TY - JOUR
T1 - Multiscale modeling of the dynamics of solids at finite temperature
AU - Li, Xiantao
AU - E, Weinan
N1 - Funding Information:
We are grateful to Li-Tien Cheng, Bjorn Engquist, Zhongyi Huang, Pingbing Ming, Weiqing Ren and Richard Tsai for very interesting discussions. The work reported here is supported in part by an ONR grant N00014-01-0674 and the National Science Foundation of China through a Class B award for distinguished young scholars 10128102.
Copyright:
Copyright 2008 Elsevier B.V., All rights reserved.
PY - 2005/7
Y1 - 2005/7
N2 - We develop a general multiscale method for coupling atomistic and continuum simulations using the framework of the heterogeneous multiscale method (HMM). Both the atomistic and the continuum models are formulated in the form of conservation laws of mass, momentum and energy. A macroscale solver, here the finite volume scheme, is used everywhere on a macrogrid; whenever necessary the macroscale fluxes are computed using the microscale model, which is in turn constrained by the local macrostate of the system, e.g. the deformation gradient tensor, the mean velocity and the local temperature. We discuss how these constraints can be imposed in the form of boundary conditions. When isolated defects are present, we develop an additional strategy for defect tracking. This method naturally decouples the atomistic time scales from the continuum time scale. Applications to shock propagation, thermal expansion, phase boundary and twin boundary dynamics are presented.
AB - We develop a general multiscale method for coupling atomistic and continuum simulations using the framework of the heterogeneous multiscale method (HMM). Both the atomistic and the continuum models are formulated in the form of conservation laws of mass, momentum and energy. A macroscale solver, here the finite volume scheme, is used everywhere on a macrogrid; whenever necessary the macroscale fluxes are computed using the microscale model, which is in turn constrained by the local macrostate of the system, e.g. the deformation gradient tensor, the mean velocity and the local temperature. We discuss how these constraints can be imposed in the form of boundary conditions. When isolated defects are present, we develop an additional strategy for defect tracking. This method naturally decouples the atomistic time scales from the continuum time scale. Applications to shock propagation, thermal expansion, phase boundary and twin boundary dynamics are presented.
KW - Multiscale modeling
KW - Phase transformation
UR - http://www.scopus.com/inward/record.url?scp=18544383450&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=18544383450&partnerID=8YFLogxK
U2 - 10.1016/j.jmps.2005.01.008
DO - 10.1016/j.jmps.2005.01.008
M3 - Article
AN - SCOPUS:18544383450
SN - 0022-5096
VL - 53
SP - 1650
EP - 1685
JO - Journal of the Mechanics and Physics of Solids
JF - Journal of the Mechanics and Physics of Solids
IS - 7
ER -