Gracie, Robert; Belytschko, Ted An adaptive concurrent multiscale method for the dynamic simulation of dislocations. (English) Zbl 1216.74021 Int. J. Numer. Methods Eng. 86, No. 4-5, 575-597 (2011). MSC: 74S05 74A25 74A60 PDFBibTeX XMLCite \textit{R. Gracie} and \textit{T. Belytschko}, Int. J. Numer. Methods Eng. 86, No. 4--5, 575--597 (2011; Zbl 1216.74021) Full Text: DOI
Belytschko, Ted; Gracie, Robert; Xu, Mei Concurrent coupling of atomistic and continuum models. (English) Zbl 1221.82036 Fish, Jacob (ed.), Multiscale methods. Bridging the scales in science and engineering. Oxford: Oxford University Press (ISBN 978-0-19-923385-4/hbk). 93-133 (2010). MSC: 82B21 74A25 PDFBibTeX XMLCite \textit{T. Belytschko} et al., in: Multiscale methods. Bridging the scales in science and engineering. Oxford: Oxford University Press. 93--133 (2010; Zbl 1221.82036) Full Text: DOI
Xu, Mei; Gracie, Robert; Belytschko, Ted A continuum-to-atomistic bridging domain method for composite lattices. (English) Zbl 1183.74012 Int. J. Numer. Methods Eng. 81, No. 13, 1635-1658 (2010). MSC: 74A25 74A40 PDFBibTeX XMLCite \textit{M. Xu} et al., Int. J. Numer. Methods Eng. 81, No. 13, 1635--1658 (2010; Zbl 1183.74012) Full Text: DOI
Rabczuk, Timon; Gracie, Robert; Song, Jeong-Hoon; Belytschko, Ted Immersed particle method for fluid-structure interaction. (English) Zbl 1183.74367 Int. J. Numer. Methods Eng. 81, No. 1, 48-71 (2010). MSC: 74S30 74F10 76M28 PDFBibTeX XMLCite \textit{T. Rabczuk} et al., Int. J. Numer. Methods Eng. 81, No. 1, 48--71 (2010; Zbl 1183.74367) Full Text: DOI
Oswald, Jay; Gracie, Robert; Khare, Roopam; Belytschko, Ted An extended finite element method for dislocations in complex geometries: thin films and nanotubes. (English) Zbl 1227.74085 Comput. Methods Appl. Mech. Eng. 198, No. 21-26, 1872-1886 (2009). MSC: 74S05 74K35 74M25 PDFBibTeX XMLCite \textit{J. Oswald} et al., Comput. Methods Appl. Mech. Eng. 198, No. 21--26, 1872--1886 (2009; Zbl 1227.74085) Full Text: DOI
Ventura, Giulio; Gracie, Robert; Belytschko, Ted Fast integration and weight function blending in the extended finite element method. (English) Zbl 1195.74201 Int. J. Numer. Methods Eng. 77, No. 1, 1-29 (2009). MSC: 74S05 PDFBibTeX XMLCite \textit{G. Ventura} et al., Int. J. Numer. Methods Eng. 77, No. 1, 1--29 (2009; Zbl 1195.74201) Full Text: DOI
Gracie, Robert; Belytschko, Ted Concurrently coupled atomistic and XFEM models for dislocations and cracks. (English) Zbl 1183.74278 Int. J. Numer. Methods Eng. 78, No. 3, 354-378 (2009). MSC: 74S05 74R10 74A25 PDFBibTeX XMLCite \textit{R. Gracie} and \textit{T. Belytschko}, Int. J. Numer. Methods Eng. 78, No. 3, 354--378 (2009; Zbl 1183.74278) Full Text: DOI
Gracie, Robert; Wang, Hongwu; Belytschko, Ted Blending in the extended finite element method by discontinuous Galerkin and assumed strain methods. (English) Zbl 1195.74175 Int. J. Numer. Methods Eng. 74, No. 11, 1645-1669 (2008). MSC: 74S05 74R10 PDFBibTeX XMLCite \textit{R. Gracie} et al., Int. J. Numer. Methods Eng. 74, No. 11, 1645--1669 (2008; Zbl 1195.74175) Full Text: DOI
Gracie, Robert; Oswald, Jay; Belytschko, Ted On a new extended finite element method for dislocations: Core enrichment and nonlinear formulation. (English) Zbl 1162.74464 J. Mech. Phys. Solids 56, No. 1, 200-214 (2008). MSC: 74S05 74A60 PDFBibTeX XMLCite \textit{R. Gracie} et al., J. Mech. Phys. Solids 56, No. 1, 200--214 (2008; Zbl 1162.74464) Full Text: DOI
Belytschko, Ted; Song, Jeong-Hoon; Wang, Hongwu; Gracie, Robert On applications of XFEM to dynamic fracture and dislocations. (English) Zbl 1209.74043 Combescure, Alain (ed.) et al., IUTAM symposium on discretization methods for evolving discontinuities. Proceedings of the IUTAM symposium held in Lyon, France, September 4–7, 2006. Dordrecht: Springer (ISBN 978-1-4020-6529-3/hbk). IUTAM Bookseries 5, 155-170 (2007). MSC: 74S05 74R10 PDFBibTeX XMLCite \textit{T. Belytschko} et al., IUTAM Bookser. 5, 155--170 (2007; Zbl 1209.74043) Full Text: DOI
Gracie, Robert; Ventura, Giulio; Belytschko, Ted A new fast finite element method for dislocations based on interior discontinuities. (English) Zbl 1194.74402 Int. J. Numer. Methods Eng. 69, No. 2, 423-441 (2007). MSC: 74S05 PDFBibTeX XMLCite \textit{R. Gracie} et al., Int. J. Numer. Methods Eng. 69, No. 2, 423--441 (2007; Zbl 1194.74402) Full Text: DOI
Belytschko, Ted; Gracie, Robert On XFEM applications to dislocations and interfaces. (English) Zbl 1126.74046 Int. J. Plast. 23, No. 10-11, 1721-1738 (2007). MSC: 74S05 74A60 PDFBibTeX XMLCite \textit{T. Belytschko} and \textit{R. Gracie}, Int. J. Plast. 23, No. 10--11, 1721--1738 (2007; Zbl 1126.74046) Full Text: DOI