Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
10
3
2012
APPLICATION OF THE MULTISCALE FEM TO THE MODELING OF NONLINEAR COMPOSITES WITH A RANDOM MICROSTRUCTURE
213-227
Sandra
Klinge
Institute of Mechanics, Ruhr-University Bochum, D-44780 Bochum, Germany
Klaus
Hackl
Institute of Mechanics of Materials, Ruhr-Universität Bochum
In this contribution the properties and application of the multiscale finite element program MSFEAP are presented. This code is developed on basis of coupling the homogenization theory with the finite element method. According to this concept, the investigation of an appropriately chosen representative volume element yields the material parameters needed for the simulation of a macroscopic body. The connection of scales is based on the principle of volume averaging and the Hill-Mandel macrohomogeneity condition. The latter leads to the determination of different types of boundary conditions for the representative volume element and in this way to the postulation of a well-posed problem at this level. The numerical examples presented in the contribution investigate the effective material behavior of microporous media. An isotropic and a transversally anisotropic microstructure are simulated by choosing an appropriate orientation and geometry of the representative volume element in each Gauss point. The results are verified by comparing them with Hashin-Shtrikman's analytic bounds. However, the chosen examples should be understood as simply an illustration of the program application, while its main feature is a modular structure suitable for further development.
A LATTICE BOLTZMANN MODEL FOR HIGH-ENERGY MATERIALS PROCESSING APPLICATION
229-247
Dipankar
Chatterjee
Academy of Scientific and Innovative Research (AcSIR), CSIR-Central Mechanical
Engineering Research Institute, Durgapur-713209, India; Advanced Design and Analysis Group, CSIR-Central Mechanical Engineering Research
Institute Durgapur-713209, India
A three-dimensional lattice Boltzmann (LB) scheme is presented in this article to address the incompressible transport phenomena in the presence of a continuously evolving phase change interface typically encountered in high-energy materials processing applications. The proposed LB scheme utilizes three separate distribution functions to monitor the underlying hydrodynamic, thermal, and compositional fields. Accordingly, the kinematic viscosity, and thermal and mass diffusivities can be adjusted independently, which makes the model suitable for a wide range of phase change problems in high-power materials processing applications. The phase-changing aspects are incorporated into the LB model by inserting appropriate source terms in the respective kinetic equations through the most formal technique - following the extended Boltzmann equations along with an adapted enthalpy updating scheme in association with the classical enthalpy-porosity technique for solid-liquid phase transition problems. The model is used to simulate a conventional high-power laser surface alloying process and excellent agreement with the available experimental results is observed.
BUCKLING ANALYSIS OF RECTANGULAR FLEXURAL MICROPLATES USING HIGHER CONTINUITY P-VERSION FINITE-ELEMENT METHOD
249-259
A. R.
Ahmadi
International Center for Science and High Technology and Environmental Sciences, Kerman, Iran
H.
Farahmand
Department of Mechanical Engineering, Islamic Azad University of Kerman Branch, Kerman, Iran
S.
Arabnejad
Young Researchers Club, Kerman branch, Islamic Azad University, Kerman, Iran
In this article, elastic buckling of rectangular
flexural micro plates (FMPs), using a higher continuity
p-version finite-element framework based on Galerkin
formulation, is investigated. The invariant form of governing
equation for microplates with nonlocal effects based on "modified
couple stress theory" is extended for buckling analysis of FMPs
by considering the strain gradient effects, for which the
constitutive equation of the strain gradient model contains only
one constant. The Galerkin weak form of the governing equation
is derived and subsequently solved for a variety of boundary
conditions, using higher continuity p finite elements,
to extract critical buckling loads. Here the computational
procedure is verified by comparing the results to those of the
classical theory and microplate studies reported in literature.
Investigations indicate that the length scale parameter affects
the computed flexural stiffness of a plate directly proportional
to the value of gradient coefficient considered for that plate. Hence there is a strong influence of length scale parameter on the
value of the buckling load. Depending on boundary conditions and
the length scale parameter value, the classical plate model
severely underestimates (up to 90%) the buckling load of
microplates. Therefore it is concluded that the classical plate
theory cannot be used to predict structural response when length
scale effects are present.
