Abstract
Multiscale modeling and computation has recently become one of the most active research areas in applied science. With rapidly growing computing power, we are increasingly more capable of modeling the details of physical processes. Nevertheless, we still face the challenge that the phenomena of interest are oftentimes the result of strong interaction between multiple spatial and temporal scales, and the physical processes are described by radically different models at different scales.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E.B. Tadmor, M. Ortiz, and R. Phillips, “Quasicontinuum analysis of defects in crystals,” Phil. Mag. A, 73, 1529, 1996.
R.E. Miller and E.B. Tadmor, “The quasicontinuum method: overview, applications and current directions,” J. Comput.-Aided Mater. Des., in press, 2003.
J. Knap and M. Ortiz, “An analysis of the quasicontinuum method,” J. Mech. Phys. Solid, 49, 1899, 2001.
V. Shenoy and R. Phillips, “Finite temperature quasicontinuum methods,” Mat. Res. Soc. Symp. Proc., 538, 465, 1999.
F.F. Abraham, J.Q. Broughton, N. Bernstein, and E. Kaxiras, “Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture,” Europhys. Lett., 44(6), 783, 1998.
J.Q. Broughton, F.F. Abraham, N. Bernstein, and E. Kaxiras, “Concurrent coupling of length scales: methodology and application,” Phys. Rev. B, 60(4), 2391, 1999.
R.E. Rudd and J.Q. Broughton, “Coarse-grained molecular dynamics and the atomic limit of finite element,” Phys. Rev. B, 58(10), R5893, 1998.
R.E. Rudd and J.Q. Broughton, Unpublished, 2000.
X.T. Li and W.E, “Multiscal modeling of solids,” Preprint, 2003.
W.E and B. Engquist, “The heterogeneous multi-scale methods,” Comm. Math. Sci., 1(1), 87, 2002.
E. Godlewski, and P.A. Raviart, Numerical Approximation of Hyperbolic systems of Conservation Laws, Springer-Verlag, New York, 1996.
H. Nessyahu and E. Tadmor, “Nonoscillatory central differencing for hyperbolic conservation laws,” J. Comp. Phys., 87(2), 408, 1990.
G.J. Wagner, G.K. Eduard, and W.K. Liu, Molecular Dynamics Boundary Conditions for Regular Crystal Lattice, Preprint, 2003.
W.E and Z. Huang, “Matching conditions in atomistic-continuum modeling of material,” Phys. Rev. Lett., 87(13), 135501, 2001.
W.E and Z. Huang, “A dynamic atomistic-continuum method for the simulation of crystalline material,” J. Comp. Phys., 182, 234, 2002.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer
About this chapter
Cite this chapter
E, W., Li, X. (2005). Multiscale Modeling Of Crystalline Solids. In: Yip, S. (eds) Handbook of Materials Modeling. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-3286-8_74
Download citation
DOI: https://doi.org/10.1007/978-1-4020-3286-8_74
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-3287-5
Online ISBN: 978-1-4020-3286-8
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)