain (UCL), CESAME, 4 Avenue G. Lemaître, B-1348 Louvain-la-Neuve, Belgium
Issam
Doghri
Université Catholique de Louvain (UCL), CESAME, 4 Avenue G. Lemaître, B-1348 Louvain-la-Neuve, Belgium
This paper contains a theoretical and numerical investigation of the incremental formulation for the mean-field homogenization of two-phase elastoplastic composites. We study several variants of the formulation and try to understand why some of them give good predictions while others do not. We define six instantaneous operators for a fictitious homogeneous reference matrix (two anisotropic, two isotropic, and two transversely isotropic) and various estimates of the macroscopic tangent operator. Theoretically, we present mathematical results that prove that some estimates are stiffer or softer than others. Numerically, we carry out a wide range of validated simulations with different types of inclusions under various loads. The findings confirm the theoretical results and shed new light on a rather complicated problem.