RANDOM RESIDUAL STRESSES IN ELASTICITY HOMOGENEOUS MEDIUM WITH INCLUSIONS OF NONCANONICAL SHAPE
261-279
Valeriy A.
Buryachenko
Civil Engineering Department, University of Akron, Akron, Ohio 44325-3901, USA and Micromechanics and Composites LLC, 2520 Hingham Lane, Dayton, Ohio 45459, USA
Michele
Brun
Department of Structural Engineering, University of Cagliari, 09124 Cagliari, Italy ; Istituto Officina dei Materiali del CNR (CNR-IOM) Unita SLACS, Cittadella Universitaria, 09042 Monserrato (Ca), Italy
We consider a linearly elastic composite medium, which consists of a homogeneous matrix containing a statistically inhomogeneous random set of noncanonical inclusions. The elastic properties of the matrix and the inclusions are the same, but the stress-free strains are different. The new general volume integral equation (VIE) is proposed. These equations are obtained by a centering procedure without any auxiliary assumptions such as the effective field hypothesis implicitly exploited in the known centering methods. The results of this abandonment are quantitatively estimated for some modeled composite with homogeneous fibers of nonellipsoidal shape. New effects are detected that are impossible within the framework of a classical background of micromechanics.
AVERAGING PROPERTIES FOR PERIODIC HOMOGENIZATION AND LARGE DEFORMATION
281-293
Mohamed
Ben Bettaieb
ArGEnCo Department, MS2F Division, University of Liege, Chemin des Chevreuils 1, 4000 Liege, Belgium
Olivier
Debordes
LMA & ECM, IMT, Technopole Chateau-Gombert, F13383 Marseille Cedex 13, France
Abdelwaheb
Dogui
LGM, ENIM, 5019 Monastir, Tunisia
Laurent
Duchene
ArGEnCo Department, MS2F Division, University of Liege, Chemin des Chevreuils 1, 4000 Liege, Belgium
The main motivation of this paper consists of using the periodic homogenization theory to derive several relations between macroscopic Lagrangian (e.g., deformation gradient, Piola−Kirchhoff tensor) and Eulerian (e.g., velocity gradient, Cauchy stress) quantities. These relations demonstrate that these macroscopic quantities behave formally in the same way as their microscopic counterparts. We say therefore that these relations are stable with respect to the periodic homogenization. We also demonstrate the equivalence between the two forms of the macroscopic power density expressed in the Lagrangian and Eulerian formulations. Two simple examples illustrate these results, and indicate also that the Green−Lagrange strain tensor and the second Piola−Kirchhoff stress tensor are not stable with respect to periodic homogenization.
EFFECTS OF RIPPLING DEFORMATION AND MIDPLANE STRETCHING ON NONLINEAR VIBRATION OF EMBEDDED CARBON NANOTUBE
295-305
Iman
Mehdipour
Department of Mechanical Engineering, Semnan Branch, Islamic Azad University, Semnan, Iran ; Young Researcher Club, Semnan Branch, Islamic Azad University, Semnan, Iran
Amin
Barari
Aalborg University
Ganji
Domairry
Department of Mechanical Engineering, Babol University of Technology, Babol, Iran
In this study, based on continuum mechanics and an elastic beam model, nonlinear free vibration of embedded single-walled carbon nanotube considering the effects of rippling deformation and midplane stretching on nonlinear frequency is investigated. By utilizing He's energy balance method, the relationship of nonlinear amplitude and frequency for the single-walled carbon nanotube is expressed. The amplitude frequency response curves of the nonlinear free vibration for the single-walled carbon nanotube are obtained and the effects of rippling deformation, midplane stretching, and surrounding elastic medium on the amplitude frequency response characteristics are discussed. In addition, the rippling instability of carbon nanotubes and the effective parameters on their behavior are briefly discussed.