Abstract
AbstractA generalized space–time mathematical homogenization theory, which constructs an equivalent continuum description directly from molecular dynamics (MD) equations, is developed. The noteworthy theoretical findings of this work are: (i) the coarse‐scale continuum equations (PDEs) obtained from the homogenization of MD equations are identical to those obtained from the classical homogenization of the fine‐scale continuum, (ii) the lower order effective continuum properties (such as the fourth‐order elasticity tensor) have similar characteristics to those resulting from the homogenization of fine‐scale continuum, (iii) the higher order effective properties, such as polarization and dispersion tensors, substantially differ from those of continuum due to the discreteness effect. (Both the heterogeneous continuum and discrete media possess the size effect, but only atomistic medium has the discreteness effect.) Some demonstrative numerical examples are presented to verify the formulation. Copyright © 2005 John Wiley & Sons, Ltd.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal for Numerical Methods in Engineering
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
