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Volume 2, Number 1, March 2009
Abstract
This paper proposes an interaction field concept based on the field theory of plasticity. Relative deformation between two arbitrary scales, e.g., macro and micro fields, is defined which can be implemented in the crystal plasticity-based constitutive framework. Differential geometrical quantities responsible for describing dislocations and defects in the interaction field are obtained, based on which dislocation density and incompatibility tensors are further derived. It is shown that the explicit interaction exists in the curvature or incompatibility tensor field, whereas no interaction in the torsion or dislocation density tensor field. General expressions of the interaction fields over multiple scales with more than three scale levels are derived and implemented into the present constitutive equation.
Key Words
multiscale modeling; crystal plasticity; field theory; differential geometry; non-Riemannian
plasticity.
Address
Tadashi Hasebe; Kobe University, Rokkodai, Nada, Kobe 657-8501, Japan
Abstract
The theoretical framework of the interaction fields for multiple scales based on field theory is applied to one-dimensional problem mimicking dislocation substructure sensitive intra-granular inhomogeneity evolution under fatigue of Cu-added steels. Three distinct scale levels corresponding respectively to the orders of (A)dislocation substructures, (B)grain size and (C)grain aggregates are set-up based on FE-RKPM (reproducing kernel particle method) based interpolated strain distribution to obtain the incompatibility term in the interaction field. Comparisons between analytical conditions with and without the interaction, and that among different cell size in the scale A are simulated. The effect of interaction field on the B-scale field evolution is extensively examined. Finer and larger fluctuation is demonstrated to be obtained by taking account of the field interactions. Finer cell size exhibits larger field fluctuation whereas the coarse cell size yields negligible interaction effects.
Key Words
multiscale modeling; crystal plasticity; field theory; differential geometry; non-Riemannian plasticity.
Address
Tadashi Hasebe; Kobe University, Rokkodai, Nada, Kobe 657-8501, Japan
Abstract
While the classical theory of Griffith is the foundation of modern understanding of brittle fracture, it has a number of significant shortcomings: Griffith theory does not predict crack initiation and path and it suffers from the presence of unphysical stress singularities. In 1998, Francfort and Marigo presented an energy functional minimization method, where the crack (or its absence) as well as its path are part of the problem
Key Words
crack propagation; brittle fracture; cohesive forces; reversibility; energy minimization.
Address
Peter Philip; Department of Mathematics, Ludwig-Maximilians University (LMU) Munich, Theresienstrasse 39, 80333 Munich, Germany
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Extended-FEM for the solid-fluid mixture two-scale problems with BCC and FCC microstructures
Tomohiro Sawada, Shogo Nakasumi, Akira Tezuka, Manabu Fukushima and Yu-ichi Yoshizawa
Abstract;
Full Text (1314K)
Abstract
An aim of the study is to develop an efficient numerical simulation technique that can handle the two-scale analysis of fluid permeation filters fabricated by the partial sintering technique of small spherical ceramics. A solid-fluid mixture homogenization method is introduced to predict the mechanical characters such as rigidity and permeability of the porous ceramic filters from the micro-scale geometry and configuration of partially-sintered particles. An extended finite element (X-FE) discretization technique based on the enriched interpolations of respective characteristic functions at fluid-solid interfaces is proposed for the non-interface-fitted mesh solution of the micro-scale analysis that needs non-slip condition at the interface between solid and fluid phases of the unit cell. The homogenization and localization performances of the proposed method are shown in a typical two-dimensional benchmark problem whose model has a hole in center. Three-dimensional applications to the body-centered cubic (BCC) and face-centered cubic (FCC) unit cell models are also shown in the paper. The 3D application is prepared toward the computer-aided optimal design of ceramic filters. The accuracy and stability of the XFEM based method are comparable to those of the standard interface-fitted FEM, and are superior to those of the voxel type FEM that is often used in such complex micro geometry cases.
Key Words
solid-fluid mixtures; porous media; permeation flow; incompressibility; homogenization method; extended finite element method (X-FEM); level set method; fluid-solid interface; ceramic filters; partial sintering.
