每年出版 6 期
ISSN 打印: 1543-1649
ISSN 在线: 1940-4352
Indexed in
Constitutive Modeling Based on Atomistics
摘要
Mathematical homogenization theory, which serves as a foundation for bridging multiple spatial and temporal scales for continuum systems, is generalized to provide a unified mathematical framework for bridging not only multiple continuum scales in space and time, but also multiple continuum and discrete scales. In this article, we study the one-dimensional chain of atoms and BCC crystals. The solution of the one-dimensional model problem is found to be in good agreement with the molecular dynamics simulation of the chain of atoms, whereas the classic approach based on the Cauchy–Born hypothesis is shown to produce significant errors.
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De Subhranil, Fish Jacob, Shephard Mark S., Keblinski Pawel, Kumar Sanat K., Multiscale modeling of polymer rheology, Physical Review E, 74, 3, 2006. Crossref
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Fish Jacob, Chen Wen, Discrete-to-continuum bridging based on multigrid principles, Computer Methods in Applied Mechanics and Engineering, 193, 17-20, 2004. Crossref
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Li Aiqin, Li Renge, Fish Jacob, Generalized Mathematical Homogenization: From theory to practice, Computer Methods in Applied Mechanics and Engineering, 197, 41-42, 2008. Crossref
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Cho Maenghyo, Yang Seunghwa, Chang Seongmin, Yu Suyoung, A study on the prediction of the mechanical properties of nanoparticulate composites using the homogenization method with the effective interface concept, International Journal for Numerical Methods in Engineering, 85, 12, 2011. Crossref
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Fish Jacob, Chen Wen, Multiscale Approaches for Bridging Discrete and Continuum Scales, in III European Conference on Computational Mechanics, 2006. Crossref