A multiscale manifold method using particle representations of the physical domain

References

• Belytschko, T., Loehnert, S. and Song, J.H., 2008. Multiscale aggregating discontinuities: A method for circumventing loss of material stability. International Journal for Numerical Methods in Engineering, 73 (6), 869–894.
   Web of Science ®Google Scholar
• Cai, M., Kaiser, P.K., Morioka, H., Minami, M., Maejima, T., Tasaka, Y. and Kurose, H., 2007. FLAC/PFC coupled numerical simulation of AE in large-scale underground excavations. International Journal of Rock Mechanics and Mining Sciences, 44 (4), 550–564.
   Web of Science ®Google Scholar
• Cundall, P.A., 1971. A computer model for simulating progressive large scale movements in blocky rock systems. In: Proceedings of the international symposium on rock fracture. Nancy: International Society for Rock Mechanics (ISRM), 1 (8), 129–136.
   Google Scholar
• Cundall, P.A. and Strack, O.D.L., 1979. Discrete numerical model for granular assemblies. Geotechnique, 29 (1), 47–65.
   Web of Science ®Google Scholar
• Haidar, K., Dube, J.F. and Pijaudier-Cabot, G., 2003. Modelling crack propagation in concrete structures with a two scale approach. International Journal for Numerical and Analytical Methods in Geomechanics, 27 (13), 1187–1205.
   Web of Science ®Google Scholar
• Horstemeyer, M.F., 2010. Multiscale modeling: a review. In: J. Leszczynski and M. K. Shukla, eds. Practical aspects of computational chemistry. Amsterdam: Springer, 87–135.
   Google Scholar
• McGinnis, P.M., 2005. Biomechanics of sport and exercise. Champaign: Human Kinetics Publishers.
   Google Scholar
• Melenk, J.M. and Babuska, I., 1996. The partition of unity finite element method: Basic theory and applications. Computer Methods in Applied Mechanics and Engineering, 139 (1-4), 289–314.
   Web of Science ®Google Scholar
• Mullins, M. and Dokainish, M.A., 1982. Simulation of the (001) plane crack in alpha-iron employing a new boundary scheme. Philosophical Magazine A: Physics of Condensed Matter Structure Defects and Mechanical Properties, 46 (5), 771–787.
   Web of Science ®Google Scholar
• Noguchi, H. and Furuya, Y., 1997. A method of seamlessly combining a crack tip molecular dynamics enclave with a linear elastic outer domain in simulating elastic-plastic crack advance. International Journal of Fracture, 87 (4), 309–329.
   Web of Science ®Google Scholar
• Saiang, D., 2010. Stability analysis of the blast-induced damage zone by continuum and coupled continuum-discontinuum methods. Engineering Geology, 116 (1-2), 1–11.
   Web of Science ®Google Scholar
• Sansoz, F. and Molinari, J.F., 2007. Size and microstructure effects on the mechanical behavior of FCC bicrystals by quasicontinuum method. Thin Solid Films, 515 (6), 3158–3163.
   Web of Science ®Google Scholar
• Shi, G.H., 1988. Discontinuous deformation analysis, a new numerical model for the statics and dynamics of block systems. Thesis (PhD). University of California.
   Google Scholar
• Shi, G.H., 1991. Manifold method of material analysis. 9th Army Conference on Applied Mathematics and Computing, Minneapolis. Army Research Office, Research Triangle Park, NC:57–76.
   Google Scholar
• Shi, G.H., 1995. Numerical manifold method. In: J.C. Lin, C.Y. Wang and J. Sheng, eds. 1st International Conference on Analysis of Discontinuous Deformation (ICADD-1), Chungli, Taiwan: National Central University, 187–222.
   Google Scholar
• Shi, G.H., 1996. Simplex integration for manifold method, FEM, DDA and analytical analysis. In: M.R. Salami and D. Banks, eds. 1st International Forum on Discontinuous Deformation Analysis (DDA) and Simulation of Discontinuous Media, Albuquerque: TSI Press, 205–262.
   Google Scholar
• Sun, L., 2012. Particle manifold nethod (PMM) for multiscale continuous-discontinuous analysis. Thesis (PhD), EPFL.
   Google Scholar
• Sun, L., Zhao, G.F. and Zhao, J., 2011. Contact description in numerical simulation for rock mechanics. 12th Congress of the International Society for Rock Mechanics, Beijing: Taylor & Francis Group, 541–544.
   Google Scholar
• Sun, L., Zhao, G.F. and Zhao, J., 2013. Particle manifold method (PMM): a new continuum-discontinuum numerical model for Geomechanics. International Journal for Numerical and Analytical Methods in Geomechanics, 37 (12), 1711–1736.
   Web of Science ®Google Scholar
• Tadmor, E.B., Ortiz, M. and Phillips, R., 1996a. Quasicontinuum analysis of defects in solids. Philosophical Magazine A: Physics of Condensed Matter Structure Defects and Mechanical Properties, 73 (6), 1529–1563.
   Web of Science ®Google Scholar
• Tadmor, E.B., Phillips, R. and Ortiz, M., 1996b. Mixed atomistic and continuum models of deformation in solids. Langmuir, 12 (19), 4529–4534.
   Web of Science ®Google Scholar
• Wu, C.D. and Lin, J.F., 2008. Multiscale particle dynamics in nanoimprint process. Applied Physics A: Materials Science & Processing, 91 (2), 273–279.
   Web of Science ®Google Scholar
• Zhao, G.F., Fang, J.N. and Zhao, J., 2011a. A 3D distinct lattice spring model for elasticity and dynamic failure. International Journal for Numerical and Analytical Methods in Geomechanics, 35 (8), 859–885.
   Web of Science ®Google Scholar
• Zhao, J., Ohnishi, Y., Zhao, G.F. and Sasaki, T., 2011b. Advances in discontinuous numerical methods and applications in Geomechanics and Geoengineering. Honolulu: CRC Press/Balkema.
   Google Scholar
• Zhou, F., Molinari, J.-F. and Shioya, T., 2005. A rate-dependent cohesive model for simulating dynamic crack propagation in brittle materials. Engineering Fracture Mechanics, 72 (9), 1383–1410.
   Web of Science ®Google Scholar
• Zienkiewicz, O.C. and Taylor, R.L., 2005. The Finite Element Method. Oxford: Butterworth-Heinemann.
   Google Scholar