Address
Tomohiro Sawada, Shogo Nakasumi and Akira Tezuka; Process-oriented Computational Applied Mechanics Group, AMRI, National Institute of Advanced Industrial Science and Technology (AIST), 1-2-1 Namiki, Tsukuba, Ibaraki, 305-8564, Japan
Manabu Fukushima and Yu-ichi Yoshizawa; High-performance Component Processing Group, AMRI, National Institute of Advanced Industrial Science and Technology (AIST), 2266-98 Anagahora, Shimo-Shidami, Nagoya, Aichi, 463-8560, Japan
Abstract
Reinforced and prestressed concrete (RC and PC) thin walls are crucial to the safety and serviceability of structures subjected to shear. The shear strengths of elements in walls depend strongly on the softening of concrete struts in the principal compression direction due to the principal tension in the perpendicular direction. The past three decades have seen a rapid development of knowledge in shear of reinforced concrete structures. Various rational models have been proposed that are based on the smeared-crack concept and can satisfy Navier's three principles of mechanics of materials (i.e., stress equilibrium, strain compatibility and constitutive laws). The Cyclic Softened Membrane Model (CSMM) is one such rational model developed at the University of Houston, which is being efficiently used to predict the behavior of RC/PC structures critical in shear. CSMM for RC has already been implemented into finite element framework of OpenSees (Fenves 2005) to come up with a finite element program called Simulation of Reinforced Concrete Structures (SRCS) (Zhong 2005, Mo et al. 2008). CSMM for PC is being currently implemented into SRCS to make the program applicable to reinforced as well as prestressed concrete. The generalized program is called Simulation of Concrete Structures (SCS). In this paper, the CSMM for RC/PC in material scale is first introduced. Basically, the constitutive relationships of the materials, including uniaxial constitutive relationship of concrete, uniaxial constitutive relationships of reinforcements embedded in concrete and constitutive relationship of concrete in shear, are determined by testing RC/PC full-scale panels in a Universal Panel Tester available at the University of Houston. The formulation in element scale is then derived, including equilibrium and compatibility equations, relationship between biaxial strains and uniaxial strains, material stiffness matrix and RC plane stress element. Finally the formulated results with RC/PC plane stress elements are implemented in structure scale into a finite element program based on the framework of OpenSees to predict the structural behavior of RC/PC thin-walled structures subjected to earthquake-type loading. The accuracy of the multiscale modeling technique is validated by comparing the simulated responses of RC shear walls subjected to reversed cyclic loading and shake table excitations with test data. The response of a post tensioned precast column under reversed cyclic loads has also been simulated to check the accuracy of SCS which is currently under development. This multiscale modeling technique greatly improves the simulation capability of RC thin-walled structures available to researchers and engineers.
Key Words
multiscale modeling; reinforced concrete; thin-walled structure; constitutive law; nonlinear finite element.
Address
Arghadeep Laskar, Y.L. Mo, Thomas T.C. Hsu; Department of Civil and Environmental Engineering, University of Houston, Houston, 77204-4003, USA
Jianxia Zhong; 11MMI Engineering Inc., Houston, Texas, USA
Abstract
In order to accurately estimate the seismic behavior of buildings, it is important to consider both nonlinear characteristics of the buildings and the frequency dependency of the soil impedance. Therefore, transform methods of the soil impedance in the frequency domain to the impulse response in the time domain are needed because the nonlinear analysis can not be carried out in the frequency domain. The author has proposed practical transform methods. In this paper, seismic response analyses considering frequency dependent soil impedance in the time domain are shown. First, the formulation of the proposed transform methods is described. Then, the linear and nonlinear earthquake response analyses of a building on 2-layered soil were carried out using the transformed impulse responses. Through these analyses, the validity and efficiency of the methods were confirmed.
Key Words
frequency dependency; time domain; earthquake response; soil impedance; impulse response.
Address
R&D Institute, Takenaka Corporation, 1-5-1, Ohtsuka, Inzai, Chiba, 270-1395, Japan
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Editors-in-Chief
Analytical, computational, and experimental multiscale and interaction mechanics
