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M. Zimmerman, “A Continuum Theory with Long-Range Forces for Solids,” Ph.D. Thesis, Massachusetts Institute of Technology, Boston, 2005.
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[2]
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S. A. Silling, “Reformulation of Elasticticity Theory for Discontinuities and Long Range Forces,” Journal of the Mechanics and Physics of Solids, Vol. 48, No. 1, 2000, pp. 175-209. doi:10.1016/S0022-5096(99)00029-0
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[3]
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S. A. Silling and E. Askari, “A Meshfree Method Based on the Peridynamic Model of Solid Mechanics,” Journal of Computers and Structures, Vol. 83, No. 17-18, June 2005, pp. 1526-1535.
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[4]
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S. A. Silling and F. Bobaru, “Peridynamic Modeling of Membranes and Fibers,” International Journal of Non- Linear Mechanics, Vol. 40, 2005, pp. 395-409.
doi:10.1016/j.ijnonlinmec.2004.08.004
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[5]
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S. A. Silling, M. Zimmerman and R. Abeyaratne, “Deformation of a Peridy-namic Bar,” Journal of Elasticity, Vol. 73, No. 1-3, 2003, pp. 173-190.
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S. A. Silling, “Peridynamic Modeling of the Failure of the Heterogeneous Solids,” 2002.
http://www.sandia.gov/emu/aro-vg.pdf
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[7]
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E. Emmrich and O. Weckner, “Analysis and Numerical Approximation of an Inte-gro Diff. Equ. Modeling Non_Local effects in linear elasticity,” Mathematics and Mechanics of Solids, Vol. 12, No. 4, 2005, pp. 363-384.
doi:10.1177/1081286505059748
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A. Chakraborty, “Wave Propagation in Anisotropic Media with Non-Local Elasticity,” International Journal of Solids and Structures, Vol. 44, No. 17, August 2007, pp. 5723- 5741. doi:10.1016/j.ijsolstr.2007.01.024
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[9]
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S. A. Silling, M. Epton, O. Weckner, C. Xu?and E. Askari, “Peridynamic States and Constitutive Modeling,” Journal of Elasticity, Vol. 88, No. 2, 2007, pp. 151-184.
doi:10.1007/s10659-007-9125-1
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[10]
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R. B. Lehoucq and S. A. Silling, “Force Flux and the Peridynamic Stress Tensor,” Composite Structures, Vol. 56, No. 4, April 2008, pp. 1566-1577.
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[11]
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T. L. Warren, S. A. Silling, A. Askari, O. Weckner, M. N. Epton and J. Xu, “A Non-Ordinary State-Based Peridynamic Method to Model Solid Material De-formation and Fracture,” International Journal of Solids and Structures, Vol. 46, No. 5, March 2008, pp. 1186-1195.
doi:10.1016/j.ijsolstr.2008.10.029
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[12]
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R. W. Macek and S. A. Silling, “Peridynamics via Finite Element Analysis,” Finite Elements in Analysis and Design, Vol. 43, No. 15, November 2007, pp. 1169-1178.
doi:10.1016/j.finel.2007.08.012
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[13]
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S. A. Silling and R. B. Lehoucq, “Convergence of Peridynamics to Classical Elastic-ity,” Journal of Elasticity, Vol. 93, No. 1, 2007, pp. 13-37.
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[14]
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M. L. Parks, R. B. Lehoucq, S. J. Plimpton and S. A. Silling, “Implementing Peridynamics within a Molecular Dynamics Code,” Computer Physics Communications, Vol. 179, No. 11, December 2008, pp. 777-783.
doi:10.1016/j.cpc.2008.06.011
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[15]
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B. Kilic, A. Agwai and E. Madenci, “Peridynamic Theory for Progressive Damage Pre-diction in Center-Cracked Composite Laminates,” Composite Structures, Vol. 90, No. 2, September 2009, pp. 141-151.
doi:10.1016/j.compstruct.2009.02.015
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[16]
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B. Kilic and E. Madenci, “Structural Stability and Failure Analysis Using Peridynamic Theory,” International Journal of Non-Linear Mechanics, Vol. 44, No. 8, October 2009, pp. 845-854.
doi:10.1016/j.ijnonlinmec.2009.05.007
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[17]
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W. Gerstle, N. Sau and S. Silling, “Peridynamic Modeling of Concrete Struc-tures,” Nuclear Engineering and Design, Vol. 237, No. 12-13, July 2006, pp. 1250-1258.
doi:10.1016/j.nucengdes.2006.10.002
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[18]
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N. Sau, “Peridy-namic Modeling of Quasibrittle Structures,” PhD Thesis, The University of New Mexico, Albuquerque, 2008.
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A. P. Boresi, R. J. Schmidt and O. M. Sidebottom, “Advanced Me-chanics of Materials,” John Wiley and Sons, 5th Edition, New York, 1993.
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[20]
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J. R. Barber, “Elasticity,” 2nd Edition, Klu-wer Academic Publishers, New York, 2004, pp. 114-115.
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