Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
10
4
2012
A MOLECULAR DYNAMICS-CONTINUUM CONCURRENT MULTISCALE MODEL FOR QUASI-STATIC NANOSCALE CONTACT PROBLEMS
307-326
10.1615/IntJMultCompEng.2012002133
Tianxiang
Liu
Department of Engineering, University of Leicester, Leicester, LE1 7RH, United Kingdom
Peter
Wriggers
Institute of Continuum Mechanics, Leibniz Universität Hannover, Appelstrasse 11, 30167
Hannover, Germany
Geng
Liu
School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an, 710072, China
multiscale modeling
molecular dynamics
continuum mechanics
nanoscale contacts
Analyzing contact performances between two surfaces plays a key role in studying friction, wear, and lubrication
in tribological systems. Advancements of micro/nano-electromechanical system (MEMS/NEMS) and nanotechnology
in recent years demand the developments of multiscale contact mechanics. By using multiscale methods, calculation
domains which consider local mechanical behaviors with nanoscale characteristics could be simulated by atomistic
methods, and other domains can still use conventional methods for larger lengths and time scales in order
to save computational costs or achieve high-performance calculations for larger scale systems. A molecular
dynamics-continuum concurrent multiscale model for quasi-static nanoscale contacts is presented, which can both
implement equilibrium of the energy field and force field in different scale domains. In molecular dynamics simulations,
since the speed of the approaching probe is very small in comparison with the longitudinal sound speed, which is usually
in the order of 103 m/s, the results of the contact process can be treated approximately as the quasi-static case in nature.
For continuum simulations, the Cauchy-Born rule is employed to evaluate the nonlinear constitutive relationship of
the coarse scale. By using the present multiscale model, simulations of nanoscale adhesive contacts between a cylinder
and a substrate are implemented. The results show that the boundary conditions are effective for the contact problems.
Furthermore, 2-D adhesive contacts of rough surfaces are investigated. Some behaviors of the nanoscale contact processes
are discussed, and differences between the multiscale model and the pure molecular dynamics simulation are revealed.
MULTISCALE PARAMETER IDENTIFICATION
327-342
10.1615/IntJMultCompEng.2012002175
Ulrike
Schmidt
Chair of Applied Mechanics, University of Erlangen-Nuremberg, Egerlandstr. 5,91058 Erlangen, Germany
Julia
Mergheim
Chair of Applied Mechanics, University of Erlangen-Nuremberg, Egerlandstr. 5,91058 Erlangen, Germany
Paul
Steinmann
Chair of Applied Mechanics, University of Erlangen-Nuremberg, Egerlandstr. 5,91058 Erlangen, Germany
multiscale
homogenization
parameter identification
In this work a multiscale approach is introduced which allows for the identification of small scale mechanical properties by means of large scale test data. The proposed scheme is based on the computational homogenization method in which a small scale representative volume element is related to each large scale material point and the large scale material response is directly obtained via homogenization of the small scale field variables. Application of this computational homogenization method usually requires that the microstructure of the material be well characterized, i.e., that the constitutive behavior of all constituents of the heterogeneous material is known. This condition is circumvented here by the solution of an inverse optimization problem, which provides the fine scale material properties as a result. Therefore the objective function compares large scale experimental results to field values, simulated with the computational homogenization method. Discrete analytical expressions for the sensitivities are derived, and the performance of different gradient-based optimization algorithms is compared for linear elastic problems with various microstructures.
A NEW CRACK TIP ENRICHMENT FUNCTION IN THE EXTENDED FINITE ELEMENT METHOD FOR GENERAL INELASTIC MATERIALS
343-360
10.1615/IntJMultCompEng.2012002827
Xia
Liu
Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, New York 10027, USA
Haim
Waisman
Department of Civil Engineering and Engineering Mechanics, Columbia University, New York, New York 10027, USA
Jacob
Fish
Civil Engineering and Engineering Mechanics, Columbia University, New York, New York
10027, USA
extended finite element method
XFEM
branch functions
ramp function
heavisidefunction
plasticity
viscoplasticity
Branch functions are commonly used as crack tip enrichments in the extended finite element method (XFEM). Typically, these are four functions derived from linear elasticity and added as additional degrees of freedom. However, for general inelastic material behavior, where the analytical solution and the order of singularity are unknown, Branch functions are typically not used, and only the Heaviside function is employed. This, however, may introduce numerical error, such as inconsistency in the position of the crack tip. In this paper we propose a special construction of a Ramp function as tip enrichment, which may alleviate some of the problems associated with the Heaviside function when applied to general inelastic materials, especially ones with no analytical solutions available. The idea is to linearly ramp down the displacement jump on the opposite sides of the crack to the actual crack tip, which may stop the crack at any point within an element, employing only one enrichment function. Moreover, a material length scale that controls the slope of the ramping is introduced to allow for better flexibility in modeling general materials. Numerical examples for ideal and hardening elastoplastic and elastoviscoplastic materials are given, and the convergence studies show that a better performance is obtained by the proposed method in comparison with the Heaviside function. Nevertheless, when analytical functions, such as the Hutchinson-Rice-Rosengren (HRR) fields, do exist (for very limited material models), they indeed perform better than the proposed Ramp function. However, they also employ more degrees of freedom per node and hence are more expensive.
INVERSE ANALYSIS FOR MULTIPHASE NONLINEAR COMPOSITES WITH RANDOM MICROSTRUCTURE
361-373
10.1615/IntJMultCompEng.2012002946
Sandra
Klinge
Institute of Mechanics, Ruhr-University Bochum, D-44780 Bochum, Germany
inverse analysis
multiscale FEM
homogenization
composite materials
nonlinearelasticity
The contribution considers the application of inverse analysis to the identification of the material parameters of nonlinear composites. For this purpose a combination of the Levenberg-Marquardt method with the multiscale finite element method is used. The first one belongs to the group of gradient-based optimization methods, and the latter is a numerical procedure for modeling heterogeneous materials which is applicable in the case when the ratio of characteristic sizes of the scales tends to zero. Emphasis is placed on the investigation of problems with an increasing number of unknown materials parameters, as well as on the manifestation of the ill-posedness of inverse problems. These effects first occurred in the case of three-phase materials. The illustrative examples are concerned with cases where such a combination of experimental data is used that effects of ill-posedness are alleviated and a unique solution is achieved.
A MULTISCALE METHOD FOR GEOPHYSICAL FLOW EVENTS
375-390
10.1615/IntJMultCompEng.2012003264
James E.
Hilton
CSIRO Mathematics, Informatics and Statistics, Clayton, Victoria 3169, Australia
Paul W.
Cleary
CSIRO Mathematics, Informatics and Statistics, Clayton, Victoria 3169, Australia
shallow water equations
smoothed particle hydrodynamics
Large-scale prediction of events such as coastal inundation, flooding, and dam collapse is becoming increasingly necessary from both a geophysical and geoengineering standpoint. Current computational models can only capture large-scale flow events and are unable to resolve three-dimensional mesoscale local flow features. We present a multiscale coupled fluid method, with large-scale flow over the full domain coupled with a smaller-scale model to more accurately resolve local flow features in regions of interest. The macroscale model uses a finite volume method based on the shallow water (SW) formulation. This is coupled to a mesoscale smoothed particle hydrodynamics (SPH) method for solving the three-dimensional Navier-Stokes equations for the fluid flow. We show the viability of this multiscale method for predicting both large-scale and smaller-scale flow effects in geophysical flow applications.