Enriched space-time finite element method: a new paradigm for multiscaling from elastodynamics to molecular dynamics

SUMMARY The main objective of this paper is to present an enriched version of the space–time FEM method to incorporate multiple temporal scale features with a focus on dynamics problems. The method is established by integrating the basic framework of the space–time discontinuous Galerkin method with...

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Bibliographic Details
Published in:International journal for numerical methods in engineering Vol. 92; no. 2; pp. 115 - 140
Main Authors: Yang, Ye, Chirputkar, Shardool, Alpert, David N., Eason, Thomas, Spottswood, Stephen, Qian, Dong
Format: Journal Article
Language:English
Published: Chichester, UK John Wiley & Sons, Ltd 12.10.2012
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Subjects:
bridging-scale method
enrichment
Exact sciences and technology
extended FEM
Fracture mechanics (crack, fatigue, damage...)
Fundamental areas of phenomenology (including applications)
Galerkin least-square stabilization
lattice fracture
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical approximation
Partial differential equations, initial value problems and time-dependant initial-boundary value problems
Physics
Sciences and techniques of general use
Solid mechanics
space-time FEM
Structural and continuum mechanics
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
Enrichment
Harmonic
lattice fracture
Stabilization
Molecular dynamics
Elastic wave
Galerkin least-square stabilization
Modeling
space-time FEM
Crack propagation
Continuum
Finite element method
Least squares method
bridging-scale method
Robustness
Elastodynamics
Numerical convergence
Discontinuity
Rupture
Space time
extended FEM
Lattice
Time domain method
Atomistic model
Multiscale method
Galerkin method
Dynamic load
eXtended Finite Element Method
ISSN:0029-5981, 1097-0207
Online Access:Get full text
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Summary:SUMMARY The main objective of this paper is to present an enriched version of the space–time FEM method to incorporate multiple temporal scale features with a focus on dynamics problems. The method is established by integrating the basic framework of the space–time discontinuous Galerkin method with the extended finite element method. Two versions of the method have been developed: one at the continuum scale (elastodynamics) and the other focuses on the dynamics at the molecular level. After an initial outline of the formulation, we explore the incorporation of different types of enrichments based on the length scale of interest. The effects of both continuous and discontinuous enrichments are demonstrated through numerical examples involving wave propagations and dynamic fracture in harmonic lattice. The robustness of the method is evaluated in terms of convergence and the ability to capture the fine scale features. It is shown that the enriched space–time FEM leads to an improvement in the convergence properties over the traditional space–time FEM for problems with multiple temporal features. It is also highly effective in integrating atomistic with continuum representations with a coupled framework. Copyright © 2012 John Wiley & Sons, Ltd.
Bibliography:ArticleID:NME4323
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istex:813E2775A2F0423C24DD9F3CC213957F06F1D84C
ObjectType-Article-1
SourceType-Scholarly Journals-1
content type line 14
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.4323