Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
17
5
2019
XFEM SIMULATION OF FATIGUE CRACK GROWTH IN ALUMINUM ZIRCONIA REINFORCED COMPOSITES
469-481
10.1615/IntJMultCompEng.2019029470
Rahman
Bajmalu Rostami
Materials Testing Institute (IMWF), University of Stuttgart, Stuttgart 70569, Germany
Siegfried
Schmauder
Institute for Materials Testing, Materials Science and Strength of Materials (IMWF)
University of Stuttgart, Pfaffenwaldring 32, D-70569 Stuttgart, Germany
XFEM
finite element method
fatigue crack growth
composites
The effects of particles as reinforcement on fatigue crack growth behavior of Al 6061/ZrO2 composite material was investigated by the eXtended Finite Element Method (XFEM). This developed methodology represents the entire crack independently, so remeshing is not necessary. Results show that the crack propagation rate increased as volume fraction increased. The same trend was also observed as the particle size decreased in a constant volume fraction. The stress values within the reinforcements were much higher than that in the matrix, and as a consequence, the transferred load to the reinforcing particles slowed down the crack propagation speed by reduction in the stress concentration at the crack tip, and thus enhanced fatigue performance.
A SIMPLIFIED COMPUTATIONAL MODEL FOR MICROPLATES BASED ON A MODIFIED COUPLE STRESS THEORY
483-505
10.1615/IntJMultCompEng.2019030572
Shengqi
Yang
State Key Laboratory of Structural Analysis for Industrial Equipment, Department of
Engineering Mechanics, Dalian University of Technology, Dalian, 116024, China
Shutian
Liu
State Key Laboratory of Structural Analysis for Industrial Equipment, Department of
Engineering Mechanics, Dalian University of Technology, Dalian, 116024, China
Liyong
Tong
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney,
Sydney, NSW 2006, Australia
microplates
couple stress theory
finite element
scale effect
A novel simplified computational model (SCM) is developed for couple stress microplates by using a third-order deformation plate theory and by assuming the rotation about the z-axis is zero in the modified couple stress theory. Analytical solutions are obtained for bending, free vibration, and buckling behaviors of couple stress microplates. Using the present model, a three-node triangular plate element is constructed, in which each node has only seven degrees of freedom. Numerical results of the SCM are compared with those calculated using the complete model (CM) and the original simplified model (SM) available in the literature. The results reveal that the present SCM shows a significant improvement in computational efficiency, while maintaining minimum loss in accuracy, compared with the CM. The computing time used in the CM is 2−5.7 times that used in the SCM.
A NOVEL APPROACH FOR FINDING APPROXIMATE SOLUTIONS OF FRACTIONAL SYSTEMS OF LINEAR PARTIAL DIFFERENTIAL EQUATIONS USING THE FRACTIONAL NATURAL DECOMPOSITION METHOD
507-527
10.1615/IntJMultCompEng.2019026164
Mahmoud
Rawashdeh
Jordan University of Science and Technology
Amer H.
Darweesh
Jordan University of Science and Technology, Irbid, Jordan, 22110
fractional natural decomposition method (FNDM)
system of fractional partial differential equations
Caputo fractional derivative
In this work, we propose a new approach to find exact solutions to systems of linear fractional partial differential equations (PDEs) using the Fractional Natural Decomposition Method (FNDM). We were be able to find exact solutions for different values of α and β, specifically when α = β = 1, 3/4, 1/2, and 1/4. To the best of our knowledge, we are the first to find such exact solutions for the proposed systems. We employ the FNDM to obtain approximate numerical solutions for two systems of fractional linear PDEs. The FNDM is investigated for these systems of equations and is calculated in the form of power series. The numerical computations in the tables show that our analytical solutions converge very rapidly to the exact solutions.
SPACE-TIME NONLINEAR UPSCALING FRAMEWORK USING NONLOCAL MULTICONTINUUM APPROACH
529-550
10.1615/IntJMultCompEng.2019031829
Wing T.
Leung
Center for Subsurface Modeling, Institute for Computational Engineering and Sciences, The
University of Texas, Austin, TX 78712, USA
Eric T.
Chung
Department of Mathematics, The Chinese University of Hong Kong, Shatin, New Territories,
Hong Kong SAR, China
Yalchin
Efendiev
Department of Mathematics and Institute for Scientific Computation (ISC),
Texas A&M University, College Station, TX 77840, USA; Multiscale Model Reduction Laboratory, North-Eastern Federal University,
Yakutsk, Russia, 677980
Maria
Vasilyeva
Department of Mathematics & Institute for Scientific Computation (ISC), Texas A&M
University, College Station, TX 77840, USA; Multiscale Model Reduction Laboratory, North Eastern Federal University, Yakutsk, Russia
Mary
Wheeler
Center for Subsurface Modeling, Institute for Computational Engineering and Sciences, The
University of Texas, Austin, TX 78712, USA
multiscale
multicontinua
upscaling
nonlocal multicontinua
porous media
space-time
In this paper, we develop a space-time upscaling framework that can be used for many challenging porous media applications without scale separation and high contrast. Our main focus is on nonlinear differential equations with multiscale coefficients. The framework is built on a nonlinear nonlocal multicontinuum upscaling concept and significantly extends the results of earlier work. Our approach starts with a coarse space-time partition and identifies test functions for each partition, which play the role of multicontinua. The test functions are defined via optimization and play a crucial role in nonlinear upscaling. In the second stage, we solve nonlinear local problems in oversampled regions with some constraints defined via test functions. These local solutions define a nonlinear map from macroscopic variables determined with the help of test functions to the fine-grid fields. This map can be thought as a downscaled map from macroscopic variables to the fine-grid solution. In the final stage, we seek macroscopic variables in the entire domain such that the downscaled field solves the global problem in a weak sense defined using the test functions. We present an analysis of our approach for an example nonlinear problem. Our unified framework plays an important role in designing various upscaled methods. Because local problems are directly related to the fine-grid problems, it simplifies the process of finding local solutions with appropriate constraints. Using machine learning (ML), we identify the complex map from macroscopic variablesto fine-grid solution. We present numerical results for several porous media applications, including two-phase flow and transport.
COMPUTATIONAL FRAMEWORK FOR SHORT-STEEL FIBER-REINFORCED ULTRA-HIGH PERFORMANCE CONCRETE (COR-TUF)
551-562
10.1615/IntJMultCompEng.2019031517
Shanqiao
Huang
Department of Astronautic Science and Mechanics, Harbin Institute of Technology, Harbin,
People's Republic of China
Zifeng
Yuan
Jacob
Fish
Department of Civil Engineering and Engineering Mechanics, Columbia University, New
York, 10025, USA
ultrahigh-performance
concrete
Cor-Tuf
short-steel fiber reinforcement
multiscale
reduced order model
We present a novel computational framework aimed at predicting the behavior of a short-steel fiber-reinforced ultrahigh-performance concrete (Cor-Tuf) at a scale of its microconstituents given limited experimental data. By this approach, a high-fidelity model (HFM) that approximates microstructural behavior using direct numerical simulation is constructed first. The rational for utilizing HFM at the initial stage stems from the fact that constitutive laws of its individual microphases are rather simple and, by at large, can be found in the available literature. The calibrated HFM is then employed to construct a digital database that represents additional load cases not available in the original physical experimental database. In comparison to HFM, the added complexity of material models in a lower fidelity model (LFM) based on the statistical sliced reduced order homogenization stems from simplified kinematical assumptions made in the LFM. Validation studies are conducted against a physical experiment of a notched three-point beam bending (TPBB) problem.