The DOI matches its Crossref record; 102 of the 102 references it cites were found in a registry or an index.
An introduction to computational nanomechanics and materials
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Citations
Cites
Self-Consistent Equations Including Exchange and Correlation Effects
Kohn, W., & Sham, L. J. (1965) · Physical Review · doi:10.1103/physrev.140.a1133 · Cited by 64,135
Hohenberg, P., & Kohn, W. (1964) · Physical Review · doi:10.1103/physrev.136.b864 · Cited by 53,541
Molecular dynamics with coupling to an external bath
Berendsen, H. J. C., Postma, J. P. M., van Gunsteren, W. F., DiNola, A., & Haak, J. R. (1984) · The Journal of Chemical Physics · doi:10.1063/1.448118 · Cited by 30,700
Computer Simulation of Liquids
Allen, M. P., & Tildesley, D. J. (2017) · doi:10.1093/oso/9780198803195.001.0001 · Cited by 20,945
Computer Simulation of Liquids
P, S., & J, K. (1988) · Journal of Molecular Liquids · doi:10.1016/0167-7322(88)80022-9 · Cited by 15,812
Zienkiewicz, O. C. (1989) · Cited by 14,802
Unified Approach for Molecular Dynamics and Density-Functional Theory
Car, R., & Parrinello, M. (1985) · Physical Review Letters · doi:10.1103/physrevlett.55.2471 · Cited by 10,754
Goldstein, H. (1951) · UCLA - Biblioteca de Ciencias y Tecnologia Felix Morales Bueno · Cited by 10,004
Payne, M. C., Teter, M. P., Allan, D. C., Arias, T. A., & Joannopoulos, J. D. (1992) · Reviews of Modern Physics · doi:10.1103/revmodphys.64.1045 · Cited by 9,728
Alexandre, M., & Dubois, P. (2000) · Materials Science and Engineering: R: Reports · doi:10.1016/s0927-796x(00)00012-7 · Cited by 6,377
Cited by
Heterogeneous Multiscale Methods: A Review
Weinan, E., Engquist, B., Li, X., Ren, W., & Vanden‐Eijnden, E. (2007) · Communications in Computational Physics · doi:10.4208/cicp.2007.v2.p367 · Cited by 687
Lejaeghere, K., Van Speybroeck, V., Van Oost, G., & Cottenier, S. (2014) · Critical Reviews in Solid State and Materials Sciences · doi:10.1080/10408436.2013.772503 · Cited by 560
Immersed finite element method and its applications to biological systems
Liu, W. K., Liu, Y., Farrell, D., Zhang, L., Wang, X. S., Fukui, Y., Patankar, N., Zhang, Y., Bajaj, C., Lee, J., et al. (2006) · Computer Methods in Applied Mechanics and Engineering · doi:10.1016/j.cma.2005.05.049 · Cited by 309
Self-citationChallenges in Multiscale Modeling of Polymer Dynamics
Li, Y., Abberton, B., Kröger, M., & Liu, W. (2013) · Polymers · doi:10.3390/polym5020751 · Cited by 222
“There is a tremendous amount of concurrent multiscale modeling methods developed in the recent ten years with rigorous mathematical foundations, but mostly for metals [344,346–350] and carbon nanomaterials [345,351–354].”
BackgroundSelf-citationA predictive multiscale computational framework for viscoelastic properties of linear polymers
Li, Y., Tang, S., Abberton, B. C., Kröger, M., Burkhart, C., Jiang, B., Papakonstantopoulos, G. J., Poldneff, M., & Liu, W. K. (2012) · Polymer · doi:10.1016/j.polymer.2012.09.055 · Cited by 139
Self-citation
Metadata
- Authors
- Liu, W. K., Karpov, E. G., Zhang, S., & Park, H. S.
- Venue
- Computer Methods in Applied Mechanics and Engineering
- Publisher
- Elsevier BV
- Published
- 2004-05
- Volume
- 193
- Issue
- 17-20
- Pages
- 1529-1578
- ISSN
- 0045-7825 (ISSN-L)
- OpenAlex
- W2145639484
- Cited by
- 406
- References
- 102
- FWCI
- 26.87
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: An introduction to computational nanomechanics and materials. https://app.cochat.ai/papers/10.1016/j.cma.2003.12.008
- The paper
- Liu, W. K., Karpov, E. G., Zhang, S., & Park, H. S. (2004). An introduction to computational nanomechanics and materials. Computer Methods in Applied Mechanics and Engineering. https://doi.org/10.1016/j.cma.2003.12.008
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.